AN ABSTRACT OF THE THESIS OF
Jing Wu for the degree of Master of Science in Agricultural and Resource Economics and
Computer Science presented on June 27, 2003.
Title: A Comparison of Box-Cox and Additive Exponential Models to Estimate the
Depreciation of Farm Machinery
Redacted for privacy
Redacted for privacy
Abstract approved:
ory M. Perry I Toshimi Minoura
Farm machinery continues to increase in its importance to the agricultural sector.
Depreciation, the decline in value of a durable asset over time, represents one of the
largest costs of agricultural production. The general objectives of this study were to
update and expand the number of Remaining Value (RV) functions for farm machinery;
estimate and compare the depreciation patterns for Box-Cox (B-C) and AdditiveExponential (A-E) functional forms; and compare the predictive abilities of the two
models.
Data used in estimation were obtained from 15 years of machinery auction sales.
Based on the hedonic approach, the Box-Cox and Additive-Exponential models were
formulated to include variables for age, usage per year, condition, manufacturer, auction
type and macroeconomic variables. Models were tested for potential correlation and
heteroscedasticity problems. A Mean Absolute Percentage Error (MAPE) method was
used to compare the predictive abilities.
Depreciation functions were estimated for 17 types of machinery in four major
categories: tractors, harvesting equipments, planting and tillage equipment and other
equipment. A series of comparisons were conducted to examine the difference in
depreciation patterns within and between major categories. B-C and A-E functions were
estimated and compared for each data set. The comparison results showed that B-C
always generated higher Log-likelihood values, but was relatively weak in predictive
ability. The predictive ability of the Exponential model was also examined and the
MAPE results showed that the Exponential model generaliy exhibited an overall best
predictive ability.
©Copyright by Jing Wu
June 27, 2003
All Rights Reserved
A COMPARISON OF BOX-COX AND
ADDITIVE EXPONENTIAL MODELS
TO ESTIMATE THE DEPRECIATION OF FARM MACHINERY
By
Jing Wu
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
Presented June 27, 2003
Commencement June 2004
Master of Science thesis of Jing Wu presented on June 27, 2003
APPROVED:
Redacted for privacy
Co-Major P?
sor, Representing Agricultural and Resource Economics
Redacted for privacy
Co-Major Professor, Representing Computer Science
Redacted for privacy
(J
Head of Department of Agricultural and Resource Economics
Redacted for privacy
Director of School of Electrical Engineering and Computer Science
Redacted for privacy
Dean of
diiãte School
I understand that my thesis will become part of the permanent collection of the Oregon
State University libraries. My signature below authorizes release of my thesis to any
reader upon request.
Redacted for privacy
Jing W Author
ACKNOWLEDGMENTS
First of all, I would like to thank my major professor, Dr. Gregory Perry, to whom I
owe the most overwhelming debt of gratitude. Without his continued encouragement,
patience and advice, this thesis camiot be integrated as it is. Unforgettable is his careful
modification on each page of this thesis, never failing support and guidance whenever
needed and selfless concern for his students. His contribution and helpful suggestion have
been too numerous to mention.
I also owe Dr. M. Gopinath a special thank for his generous insights, helpful
suggestions and being available at any time to assist me with the econometric analysis.
I am very thankful for my committee members for their participation and
contribution to my committee. Special thanks go to Dr. Ed Schmisseur for his sincere
help during my graduate studies and also go to Dr. Bart Eleveld for sharing his time and
knowledge with me.
Thanks also go to other faculty, staff and graduate students in the Department of
Agricultural and Resource Economics for sharing enjoyable moments in and out of the
department.
Finally, I want to thank my parents, who will come to visit America in the next
month. Their endless love and care to me deserve more than a 'thank you'. I also want to
thank all my friends. I enjoy the time of being with them and appreciate their constant
help, encouragement and moral support in my life and studies.
TABLE OF CONTENTS
CHAPTER
PAGE
INTRODUCTION
1
1.1 Problem Statement
1
1.2 Objectives and Organization
7
LITERATURE REVIEW AND THEORETICAL DEVELOPMENT
2.1 Literature Review
2.1.1 Accounting Approaches
2.1.2 Hedonic Approach
2.2 Theoretical Development
2.2.1 Theoretical Development in Box-Cox model
2.2.2 Theoretical Development in Exponential model
DATA, MODEL AND COMPARISON
8
8
8
9
10
14
16
20
3.1 Data Description
20
3.2 Specification of Models
21
3.2.1 Variables Identification
3.2.1.1 Age
3.2.1.2 Usage
3.2.1.3 Care
3.2.1.4 Manufacture
3.2.1.5 Loader
3.2.1.6 Auction Type
3.2.1.7 Macroeconomic Variables
3.2.1.8 Remaining Value
3.2.2 Specification of Models
3.2.2.1 Box-Cox Model
3.2.2.2 Additive-Exponential Model
3.2.3 Model Testing
3.2.3.1 Correlation
3.2.3.2 Heteroscedascity
3.3 Comparison Method
21
21
21
22
23
23
24
24
26
26
26
27
30
30
31
34
TABLE OF CONTENTS, (CONTINUED)
CHAPTER
PAGE
4. EMPIRICAL RESULTS
36
4.1 Tractors
4.1.1 Tractors with less than 80 HP
4.1.1.1 Data Description
4.1.1.2 Models Estimation
4.1 .1.3 Comparison Between Models
4.1.2 Tractors with 80-120 HP
4.1.2.1 Data Description
4.1.2.2 Models Estimation
4.1.2.3 Comparison Between Models
4.1.3 Tractors with 120+ HP with four-wheel drive
4.1.3.1 Data Description
4.1.3.2 Models Estimation
4.1.3.3 Comparison Between Models
4.1.4 Tractors with 120-145 HP, without four-wheel drive
4.1.4.1 Data Description
4.1.4.2 Models Estimation
4.1.4.3 Comparison Between Models
4.1.5 Tractors with 145+ HP, without four-wheel drive
4.1.5.1 Data Description
4.1.5.2 Models Estimation
4.1.5.3 Comparison Between Models
4.2 Harvesting Equipment
4.2.1 Combines
4.2.1.1 Data Description
4.2.1.2 Models Estimation
4.2.1.3 Comparison Between Models
4.2.2 Corn Headers
4.2.2.1 Data Description
4.2.2.2 Models Estimation
4.2.2.3 Comparison Between Models
4.2.3 Cotton Harvesters
4.2.3.1 Data Description
4.2.3.2 Models Estimation
4.2.3.3 Comparison Between Models
4.2.4 Swathers
4.2.4.1 Data Description
4.2.4.2 Models Estimation
36
37
37
38
40
41
41
42
45
46
46
46
49
50
50
50
53
54
54
54
57
58
58
58
59
61
62
62
62
65
66
66
66
69
70
70
70
TABLE OF CONTENTS, (CONTiNUED)
CHAPTER
PAGE
4.2.4.3 Comparison Between Models
4.2.5 Balers
4.2.5.1 Data Description
4.2.5.2 Models Estimation
4.2.5.3 Comparison Between Models
4.2.6 Forage Harvesters
4.2.6.1 Data Description
4.2.6.2 Models Estimation
4.2.6.3 Comparison Between Models
4.2.7 Mower Conditioners
4.2.7.1 Data Description
4.2.7.2 Models Estimation
4.2.7.3 Comparison Between Models
4.2.8 Mower Cufters
4.2.8.1 Data Description
4.2.8.2 Models Estimation
4.2.8.3 Comparison Between Models
4.3 Planting and Tillage Equipment
4.3.1 Planters
4.3.1.1 Data Description
4.3.2.2 Models Estimation
4.3.3.3 Comparison Between Models
4.3.2 Disks
4.3.2.1 Data Description
4.3.2.2 Models Estimation
4.3.2.3 Comparison Between Models
4.3.3 Plows
4.3.3.1 Data Description
4.3.3.2 Models Estimation
4.3.3.3 Comparison Between Models
4.3.4 Drills
4.3.4.1 Data Description
4.3.4.2 Models Estimation
4.3.4.3 Comparison Between Models
4.4 Other machinery
4.4.1 Grinder Mixers
4.4.1 .1 Data Description
4.4.1.2 Models Estimation
73
74
74
74
77
78
78
78
81
82
82
82
85
86
86
86
89
90
90
90
90
92
93
93
94
95
97
97
98
99
100
100
101
102
104
104
104
104
TABLE OF CONTENTS, (CONTINUED)
PAGE
CHAPTER
4.4.1.3 Comparison Between Models
106
4.4.2 Manure Spreaders
4.4.2.1 Data Description
4.4.2.2 Models Estimation
4.4.2.3 Comparison Between Models
4.4.3 Skid Steer Loaders
4.4.3.1 Data Description
4.4.3.2 Models Estimation
4.4.3.3 Comparison Between Models
107
107
108
110
110
110
112
4.4.4Trucks
4.4.4.1 Data Description
4.4.4.2 Models Estimation
114
114
4.4.4.3 Comparison Between Models
5. CONCLUSIONS AND LIMITITIONS
5.1 Summaries and Comparisons
5.1.1 Summary of the Data Distribution
5.1.2 Summary of the Significant Variables in the B-C
and A-E models
5.1.3 Comparison of Depreciation Patterns in Each
Category of Farm Equipment
5.1.4 Comparison of the B-C and A-E models
5.1.5 Comparison With Previous Studies
5.2 Limitations and Future Thoughts
BIBLIOGRAPHY
113
115
116
118
118
118
122
125
133
135
137
139
LIST OF FIGURES
FIGURE
PAGE
4.1
Comparison of depreciation patterns of the B-C and A-E
models for tractors with less than 80 HP
41
4.2
Comparison of depreciation patterns of the B-C and A-E
models for 80-120 HP tractors
45
4.3
Comparison of depreciation patterns of the B-C and A-E
models for 120+ HP tractors with FWD
49
4.4
Comparison of depreciation patterns of the B-C and A-E
models for 120-145 HP tractors
53
4.5
Comparison of depreciation patterns of the B-C and A-B
models for 145+ HP tractors
57
4.6
Comparison of depreciation patterns of the B-C and A-B
models for Combines
61
4.7
Comparison of depreciation patterns of the B-C and A-B
models for Corn Headers
65
4.8
Comparison of depreciation patterns of the B-C and A-B
models for Cotton Harvesters
69
4.9
Comparison of depreciation patterns of the B-C and A-E
models for Swathers
73
4.10
Comparison of depreciation patterns of the B-C and A-B
models for Balers
77
4.11
Comparison of depreciation patterns of the B-C and A-B
models for Forage Harvesters
81
4.12
Comparison of depreciation patterns of the B-C and A-B
models for Mower Conditioners
85
4.13
Comparison of depreciation patterns of the B-C and A-B
models for Mower Cutters
89
4.14
Comparison of depreciation patterns of the B-C and A-B
models for Planters
93
LIST OF FIGURES, (CONTINUED)
FIGURE
PAGE
4.15
Comparison of depreciation patterns of the B-C and A-E
models for Disks
97
4.16
Comparison of depreciation patterns of the B-C and A-E
models for Plows
100
4.17
Comparison of depreciation patterns of the B-C and A-E
models for Drills
103
4.18
Comparison of depreciation patterns of the B-C and A-E
models for Grinder Mixers
107
4.19
Comparison of depreciation patterns of the B-C and A-E
models for Manure Spreaders
110
4.20
Comparison of depreciation patterns of the B-C and A-E
models for Skid Steer Loaders
113
4.21
Comparison of depreciation patterns of the B-C and A-E
models for Trucks
117
5.1
Average Discount Values for condition variables
123
5.2
Comparison of the B-C depreciation pattern for tractors
127
5.3
Comparison of the A-E depreciation pattern for tractors
127
5.4
Comparison of the B-C depreciation pattern for harvesting equipment
128
5.5
Comparison of the A-E depreciation pattern for harvesting equipment
128
5.6
Comparison of the B-C depreciation pattern for planting and tillage
equipment
129
5.7
Comparison of the A-E depreciation pattern for planting and tillage
equipment
129
5.8
Comparison of the B-C depreciation pattern for other equipment
130
5.9
Comparison of the A-E depreciation pattern for other equipment
130
5.10
Comparison of the B-C depreciation pattern for 120-145 HP
131
LIST OF FIGURES, (CONTINUED)
FIGURE
PAGE
tractors, Mower-Conditioners, Plows and Trucks
5.11
Comparison of the A-E depreciation pattern for 120-145 HP
tractors, Mower-Conditioners, Plows and Trucks
131
LIST OF TABLES
TABLE
PAGE
1.1
Farm assets: Comparative balance sheet of the farming sector,
excluding operator households, United States, 196 1-1997
2
1.2
United States: Farm production expenses in income indicators,
1992-1996
3
1.3
Previous research in estimating the depreciation costs in all
functions for all types of farm machinery.
6
2.1
Previous research in estimating depreciation of agricultural
machinery and equipment
11
2.2
Box-Cox power transformations associated with selected
functional forms
15
3.1
Condition evaluations of farm machinery (Hot Line, Inc.)
22
3.2
Manufactures and their abbreviations used in this study
23
3.3
Net Farm Income and Real Interest Rate for farm sector, 1984-1999
25
3.4
GNP Implicit Prices Deflator (based on 1996 dollars), 1970-1999
25
3.5
Log-Likelihood values for Box-Cox and alternative functional
forms for farm equipment remaining value models
29
3.6
Statistic results of testing correlation and Heteroscedasticity
32
4.1
Summary statistics for tractors with less than 80 HP
38
4.2
Frequency statistics for tractors with less than 80 HP
38
4.3
Regression coefficients and t-statistics for tractors
with less than 80 HP
39
4.4
Comparison of B-C and A-E models for tractors
with less than 80 HP
40
4.5
Comparison of estimated functional forms of the B-C and A-E
models for tractors with less than 80 HP
41
LIST OF TABLES, (CONTiNUED)
TABLE
PAGE
4.6
Summary statistics for 80-120 HP tractors
43
4.7
Frequency statistics for 80-120 HP tractors
43
4.8
Regression coefficients and t-statistics for 80-120 HP tractors
44
4.9
Comparison of B-C and A-E models for 80-120 HP tractors
45
4.10
Summary statistics for 120+ HP tractors with FWD
47
4.11
Frequency statistics for 120+ HP tractors with FWD
47
4.12
Regression coefficients and t-statistics for 120+ HP tractors
with FWD
48
4.13
Comparison of B-C and A-E models for 120+ HP tractors
with FWD
49
4.14
Summary statistics for 120-145 HP tractors
51
4.15
Frequency statistics for 120-145 HP tractors
51
4.16
Regression coefficients and t-statistics for 120-145 HP tractors
52
4.17
Comparison of B-C and A-E models for 120-145 HP tractors
53
4.18
Summary statistics for 145+ HP tractors
55
4.19
Frequency statistics for 145+ HP tractors
55
4.20
Regression coefficients and t-statistics for 145+ HP tractors
56
4.21
Comparison of B-C and A-E models for 145+ HP tractors
57
4.22
Summary statistics for Combines
59
4.23
Frequency statistics for Combines
59
4.24
Regression coefficients and t-statistics for Combines
60
4.25
Comparison of B-C and A-E models for Combines
61
LIST OF TABLES, (CONTINUED)
TABLE
PAGE
4.26
Summary statistics for Corn Headers
63
4.27
Frequency statistics for Corn Headers
63
4.28
Regression coefficients and t-statistics for Corn Headers
64
4.29
Comparison of B-C and A-E models for Corn Headers
65
4.30
Summary statistics for Cotton Harvesters
67
4.31
Frequency statistics for Cotton Harvesters
67
4.32
Regression coefficients and t-statistics for Cotton Harvesters
68
4.33
Summary statistics for Swathers
71
4.34
Frequency statistics for Swathers
71
4.35
Regression coefficients and t-statistics for Swathers
72
4.36
Comparison of B-C and A-E models for Swathers
73
4.37
Summary statistics for Balers
75
4.38
Frequency statistics for Balers
75
4.39
Regression coefficients and t-statistics for Balers
76
4.40
Comparison of B-C and A-E models Balers
77
4.41
Summary statistics for Forage Harvesters
79
4.42
Frequency statistics for Forage Harvesters
79
4.43
Regression coefficients and t-statistics for Forage Harvesters
80
4.44
Summary statistics for Mower Conditioners
83
4.45
Frequency statistics for Mower Conditioners
83
4.46
Regression coefficients and t-statistics for Mower Conditioners
84
LIST OF TABLES, (CONTINUED)
TABLE
PAGE
4.47
Comparison of B-C and A-E models for Mower Conditioners
85
4.48
Summary statistics for Mower Cutters
87
4.49
Frequency statistics for Mower Cutters
87
4.50
Regression coefficients and t-statistics for Mower Cutters
88
4.51
Summary statistics for Planters
91
4.52
Frequency statistics for Planters
91
4.53
Regression coefficients and t-statistics for Planters
92
4.54
Comparison of B-C and A-E models for Planters
93
4.55
Summary statistics for Disks
94
4.56
Frequency statistics for Disks
95
4.57
Regression coefficients and t-statistics for Disks
96
4.58
Comparison of B-C and A-E models for Disks
96
4.59
Summary statistics for Plows
98
4.60
Frequency statistics for Plows
98
4.61
Regression coefficients and t-statistics for Plows
99
4.62
Comparison of B-C and A-E models for Plows
100
4.63
Summary statistics for Drills
101
4.64
Frequency statistics for Drills
101
4.65
Regression coefficients and t-statistics for Drills
102
4.66
Summary statistics for Grinder Mixers
105
4.67
Frequency statistics for Grinder Mixers
105
LIST OF TABLES, (CONTINUED)
TABLE
PAGE
4.68
Regression coefficients and t-statistics for Grinder Mixers
106
4.69
Summary statistics for Manure Spreaders
108
4.70
Frequency statistics for Manure Spreaders
108
4.71
Regression coefficients and t-statistics for Manure Spreaders
109
4.72
Summary statistics for Skid Steer Loaders
111
4.73
Frequency statistics for Skid Steer Loaders
111
4.74
Regression coefficients and t-statistics for Skid Steer Loaders
112
4.75
Summary statistics for Trucks
114
4.76
Frequency statistics for Trucks
115
4.77
Regression coefficients and t-statistics for Trucks
116
4.78
Comparison of B-C and A-E models for Trucks
117
5.1
Summary of Data Distribution -- Average Data and Largest
Frequency Data
119
5.2
Comparison of the Significant Variables in the Box-Cox and
Additive-Exponential Models
120
5.3
Comparison of the MAPE, R2 and Log-Likelihood Value of the
Box-Cox, Additive-Exponential, and Exponential Models
132
5.4
Comparison of previous studies with this thesis
136
A COMPARISON OF BOX-COX AND
ADDITIVE EXPONENTIAL MODELS
TO ESTIMATE THE DEPRECIATION OF FARM MACHINERY
CHAPTER 1
1.1
INTRODUCTION
PROBLEM STATEMENT
Great changes occurred in agricultural practices in the last century. Even in the last
decade, it is shown that agriculture output per unit of input increased by 20 percent
(USDA, 1997). One of the main technological changes in the 2O
century was the
mechanization of agricultural activities. Farming evolved from an individual, laborintensive process into a capital-intensive process. Farm equipment continues to increase
in its importance to the farm sector. For example, farm machinery assets as a percentage
of total farm assets increased from 8 percent in 1980 to 10 percent in 1992 (USDA,
1994).
Table 1.1 shows the distribution of total farm assets from 1961 to 1996. The fact
that machinery and motor vehicles was the largest portion in non-real estate demonstrates
the importance of farm machinery in the agricultural sector.
It is also worthy to note that the value of machinery and motor vehicles rose from
22.0 billion dollars in 1961 to 107.8 billion dollars in 1981, then declined to 84.4 billion
dollars in 1986 and then remained at about this level in the following 15 years. Several
reasons for this phenomenon could be hypothesized: because technology changes in
agricultural machinery have slowed since the 1970's, and farm income declined in the
early 1980's, after farm equipment sales reached a high in 1973, farmers bought less
machinery and continued to use the old machinery; also, the gradual shift from traditional
tillage to reduced tillage required fewer passes over the field and prolonged machinery
life.
Table 1.1
*
2
Farm assets: Comparative balance sheet of the farming sector,
excluding operator households, United States, 1961-1997 (in billion dollars).
Item
1961
Physical Assets:
Real estate
131.9
Non-real-estate:
Livestock
15.6
Machinery and
motor vehicles 22.0
Crops stored
on and off
farms
8.0
Household
furnishings and
equipment
8.9
Financial assets:
Deposits and
currency
8.7
United States
savings bonds 4.6
Investments in
cooperatives
4.7
Total
204.4
1966
1971
1976
1981
1986
1991
1996
182.5
223.2
416.9
851.7
551.1
625.5
642.8
17.5
23.7
29.5
53.5
47.6
68.1
71.0
27.1
34.4
65.0
107.8
84.4
85.9
85.4
9.7
10.7
21.3
29.1
19.1
22.2
24.2
8.6
10.0
14.2
20.8
30.5
Purchased Purchased
10.0
12.4
15.6
16.7
24.8
4.1
3.6
4.4
3.6
4.5
6.5
8.0
13.3
255.9
326
580.2
20.4
25.1
1103.7 787.1
Inputs
Inputs
2.6
4.4
11.9
28.6
844.9
17.8
31.3
1033.9
Source: Economic Research Service 1961 - 1997
Because of the great contribution of equipment and machinery to the farm sector,
the cost of owning and operating farm machinery becomes an important issue in the
decision-making process for farmers. For some crops, machinery operating and
ownership costs accounts for more than half of the crop production costs (Kastens 1997).
Total machinery costs include repairs, maintenance, fuel, lube, insurance, interest, and
depreciation.
Of course, simply examining total investment in farms is not a totally accurate way
to express machinery capital costs, because these assets can provide many years of
service. Depreciation, the decline in value of an asset over time, is a more appropriate
expression of farm equipment costs. Depreciation results from wear, obsolescence,
natural deterioration and changes of the market supply and demands. In Table 1.2, capital
3
consumption is defined as depreciation and accidental damage. Depreciation was
measured on a replacement value basis rather than purchase price in order to reflect
decreases in current market value of the capital stock. Capital consumption represented a
large portion of farm production expenses. We also notice that this portion kept a fairly
stable decrease as an important component of the farm production expenses, from 10.8%
in 1992 to 9.2% in 1996. As pointed out before, farmers continued maintaining and
repairing machinery and equipment and keeping items in service longer since the early
1980's. It is known a priori that the percent consumption of capital is usually highest in
its early years, but keeps declining at a constant rate in its late years.
Table 1.2 United States: Farm production expenses in income indicators, 1992-1996
(in $1000).
ITEM
Farm
production
expenses
Nonfactor
payments
Intermediate
Product
expenses
Capital
Consumption
Property
taxes
Contract
Labor
Factor
payments
Interest
Hired labor
compensation
Net rent to
nonoperator
landlords
162,980,647
1995
169,348,115
1996
176,064,087
121,773,299
126,419,705
130,713,995
133,769,246
91,315,202
98,332,019
102,565,703
106,551,408
109,476,374
16,102,700
16,164,380
16,321,303
16,311,971
16,186,890
5,489,945
5,505,944
5,727,259
5,881,562
5,977,147
1,717,422
1,770,956
1,805,440
1,969,054
2,128,835
34,246,322
34,717,155
36,560,941
38,634,120
42,294,842
10,472,751
12,282,246
11,337,880
13,235,320
10,776,576
13,503,184
12,303,373
14,346,758
12,782,673
15,219,042
11,187,500
11,009,084
11,719,877
11,983,988
14,293,127
1992
148,871,592
1993
156,490,454
1994
114,625,269
Source: Economics Research Service, U.S. Department of Agriculture, 1992-1996.
4
Models for estimating the depreciation of farm machinery are useful in at least
three aspects: first, they have a number of farm management applications, such as crop
enterprise selection, machinery services management, financial and tax planning, and
analysis of herbicide/tillage tradeoffs (Dumbler, Burton and Kastens, 2000); second, they
are important for machinery replacement, purchase, lease and custom-hire decisions; and
third, they are essential to the study of production, income, tax policy, and investment
behavior.
Further, an accurate estimate requires a complex model that reflects various factors
influencing the value of used equipment. Depreciation defined in farm machinery context
is more than tax depreciation, because the methods applied in tax depreciation neither
reflect year-to-year change in the "market value" of used farm machinery, nor account for
the effects of usage and care on depreciation costs (Bayaner, 1989). Therefore, a method
to estimate economic depreciation is typically used to explore the model for calculating
the depreciation costs of farm machinery.
A number of studies have examined the issue of farm equipment and most have
included estimates of a depreciation function (see Table 2.1, p11). However, some
problems have not been adequately addressed. First, although a wide variety of functional
forms have been considered to estimate depreciation, problems and limitations exist in
almost every approach. For example, the most common method, geometric function was
provided in American Society of Agricultural Engineers Standards (ASAE, 1965) and
developed by other researchers (Peacock and Brake 1970; McNeill 1979), but it imposes
a constant depreciation rate on the data (Perry et al., 1990); other pre-imposed functional
forms such as the Cobb-Douglas (Leatham and Baker 1981; Reid and Bradford 1983),
and the linear functional forms also impose similar restrictions; a Box-Cox function was
proposed because of its flexibility (Hulen and Wykoff 1981; Perry et al 1990; and Cross
and Perry 1995). Although flexibility allows the data greater freedom to determine the
appropriate form, this method has potential problems related to heteroscedasticity,
autocorrelation and data scaling (Zarembka 1974; Savin and White 1978; Seaks and
Layson 1983; Spitzer 1982, 1984).
5
Second, most researches focused on a specific type of equipment, such as tractors.
However, because age, care, usage and technical change can have different effects on the
value of various farm machinery types, one could not expect a priori that all types of
farm equipments exhibit the exactly same depreciation pattern as tractors. In fact, even
for tractors, depending on the size (measured by horse power) and the availability of
four-wheel drive (FWD) and rate of technical change, tractors may vary in the expression
of depreciation patterns. However, the previous research, with the recognition of
developing a unique model for each type, is surprisingly limited, except the ASAE
functions, the research of Cross and Perry in 1995, a case study of 60-horsepower tractors
by Hansen and Lee in 1990, and a specific model for Case tractor (James and Glen 1996),
as shown in Table 1.3.
Third, little work has been done to identify relative predictive abilities of the
various models. A conclusive comparison of this ability will be helpful for researchers
using the models to predict economic depreciation. To date, the only studies evaluating
predictive accuracy include a comparison between the depreciation method to U.S and
Canadian tax method for 60 horsepower tractors (Hansen and Lee, 1990), and a
comprehensive comparison of seven alternative depreciation methods' (Dumler, Burton,
Kastens 1998, 2000).
This study will expand on previous work by examining a new functional form Additive Exponential - to see how it compares to the previous models; develop a specific
model for each type of farm machinery, listed in Table 1.3; and compare predictive
abilities of the Box-Cox and Additive Exponential models for each data set.
The focus of this thesis is to develop more accurate models for estimating
depreciation in agricultural machinery and equipment and hopefully, provide end users
with better estimates of remaining values.
1
In their paper 'Implication of Alternative Farm Tractor Depreciation Methods' in 1998, seven
depreciation methods were compared, including American Society of Agricultural Engineers (ASAE,
1996); Cross and Perry (CP, 1995); North American Equipment Dealers Association (NAEDA, Wallace
and Maloney 1997); Kansas Management, Analysis, and Research (KMAR, 1997); U.S. Bureau of
Economics Analysis (1997); plus two U.S. income tax methods (U.S. department of Treasury, 1 997a). In
this paper, 'Use of Alternative Depreciation Methods to estimate Farm Tractor Values' in 2000, U.S.
Bureau of Economics Analysis method was omitted.
6
Table 1.3 Previous research in estimating the depreciation costs in all functions for
all types of farm machinery.
Type of Farm Machinery
Tractors
Previous Work
Horse Power less than 80
Cross and Perry (1995, 1991); and
Hansen and Lee (1990)2.
Cross and Perry (1995, 1991); and
James and Glen (1996).
(See Table 2.1 for other estimates for
tractors).
Horse Power between 80 and 120
Horse Power more than 120 with
FWD
Horse Power between 120 and 145
without FWD
Horse Power more than 145 without
FWD
Harvesting Equipment
Combine
Corn Header
Cotton Harvester
Swather
Baler
Forage_harvester
Mower_Conditioner
Leatham and Baker (1981);
Cross and Perry (1995); and
James and Glen (1996).
N/A
N/A
Cross and Perry (1995)
Cross and Perry (1995)
N/A
Cross and Perry (1995)6
Mower Cutter
Planting and Tillage Equipment
Planters
Disks
Plows
Drills
Other machinery
Grinder Mixer
*N
2
Manure_Spreader
Skid_Steer_Loader
Truck
Cross and Perry (1995)
Cross and Perry (1995)
Cross and Perry (1995)
N/A
N/A
Cross and Perry (1995)
Cross and Perry (1995)
N/A
They focused on a case study of Tractors with HP 60.
In their studies in 1995, they split Tractor type into three categories (<80 hp, 80-150 hp, and >150 hp). In
their studies in 1991, they split Tractor type into 80-120 HP, 120-140 HP and 140+ HP. FWD was not
considered in either study.
Their model focused on Case Tractor.
Their model focused on J.D. Combine and N.H. Combine.
6
they did not specify Conditioner and Cutter in the Mower type.
7
1.2 OBJECTIVES AND ORGANIZATION
OBJECTIVES:
To identify variables that will explain changes in Remaining Value for agricultural
machinery;
To explore the relationships among the remaining value of used tractors and the
identified variables, and construct Box-Cox and Additive Exponential models to
express this relationship respectively;
To apply the Box-Cox and Additive Exponential models to 17 types of agricultural
machinery and compare them by observing the accuracy in predicting the
Remaining Values in new data sets; and
To update the depreciation functions for farm equipment that have been analyzed
before, and estimate functions for those that have not been analyzed.
ORGANIZATION:
The remaining parts of this thesis are organized as follows:
After a discussion of the previous research involving estimates of depreciation
functions for farm machinery, Chapter two develops the fundamental theory of Box-Cox
and Exponential models.
Chapter three focuses on describing the characteristics of the data; identifying the
independent variables; constructing the Box-Cox and Additive-Exponential models;
testing models for correlation and heteroscedasticity; and describing the predictive ability
test - Mean Absolute Percentage Error (MAPE) method.
Chapter four provides the empirical results of the Box-Cox and Additive
Exponential models for four major categories of farm equipment, including the analysis
of the estimated coefficients and comparisons of the two models.
Chapter five summarizes the research findings, conducts further comparisons, and
suggests limitations and promises for future study.
8
CHAPTER 2
LITERATURE REVIEW AND THEORETICAL DEVELOPMENT
The earliest reference about estimating depreciation of agricultural machinery and
equipment can be traced back to the early 1900s (Debnam, 1928; Main, et al. 1928;
Woodruff, 1929). But the real progress in estimating functions to calculate depreciation
has occurred since the 1 960s. In this chapter, after a brief review of the accounting and
hedonic approaches, previous research in Box-Cox and Exponential methods will be
reviewed.
2.1 LITERATURE REVIEW
2.1 .1
Accounting Approaches
Using a simple predetermined equation may be the most common method to
calculate depreciation. Typical equations include straight-line, declining balance, double-
declining balance and sum-of-the-year's digits. These approaches are easy to understand,
convenient to use and account for depreciation in a consistently predictable manner
The disadvantages of a predetermined equation are: First, it requires several
assumptions to use each formula. For example, a linear depreciation pattern is assumed
when using the straight-line depreciation method, and a geometric pattern is imposed
when using the declining balance method. Also, one must determine the asset's life,
purchase price and salvage value; Third, predetermined equations ignore the impacts of
actual use and macroeconomic conditions on values and manufactures. In Peacock and
Brake's study in 1970, they compared the estimated results when using this approach
9
with the market value provided by Official Tractor Farm Equipment Guide, and found
that the difference was often as much as 25% to 80%.
2.1.2
Hedonic Approach
Another approach to calculate depreciation is to utilize actual equipment sales data
to estimate a hedonic function. Hedonic pricing is based on the economic theory of input
demand (Ladd and Martin, 1976), reflecting the idea that inputs are actually collections
of characteristics of assets. The production function can be expressed as Equation (2.2):
Q=F(A1,A2,...A)
(2.2)
Q is the quantity of output and A1, A2, ... A are the total input characteristic used
in this production.
The hedonic pricing models or the modified hedonic models were explored in the
studies by Griliches and Rosen to estimate quality-adjusted prices (Griliches, 1971 a, and
1971 b; Rosen 1974) and then extended to agricultural commodities (Ethridge and Davis,
1982; Brorsen, et al., 1984, 1988; Wilson, 1984). The concept of Remaining Value (RV)
was first proposed by Fenton and Fairbanks, that is, to divide current market price by
initial purchase price and then average these values across several different kinds of
equipment.
The first attempt in using a hedonic approach for used machinery was by Fettig
(1963). He used twelve years of cross section data from eight manufacturers to develop a
hedonic model for tractors. His model, by regressing on the horsepower and engine type,
achieved good statistical results by using the linear and semi-log functional forms. The
function estimated by Fettig can be summarized as:
RV= f(horse power, engine, type)
(2.3)
10
Later research further developed hedonic model in estimating depreciation costs,
including the comprehensive set of models by American Society of Agricultural
Engineers (ASAE, 1965) that provided market value of functions comprising four broad
categories of farm equipments l; Peacock and Brake (1970) demonstrated that tax
depreciation 'write-offs' did not adequately reflect economic depreciation of farm
machines. A depreciation function estimated by McNeill (1979) was used to in estimate
remaining value of tractors in British Columbia. A similar model estimated by Leatham
and Baker (1981) was used in an optimal replacement model. Reid and Bradford
estimated a Cobb-Douglas function accounted for changes in tractor supply and demand
and technological obsolescence. Hansen and Lee (1990) used Hall's (1968) approach to
examine technology change. More recent studies included the Box-Cox models estimated
by Cross and Perry in 1995, a Cobb-Douglas model using combine and tractor prices by
James and Glen (1996), a geometric model by taking a simpler approach of Box-Cox by
Stephen (1996), and so on (See Table 2.1).
By reviewing this previous research, it is not difficult to find that, although no
agreement exists as to the maimer in which economic depreciation is calculated, those
models turn out to be within two categories: Flexible and Fixed. The flexible category
includes the Box-Cox model (Hulen and Wykoff, Perry, Bayaner and Nixon, Cross and
Perry); and the fixed category contains all other functional forms, such as the Simple
Linear model (Fettig, Peacock and Brake), the Cobb-Douglas model (Hall, Leatham and
Baker, Reid and Bradford) and the Exponential (Geometric) model (ASAE, Peacock and
Brake, McNeill), shown as Table 2.1.
2.2 THEORETICAL DEVELOPMENT
This section will elaborate the fundamental theory and previous research of BoxCox and Exponential models in each category.
The four categories are: (a) tractors; (b) combines, cotton pickers, and swathers; (c) balers, forage
harvesters, blowers, and self-propelled sprayers; and (d) all other field machinery
Table 2.1 - Previous research in estimating depreciation of agricultural machinery and equipment.
Functional
Form
Authors (Year of
Publication)
General Model
Formulation
Data Source
Contributions and Conclusions
Fettig (1963)
RV= f (hp, engine,
type)
Geometric
American Society
of Agricultural
Engineers (ASAE,
1965)
RV = 68 (0.92) Age
12 years of cross-section
data from 8 manufactures
of tractor.
Prices from the late 1 960s,
provided by Official
Tractor and Farm
Equipment Guide
(NFPEDA)
1. Hedonic model was first successfully used;
2. Both linear and semilog models obtained
fairly good statistical results.
RV estimates for four types of farm machinery:
tractors; combines; cotton pickers and swathers;
balers, forage harvesters, blowers, and selfpropelled sprayers; and all other machinery.
CobbDouglas
Linear and
Geometric
Hall (1968, 1971)
PDBV'
Peacock and Brake
(1970)
Y a + bX2
Y abX
Geometric
McNeil (1979)
RV= f (age,
condition)3
Linear
Depreciation is influenced by asset wear,
embodied and disembodied technology quality.
'Official Guide' data during 1. Age, make and inflation were explanatory
the periods 1954-1963 and
variables;
1959-1963.
2. The first year's decline in market value was
usually greater than even the largest commonly
used depreciation function.
32 used tractors with hp 35- 1. Age was the primary variable;
70, in the southern interior
2. An exponential form provides a reasonably
of British Columbia in 1977 good explanation;
3. Prices fell by around 30% in the first year and
thereafter declined at constant rate;
4. Depreciation schedules for US and British
Columbia were compared; and
5. First use of auction sale data.
Where
is the observed price of the used asset, P is affected by disembodied technology changes; D measures the pure age effect of economic
depreciation and B recognizes quality differences.
2
Y is the market value, and X is the variable affecting used machinery values.
An exponential function was postulated: RV = eI3iA5e +Condition
Table 2.1, (Continued)
Functional
Form
Box-Cox
Authors (Year of
Publication)
Hulen and Wykoff
(1980)
Models
qj*=
cx + l3s + yt +
i = 1,2,. . .N
where q s and t1 are
j.t.
B-C transformed.
CobbDouglas
Ct = f (At, It, C0)4
Leatham & Baker
(1981)
Data Source
Contributions and Conclusions
A sample collected by the
U.S Treasury's office of
Industrial Economics in
1972, of 8066 observations
on 22 types of buildings.
16 years of data for 4
manufactures of tractors
and combines.
1. Depreciation patterns were accelerated by
straight-line or geometric form; and
2. The estimated depreciation rate was around
1.5% to 3.4% per year.
CobbDouglas
Reid & Bradford
(1983)
RV= F (Age, hp,
make, Technology
change, Net farm
income per farm)5
Data in the period of 19531977 tractors.
Box-Cox
Bayaner (1988) and
Perry et. al. (1990)
RV= F(Usage, Care,
Age, Size, Region,
Auction Type,
Manufacture)6
Auction sale prices on 7
major domestic tractors,
provided by Farm
Equipment Guide (Hot
Line, Inc.) from 1985 to
1987 tractors.
1. Salvage value declined at a diminishing
rate with machine age; and
2. Depreciation rates varied by manufacture
and horsepower, and large horsepower
tractors had greater initial declines in value.
Real tractor depreciation was most closely
approximated by a combination of geometric
and sum-of-the-year's digits depreciation
patterns.
"Ci is the value of a machine that is A years old, and it has an original list price of C0. It is the index of the price increase in machines. The functional
form is
expressed as: C= 3AICe6
Their estimated model is: RV= 3oAge
where NF is the Net farm income per farm, MX and MY are dummy variables for
different tractor makes, Ti and 12 are technology change time-index dummy variables.
6
The proposed model is RV=f31 + (2+f33Cj)Age* + 434C+ E35R + I3sUse* + f37Condition + 438Ak + 9HWP; where RV*, Age* and Use*
are Box-Cox
transformed variables; Ci, Rj, and Ak are dummy variables for manufactures, regions and Auction Types, respectively; and HWP is PTO horsepower.
Table 2.1, (Continued)
Functional
Form
CobbDouglas
Authors (Year of
Publication)
Hensen & Lee
(1991)
Models
Box-Cox
Cross & Perry
(1995, 1996)
RV= F (Usage, Care,
Age, Manufacture,
Auction Type,
Region,
Macroeconomics
Variables)8
CobbDouglas
James and Glen
(1996)
ln(Pt,g,v) =
Pt,g,v
11pT HDgG *
UIBVV
ln(Pt*)Tt+
Bn(Dg,v)G g,v +
E1n(B)V +
Geometric
Stephen (1996)
P P (A, t, z)'° where
A is the age of a used
asset, t is the date of
sale and Z is a vector of
the asset's
characteristics,
Data Source
Contributions and Conclusions
A single 60 hp class of
tractors, provided by
NFPEDA
Auction sale prices on 12
types of farm machinery
provided by Farm
Equipment Guide (Hot
Line, Inc.) from 1984 to
Tractors depreciated at a linear rate of 8.3%
annually, lower than previous estimates.
1 .A double square root function was the
overall best form to model depreciation over
time; and
2. Estimated depreciation pattern varied by
manufacture type.
1993.
Combine and Tractor prices
from spring 1972 to spring
1992, provided by Official
Guide.
Transactions prices for 32
models of metalcutting and
metal forming machine
tools drawn from the sale
records of dealers
belonging to the Machinery
Dealers National
Association.
1. Combines and tractors generally exhibit
constant geometric economic depreciation on
a year-to-year basis; and
2. Significant seasonal differences exist in
machinery depreciation rates.
1. Depreciation rate increases with age; and
2. Transaction prices yielded a slow rate of
economic depreciation for these machines
about 3.5 per year of aging, with little
variation over the life of the asset.
Where T, G, V are dummy variables representing the observation year, age and vintage, respectively; and P8 , P, D5, B use the same notation as note 2.
They estimated functions for equipment types: Combines, Swathers, Balers, 30-79 HP Tractors, 80-149 Tractors, 150+ HP Tractors, Planters, Plows, Disks,
Manure spreaders, and Skid steer loaders.
This equation uses the same notation as Note 1 and Note 7.
10
The proposed model is: lnP= a+ 41A + yA*t + Ewjtj+ B'z.
8
14
2.2.1 Theoretical Development in Box-Cox model
The Box-Cox functional form was proposed by Box and Cox (1964), who
suggested the following transformation on variables in case that there are no a priori
reasons to specify a functional form:
yAl
2
Y2
(2.4)
mY
2=0
The transformation imposed on variables in Equation (2.4) allows for a flexible
form. Later research extended the transformation on dependent variables to independent
variables (Zarembka, 1974; Spitzer 1982). Unlike the standard regression model, the
Box-Cox model permits the estimation algorithm to determine the transformation on each
regressor. Letting Y1 represent the market transaction price of an asset, we apply the BoxCox model to predict the value of the used asset in the following way:
j*=
io +
+ 132X2t +
...
+X + ... +X + p
i 1,2,.. .N,
(2.5)
where
= (Y? - 1 )/X; X = (X18 - 1)10
The unknown parameters (A', Oi, 02,..., O) determine the functional form within the
Box-Cox power family, while the unknown parameters (Po, P1,..., 13fl) decide the intercept
and slope(s) of the transformed form. Table 2.2 lists the functional forms subsumed
within the Box-Cox function.
Thus, the Box-Cox power transformation is highly flexible, because it contains
most of the functional forms used in estimating depreciation patterns. The Box-Cox
function allows the data to determine the most appropriate functional form (Judge, et. al.
1985) or "let the data speak" with a minimum of apriori restrictions.
15
The Box-Cox model has been utilized in many studies to estimate
depreciation of used assets. Hulen and Wykoff (1980) used vintage prices in conjunction
with Box-Cox transformations to estimate depreciation patterns over time. Their findings
showed that depreciation patterns were accelerated vis-â-vis straight line, and perhaps
also vis-à-vis the geometric form.
Table 2.2 Box-Cox power transformations associated with selected functional
forms.
Functional Form
Power Transformation for Power Transformation for
Dependent Variables
Independent Variables
Linear
1.0
1.0
Cobb-Douglas
0.0
0.0
Geometric
0.0
1.0
Logarithmic
1.0
0.0
Double Square Root
0.5
0.5
Square Root
1.0
0.5
SumofYearDigits
0.5
1.0
Revised from: Bayaner, Ahmet "An Econometric Analysis of Used Tractor Prices."
Unpublished M.S. Thesis, Oregon State University, 1988, p. 19.
Following this approach, Bayaner (1988) and Perry et al. (1990) estimated a BoxCox RV model for tractors utilizing data from monthly reports of auction and advertised
prices for farm equipment sold across the U.S. They concluded that real depreciation of a
tractor most closely mimicked a combination of geometric and sum-of-the-year's digits
depreciation patterns, as opposed to the linear, log and Cobb-Douglas pattern used in
many previous studies.
A more extensive application of the Box-Cox functional form was conducted in the
research of Cross and Perry (1995, 1996). Their Box-Cox regression results demonstrated
that a double square root functional form was generally the best form to model the
changes in prices of equipment. They also found that: (a) the remaining value was
16
influenced by machinery condition, use, manufacture, and age; (b) macroeconomic
variables were also significant for most types of machinery; and (c) the estimated
depreciation patterns varied by manufacture type.
There are some potential problems with estimating the Box-Cox model. These
problems include limited dependent variable (Poirer, 1978) and the impact of
transformations on the validity of statistical tests (Wong and Doksum, 1983). Other
researchers have expressed the concern about biases in the Box-Cox caused by
heteroscedasticity, autocorrelation and data scaling (Zarembka 1974; Savin and White
1978; Seaks and Layson 1983; Spitzer 1982, 1984). Although the research mentioned
above achieved fairly good statistical results, none of studies on farm machinery
addressed these concerns (James and Glen, 1996).
As a highly flexible functional form, however, Box-Cox is still regarded as
preferred for analyzing depreciation (Hulten and Wykoff). This thesis will utilize Box-
Cox as one of the alternatives to estimate depreciation in different types of agricultural
machinery. This study builds on the earlier Box-Cox estimates of Cross and Perry in two
ways. First, an additional 6 years of auction data (1994-1999) were added to the data sets
used by Cross and Perry. These additional observations not only provide for more
robustness in the estimates, but they better capture the impact of several variables.
Second, the auction data provided information on many types of farm equipment, but the
number of sales was often not sufficient to estimate a depreciation function. With the
additional years of auction data, some of this equipment did have enough observations to
be examined for the first time.
2.2.2 Theoretical Development in Exponential Model
Depreciation is a function of a number of underlying exogenous variables. For
example, the exponential hedonic model postulated by McNeill is
a+Ae +Condjtjon
RV
(2.6)
where RV is the remaining value as a percentage of the new replacement prices.
17
The property of this function is that the remaining value of used equipment at any
age greater than one year is a constant portion of the remaining value of the same
equipment one year younger, as the following relationship holds:
RV/RV1 =e1,
t>1
(2.7)
where t refers to the age of the equipment.
The concept of a declining balance on remaining value over time was supported by
the finding that RV/RV1 was constant for all ages except new and one year old
equipment where a lower ratio was observed (Griliches). If Equation (2.6) is transformed
logarithmically, it can be estimated by Ordinary Least-Squares (OLS):
Ln (RV) = a+3iAge +32Condition
(2.8)
McNeil! further suggested a related functional form:
RV = 1/ [1+
c1+3
Age +f3 Condition1
(2.9)
and its logit transformation form:
Log(RV/1 - RV) = a+iAge +32Condition
(2.10)
Equation (2.9) is a logistic function that has an inflection point allowing for both a
convex and concave region of the curve. And the advantage in Equation (2.10) is that the
dependent variable, log (RV/1-RV) has an unrestricted range as compared to Equation
(2.9) where the dependent variable is restricted to be between 0 and 1.
A conceptual theory for the exponential model was first postulated by McNeill,
with supporting evidence from an empirical analysis of 32 tractors sold in the southern
interior of British Columbia in 1977. However, the exponential, or geometric form had
already been used in several previous studies (ASAE; Peacock and Brake).
The American Society of Agricultural Engineering (ASAE) used National Farm and
18
Power Equipment Dealer Association (NFPEDA) data to estimate depreciation of
used agricultural machinery. For example, the equation for tractors was
RV = 68 (0.92) Age
(2.11)
Equation (2.11) was used for many years as the ASAE standard when estimating
tractor depreciation cost. In the last decade, several problems have been identified with
this equation, including the reliability of the data used and the assumption of a geometric
depreciation pattern for all equipment (Perry et al., 1990).
Peacock and Brake also estimated a semilog model, similar to Equation (2.11):
RV = 66.6 (0.935) Age
(2.12)
They also found that age, make and inflation were the most influential variables in
their model.
Later research focused on the Cobb-Douglas model (See Leatham & Baker, Reid &
Bradford, Hansen & Lee, James and Glen; See Table 2.1). The most recent research
utilizing the exponential form was conducted by Stephen in 1996. Although he derived
his model utilizing a simpler approach based on the Box-Cox model, it was also an
exponential function:
lnP= c+ 43A' + yA*t + O)f+ O'Z
(2.13)
where A is the age of a used asset, t is the date of sale and Z is a vector of the
asset's characteristics.
A geometric rate of 9.5 percent for manufacturing equipment was estimated in the
Stephen's studies, only somewhat lower than 12.25 percent estimate obtained by Hulten
and Wykoff after restricting Box-Cox to take the geometric form. This indicated that the
two estimation techniques were not different in any meaningful sense, owning to
uncertainty about proper retirement distribution with which to adjust the observed prices.
19
This thesis will propose a modified exponential model - Additive
Exponential - for use in estimating depreciation cost. This new method, combining
advantages of both linear and exponential forms, will be explained in the remaining
chapters.
20
CHAPTER 3
DATA, MODEL AND COMPARISON
This chapter focuses on describing the data collected for statistical analysis and
developing the Box-Cox and Additive-Exponential regression models for estimating
depreciation cost. The method utilized to test the fitness of the two models --MAPE
method -- will be introduced in the end of the chapter.
3.1 DATA DESCRIPTION
Most previous studies of tractor depreciation relied on equipment dealers average
resale prices, as reported semiannually by the National Farm and Power Equipment
Dealer Association (NFPEDA) (See Table 2.1). In Bayner's study, some concerns were
raised about the inadequateness of these data in estimating various depreciation patterns:
First, the prices are averages instead of actual transaction prices; second, they probably
do not fully represent 'arms length' transactions, i.e. transactions between dealers and
farmers may involve warranties and other special conditions; and finally, a geometric
depreciation rate was imposed in calculating prices for the same model of tractor
manufactured in different years.
An alternative to the price data reported by NFPEDA is to use auction data.
Following Bayner (1988), Perry, et al.
(1990)
and Cross and Perry
(1995),
models in this
thesis are based on the auction prices for farm equipments throughout U.S. provided in
monthly reports published by Hot Line, Inc. Each publication contains information about
price, manufacturer, condition, model, year manufactured and year sold, hours of use,
auction location and date, and other descriptive information, which forms the basis of
econometric analysis in this thesis.
The data sets include sales that occurred from
types of agricultural machinery (See Table 1.3).
1984
to 1999, representing most
21,
3.2 SPECIFICATION OF MODELS
Variables Identification
3.2.1
The variables used in this study are consistent with the previous studies.
3.2.1.1 Age
Since age is closely related with wear and obsolescence, it was expected to be one
of the most obvious variables affecting used farm machinery values. Age alone is capable
of explaining a large percentage of the change in market value. Peacock and Brake
(1970) claimed in their studies that age explained 57% of RV variation for 1953 tractors
and 89% for 1953 forage harvesters.'
Hence, age was considered as an explanatory variable in both Box-Cox and
Additive Exponential models. It was calculated as the difference between the year of sale
and year of manufacture.
3.2.1.2 Usage
As Keynes noted, the usage level "constitutes one of the links between the present
and future. For in deciding his scale of production an entrepreneur has to exercise a
choice between using up his equipment now and preserving it to be used later on" (pp.
69-70). Presumably, higher usage levels will shorten the life of farm machinery, thereby
reducing the stream of future returns and the asset's current market value (Perry, et al.
1990).
1
These percentages are the R2 statistics for simple linear regression equation of the type Y=a+bX, where Y
is the market value of machine as a percentage of its original cost and X is the age of the machine in years.
22
Usage was considered in the models and represented as annual hours per year
(total hours divided by age). It was included for Tractors, Combines, Skid Steer Loaders
and Trucks.
3.2.1.3 Care
Care can moderate the effect of usage. Care includes both the maintenance and
repairs regularly performed by the asset owner, and the manner in which the asset is
treated (Perry, et al. 1990). Higher levels of care will prolong the useful life of
equipment, thereby decreasing the rate of depreciation.
Care was represented as a binary variable in the models. Conditions of farm
machinery are defined in the following table:
Table 3.1 Condition evaluations of farm machinery (Hot Line, Inc.)
Conditions
Excellent
Good
Fair
Poor
Overall
Implement
has seen
little or no
use in the
field
Engine
Twe
In perfect
Have 80%condition with 100% tread
0 to 600 hours remaining, and
of use
no breaks or
cracks
In good
Have about
running
70% tread
condition
remaining
Replacemen In fair running Have about
t of parts
condition
60% tread
would
remaining with
enhance
possibly some
performance
scars visible.
Rebuilding
Needs a major Have 50% or
is necessary. overhaul to
less tread
restore power. remaining with
possible cracks
or sears.
Paints
Parts
Original and
bright in
appearance
Little or no
wear.
Original or
has a good
paint job
May be
weathered
and show
some signs
of rust
Rough and
rust is quite
evident,
Bearing are
showing little
wear
Becoming
worn.
Bearings need
replacement.
23
3.2.1.4 Manufacture
Although each manufacturer of farm equipment usually offers a wide variety of
options, one may still expect enough differences between makes for farmers to prefer one
over others. These preferences are undoubtedly developed over time on the basis of the
farmers' own experiences and information from neighbors, dealers and advertising. In
addition, reliability, frequency of repairs and difficulty in getting repair parts can all
contribute to overall used equipment value. A study of Peacock and Brake in 1970
showed that more-preferred farm equipment makes generally depreciated more slowly
than the less-preferred ones. In the research of Leatham and Baker in 1981, they further
proved this by rejecting the hypothesis that all makes depreciated at the same rate, both
for tractors and for combines.
Therefore, manufacturer is another variable worthy of consideration in our models.
Again, a binary variable was included in the models. The manufacturers and the
abbreviations used to represent them in this study are as follows:
Table 3.2
Manufacturers and their abbreviations used in this study.
Manufacturer
Allis-Chalmers
Bush Hog
Case
Case-International
Chevrolet
Ford
Gehi
Haybuster
Hesston
New Holland
3.2.1.5 Loaders
Abbreviation
AC
BH
CASE
CASEIH
CHEV
FD
GEHL
HAYBU
HT
NH
Manufacturer
International Harvester
John-Deere
Krause
Kewanee
Massey-Ferguston
Meirose
Owatonna
Manufacturing Company
White
Versatile
Abbreviation
IH
JD
KRAUS
KEWAN
MF
MR
OMC
WHITE
VS
24
Because many small tractors2 in the data set had loaders, a dummy variable was
used to account for the presence of a loader.
3.2.1.6 Auction Type
Equipment sales occurred at four types of auctions: a) farmer retirement, b)
bankruptcy, c) consignment, and d) dealer closeout. The term, "farm retirement" means
the farmer was either retiring or had passed away (estate sale), while dealer closeouts
refer to sales of equipment the dealer had taken on trade and wanted to liquidate at an
auction.
Dummy variables were assigned to each auction type.
3.2.1.7 Macroeconomic Variables
Macroeconomic variables were needed because the agricultural economy has a
direct impact on the market for equipment. When agriculture is expanding, demand for
farm equipment increases, thereby driving up prices. When contraction is occurring,
prices for equipment decline.
To address this issue, Real Net Farm Income was used as a proxy for the general
health of the agricultural economy. In addition, economic theory suggests that the cost of
borrowing money (Real Interest Rate) also influences equipment costs. These two
variables were calculated as
RNFI NNFJ .
RIR=
l+FCJR
1+ (CPI - U)
where RNFI is the Real Net Farm Income, given in Table 3.3;
2
In our models, small tractors are tractors with horsepower below 120.
(3.1)
25
NNFI is the Normal Net Farm Income, given in Table 3.3;
PPI is the GNP implicit price deflator, given in Table 3.4;
RIR is the Real Interest Rate, given in Table 3.3;
FCIR is the Farm Credit Interest Rate, given in Table 3.3; and
(CPI-U) is CPI-Urban, given in Table 3.3.
Table 3.3
Net Farm Income and Real Interest Rate for farm sector, 1984-1999
Year
NNFI
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
26.1
28.8
31.1
38.0
37.5
45.0
44.8
38.4
47.9
42.1
49.2
37.2
54.9
48.6
44.1
48.1
RNFI
18.7320
21.3278
23.5290
29.5678
30.165
37.953
38.8909
34.4678
43.9291
39.6414
47.2960
36.5267
54.9000
49.4162
45.3657
50.2212
FCIR'(CPI-U) % RIR
12.47
12.40
11.23
10.10
10.56
11.68
11.16
10.10
8.20
8.09
8.23
8.89
8.55
8.92
8.59
8.41
1.0783
1.0849
1.0916
1.0627
1.0621
1.0656
1.0546
1.0566
1.0505
1.0494
1.0549
1.0592
1.0539
1.0647
1.0688
1.0608
4.3
3.6
1.9
3.6
4.1
4.8
5.4
4.2
3.0
3.0
2.6
2.8
3.0
2.3
1.6
2.2
Table 3.4 GNP Implicit Prices Deflator (based on 1996 dollars), 1970-1999
1971
MPI
29.26
30.8
1972
1973
1974
1975
1976
1977
1978
1979
32.15
33.98
36.92
40.34
42.75
45.55
48.71
52.66
Year
1970
MPI
1980 57.35
1981 62.68
1982 66.49
1983 69.21
1984 71.77
1985 74.02
1986 75.63
1987 77.81
1988 80.44
1989 83.54
Year
Year
MPI
1990
86.81
89.76
91.71
1991
1992
1993
1994
1995
94.16
96.13
98.19
1996 1100
1997
1998
1999
101.67
102.87
104.41
26
3.2.1.8 Remaining Value
The concept of remaining value (RV) was discussed in the Chapter 2 (See pp. 9).
RV was used as the dependent variable in estimating equipment value. This approach
allows the prices for different types of agricultural machinery and attributes to be
grouped together in a common data set, thereby providing sufficient degrees of freedom
for the estimation approach (Perry et al. 1990).
List price in the data was used as a proxy for new equipment price, and both list
price and auction sale price were adjusted to 1996 dollars. Therefore, the RV calculation
can be expressed as follows:
RV=
ASP.
' MPI.
LP.MPI1
(3.2)
Where ASPi is the Auction Sales Price in sale year i;
MPI1 is Manufactured Price Index for year of sale (Given in Table 3.4);
MPIJ is Manufactured Price Index for year of manufacture of models; and
LP is the List Price in manufacturing yearj.
3.2.2
(i,
= 1970... 1999)
Specification of Models
The resulting hedonic model can be written in general terms as
RV = F (Age, Usage, Care, Manufacturer, Loader, Auction Type,
Macroeconomic Variables)
(3.3)
The next section will present two ways to express Equation (3.3): Box-Cox and
Additive-Exponential.
3.2.2.1 Box-Cox Model
27
To apply the Box-Cox transformation technique specified in Equation (2.5) to this
hedonic model required use of the generalized Box-Cox model:
RV=[fi02+2flXil+2fl1Z1+l
Ii
i
j
(3.4)
]
Where RV is the remaining value of farm equipment, 2 is the transformation on RV,
'y are transformations on independent variables X, and
Z are all other independent variables not transformed.
To be specific, X1 included the variables Age and HPY (Hours per year, if
available), and Z1 represented all other variables. The form of the estimated model is
R V2 1
2
1
= A0 + A,
Ii
CManufacturer +
I
HPYY2
A2
-
+ A3 RNFI + A4 RIR +
B1Condition +
12
-
DManufacturer1
I
Ti
+
Ek AuctionTypek
(3.5)
k
where A0, A1, A2, A3, A4, B, C, D, and Ek are estimated parameters; and
?, Ii, and 12 are Box-Cox transformations.
The model was estimated using the SHAZAM econometrics package. SAS was also
used when the Box-Cox transformations were less than 3 to verify the SHAZAM results.
3.2.2.2 Additive-Exponential Model
The idea behind the hedonic model is that it divides the value of an asset into its
component parts. For example, a tractor's value is primarily determined by its age, hours
of use, and manufacturer. These can be treated as the additive components of the tractor's
value. Other secondary variables that influence all these primary components can be
28
treated as exponential variables. An example is auction type. If the sale occurred
because a farmer was retiring, this fact should vary depending on age, use and
manufacturer. A parsimonious way to capture this would be to multiply the additive
component by an exponential function reflecting a farmer retirement auction.
Cross and Perry examined the Box-Cox and several alternative functional forms
(See Table 3.5). The unrestricted Box-Cox form generated the largest log-likelihood
value. After comparing the log-likelihood value of other functional forms with that of
Box-Cox, they concluded that the double-square root form was consistently closest to the
Box-Cox function. By comparison, the Geometric (Exponential) model was significantly
different from the Box-Cox in 9 out of 12 equipment types, and the Linear model
produced results significantly different from the Box-Cox in 11 out of 12. Even for the
three equipment types where Geometric was not significantly different from the BoxCox, the Double-square root form generally had a higher log-likelihood value. For the
only type of model where the linear form was close to the Box-Cox, the Double-square
form still generated a higher likelihood function. Therefore, both the Linear and
Exponential forms were not ideal to estimate the depreciation pattern alone.
The combined model -- Additive Exponential functional form - was therefore
evaluated in this thesis to see if it might be an improvement over other functional forms.
This form can be expressed in a general way as
RV=[/30+/31X1 ].J]IefizJ
(3.6)
where RV, X, and Z are corresponding to the RV, X1, and Z in equation (3.4).
For estimation purposes, the Additive Exponential model was formulated as:
RV = (4
+
j
C1Manufacture1 +
eTuh1
[J
k
j
D1Age Manufactured).
eARl%'
e'11'1
(3.7)
where RV, Age, HPY, RNFI, RIR, Condition1 (I = 1, 2, 3, 4), Manufacturer (j = 1, 2, 3...)
Table 3.5 Log-Likelihood values for Box-Cox and alternative functional forms for farm equipment remaining value models
Functional
Forms
Box-Cox
Geometric
Linear
Square
root
Doublesquare root
SYD
CobbDouglas
Inverted
Tractors
Mowers
Balers
Combines
Swathers
Plows
Disks
Planters
Manure
Spreaders
Skid_Steer
Loader
671.48
620.90*
572.64*
66.87
65.42
57.88*
118.54
112.59*
99.38*
1095.25
1020.89*
976.04*
112.49
111.52
100.09*
5775*
61.01
58.16
78.69
63.52*
70.82*
77.35
55.691*
71.82*
24.01
19.20*
13.091*
63.07
59.31
52.62*
1042.23*
596.52*
58.48*
101.70*
1007.95*
100.05*
58.13
7304*
72.34*
17.07*
55.61*
321.97
1440.71*
665.79*
65.81
117.49
1090.98*
110.66
60.97
76.96
76.26
22.61
60.33
316.95*
1430.61*
650.41*
65.43
116.90
1086.50*
110.78
61.01
75.04*
7595*
19.46*
58.80*
287.38
1438.22*
624.31*
65.58
107.32*
948.71*
110.39
57.63*
65.72*
54.13*
22.35
60.55
256.14*
97475*
551.54*
60.26*
97.01*
829.92*
9453*
58.13
74.46
65.96*
15.43*
56.38*
0.34
0.76
0.47
0.67
0.83
0.21
0.90
0.5
1.21
0.61
-0.32
0.64
0.63
0.36
0.29
-
-
-
0.36
-0.4
1.26
1026
107
94
116
55
63
Small
Large
<8Ohp
Medium
80-149hp
323.52
296.60*
288.43*
1480.74
1445.36*
1032.86*
296.94*
150+hp
Box-Cox Transformations for
RV
Age
Use
Sample
Size
0.45
0.76
0.24
0.5
-0.03
0.43
0.15
0.90
0.29
-0.12
433
1946
866
77
0.24
181
185
* Significantly different from the Box-Cox Model at the 95% confidence level.
Source: T,L. Cross, and G.M. Perry: "Remaining Value Functions for farm Equipment", Applied Engineering in Agriculture,
Vol.12 (5): 547-553
30
AuctionTypek (k = 1, 2, 3, 4), A0, A3 A4, B, C1, D, and Ek are defined as in Equation
(3.5). However, A1 and A2 are omitted.
The model given above was estimated by using both SHAZAM and SAS
econometrics packages. Chapter 4 will provide the statistical results and analysis for each
type of farm machinery.
3.2.3
Model Testing
Since the data used in study combined cross section3 data and time series4 data, the
data sets are characterized as panel data sets. The typical problems with panel data sets,
as Greene (1997) suggested, are correlation and heteroscedasticity. The proposed models
were examined for the presence of these problems.
3.2.3.1 Correlation
The process for examining the problem of correlation was conducted in two steps.
First, simple correlation coefficients were calculated for all variables, using the formula:
Cor() =
Cov(V,V)
Var()Var()
(3.8)
Correlation measures the strength of the linear relationship between two variables.
A correlation of 0 means that there is no linear association between two variables. A
correlation of 1 (-1) means that there is an exact positive (negative) linear association
between the two variables.
A cross section is a sample of a number of observational units all drawn at the same point in time.
A time series is a set of observations drawn on the same observational unit at a number of (usually evenly
spaced) points in time.
31
The first colunm in Table 3.6 lists the correlated variables5 in each model. It is
evident that the positive correlation between the age-manufacturer cross product variables
and manufacturer variables existed in every model and the positive correlation between
age-manufactured cross product and age occurred in 5 models. Because all manufacturer
variables were set as dummy variables, some negative correlations among manufacturers
can also be readily explained, such as International Harvester and John Deere, and Case
and Ford. Similarly, there were negative correlations among the auction type dummy
variables, such as Bankrupt and Farmer retirement, and negative correlations among the
condition variables, such as good and fair, fair and poor, and poor and good. The
macroeconomic variables RNFI and RIR were negatively correlated with each other in 13
samples, which was consistent with the economic phenomena that a prosperous economy
was characterized by low interest rate.
Auxiliary regressions test was conducted to further examine the correlation among
variables. Each individual independent variable was regressed on a constant and all the
other independent variables. If the overall R2 in the original regression, or the regression
with the original dependent variable as the regressand, is less than any of the R2 in the
individual auxiliary regressions, correlation is detected (Greene, 1997). The auxiliary
regressions statistic results were listed in Table 3.6.
Consistent with the simple correlation tests, the macroeconomic variables were
correlated with other variables in 9 of 21 models, the variables age and HPY were also
found correlated with other variables in a couple of models.
The method most frequently used to deal with correlation problem is to drop
variables suspected of causing the problem. However, this could cause biased estimation
of the model if the variable dropped is a relevant one. Actually, as subsequent results
(Table 4.88 and conclusions in 4.5.3 V, VI and VII) suggest, RIR, RNFI, HPY and Age
were significant variables in most models. Hence, all variables were kept in the models.
3.2.3.2 Heteroscedasticity
Based on absolute correlation value greater than 0.5 level.
Table 3.6 - Statistic results of testing Correlation and Heteroscedasticity
Type of Farm
Machinery
Less than 80 HP
80l20 HP
120+HPw/fwd
120'-l45wlofwd
145+ HP w/o fwd
Combine
Corn-Header
Cotton-Harvester
Swather
Baler
Forage-Harvester
Mower-Conditioner
Mower-Cutter
Planters
Disks
Plows
Drills
Grinder-Mixer
Manure-Spreader
Skid-Steer-Loader
Truck
*
Correlation Method
Correlated Variables
Correlation
Auxiliary Regressions Method
R2 when dependent variable is
Source
RV AGEIHpyIRNFIIIUR
MA/M, -RI/RN
MAIM, -F/G, -RI/RN
0.49
0.17
0.15
0.35
0.07
0.18
0.39
0.44
0.41
0.31
MAIM, -F/G
0.69
0.42
0.25
-
-
0.36
0.20
0.13
0.17
0.47
0.34
0.29
0.28
0.39
0.17
0.40
0.53
0.60
RNFI
0.15
0.18
0.18
0.46
0.23
0.02
0.004
0.04
0.008
0.08
0.19
0.48
0.23
0.20
0.31
0.66
0.47
0.27
0.28
0.37
0.17
0.42
0.56
0.73
0.11
0.61
0.73
0.17
0.10
0.10
-
0.45
-
0.41
0.14
0.29
0.03
MAIM,-F/G,-RJIRN
MAIM, -F/G, -l/D, DG/A
MAIM, -lID, -F/G
MAIM, -B/FM, -D/FM, DG/A
MAIM, -P/F, -P/G, -RI/RN, RN/A
MAIM, -FIG, -RI/RN, -B/FM
MAIM, -B/FM, -RIIRN
MA/M, F/A, -B/FM, -RI/RN
MA/M, -B/FM, -RI/RN
MAIM, -B/FM
MA/M,
MAIM, -lID, -B/FM, -RI/RN
MAIM, -lID, -RI/RN, DG/A
MAIM, IG/A, -RI/RN
MAIM, GG/A, -B/FM, -RI/RN
MAIM, NG/A, -B/FM, -RI/RN
MA/M, -C/FD, -F/G,-B/FM,-R1/RN
MAIM, -B/FM
0.40
0.55
0.37
0.34
0.44
0.41
0.36
0.31
0.13
0.42
0.19
0.03
0.01
0.10
0.28
0.11
-
-
0.44
0.49
0.35
0.42
0.44
0.08
0.48
-
Heteroscedasticity
White
Source
Statistics
21.56
4.07
-
38.06
16.60
44.98
25.70
8.10
12.88
8.58
AGE IIPY
7.41
11.51
3.55
-
-
RNFI, RIR
RNFI, RIR
AGE,
RNFI, RIR
2.59
9.47
13.90
10.62
-
-
6.50
-
6.81
-
RNFI, RIR
22.17
7.79
12.67
AGE, HPY
RNFI, RIR
-
-
-
RNFI
RNFI
-
-
RNFI, RIR
-
-
HPY
HPY
-
Unknown
-
1. The correlation matrices were based on the untransformed variables and correlated variables;
A negative sign denotes a negative correlation between variables, otherwise, the correlations are positive; and
The abbreviations are: M-Manufacturers; A-Age; MA-cross product of manufacturer and age variables; I-IH; D-John-Deere; C-Case; FD-Ford; IG, DG,
GG, NG-Cross product of IH, Deere, GE, NH and Age; F-Fair; G-Good; B-BANKRUPT; FM-MARMERET; RN-RNFI; and RI-RJR.
33
Heteroscedasticity is the effect of different processes applying to different crosssectional units (Greene). It occurs when the variance of the errors is not constant across
values of one or more regressors. Mathematically, heteroscedasticity can be expressed as
a = a * w, (i = 1,.. .n), where a, is the disturbance variance pairwise correlated with
some unknown factors.
There are several alternatives to test the presence of heteroscedasticity, such as
Glesjer's tests, Goldfeld-Quandt test, Breusch-Pagan-Godfrey test and White test. In this
thesis, the Glesjer test and White test were used to investigate the presence of
heteroscedasticity.
In the Glesjer test,
e12,
or the squared error, is taken as w1, and a preliminary
regression
2
e. =13;
is computed with the assumption that
(3.9)
; is a vector of variables causing the disturbance
variance. A joint test of the null hypothesis that the slopes, or /3, are all zeros is
performed by encompassing the Lagrange multiplier test, where a Wald statistic is
computed to carry out the test. The Wald statistics is W = b'{Var[b]}' b, where b is the
vector of the estimated slopes, and Var[b] is the asymptotic covariance matrix for the
slope parameters. Under the null hypothesis of homoscedasticity, the Wald statistic is
asymptotically distributed as chi-squared with P degrees of freedom, where P is the
number of variables in z, excluding the intercept term.
The Glesjer test facilitates identifying the heteroscedasticity form, by assuming the
2
is one of three forms: 60+Z1a, (6o+Za)2 and exp(5o+Za). However, this assumption
can be a weakness because it fails to identify other forms of heteroscedasticity, if the
heteroscedasticity does not follow any of the three patterns.
Another problem with using this method is that to perform Glesjer test for 21
models and assuming each form of heteroscedasticity, leads to a lot of econometric work.
Consequently, a White test Was conducted before the Glesjer to test the presence of
heteroscedasticity.
34
The White test is extremely general. To carry it out, we need not to make any
specific assumptions about the nature of heteroscedasticity. The rule of thumb to perform
is obtaining the white statistics nR2 in the regression of e2 on a constant and all unique
variables in XX. The statistic is asymptotically distributed as Chi-square with P-i
degrees of freedom, where P is the number of regressors in the regression, not including
the constant.
Table 3.6 also lists the White statistics that were obtained by performing the White
test in each model. Heteroscedasticity was found in 4 of 21 models. To identify the
source of heteroscedasticity, t values from the regression of e12 on a constant and all
unique variables in XcøX were examined If the origin of heteroscedasticity was from one
variable, such as in combines and tractors with 145+ HP, a weighted least square (WLS)
regression was conducted, by taking the known heteroscedasticity variable as the weight;
if the heteroscedasticity was caused by more than one variable, such as tractors with 120+
HP; or if the heteroscedasticity was temporarily unknown (because t values did not
indicate which variable was the source), the Glesjer test was performed to identify the
possible heteroscedasticity form, and the corresponding weights were calculated to
perform the WLS regression to adjust for the heteroscedasticity problem.
Statistic results showed that the adjusted models did not generate coefficients
markedly different from the standard regression technique. This result suggests
heteroscedasticity was not particularly serious in our models. As Greene (1997)
suggested: the White test may reveal heteroscedasticity, but it may instead simply
identify some other specification error (such as the omission of X2 from a simple
regression). Considering heteroscedasticity existed in only four models out of 21,
heteroscedasticity was overall not considered a serious problem.
3.3 COMPARISON METHOD
35
The analytical procedure utilized to evaluate the accuracy of remaining value
forecasts of Box-Cox and Additive-Exponential depreciation methods was MAPE (Mean
Absolute Percentage Error) method:
APE=
R Ves/ifliated - R Vactuai
MAPE =
R Vactual
APE1
(3.10)
where N is the number of observations.
A smaller MAPE value represents less error in prediction and a better fit of the
model to the data.
In our 21 data sets representing 17 types of agricultural machinery, the MAPE
method was used to explore the prediction accuracy of both models when more than 100
sales were in the data set. To carry out the test, 90% observations were used to estimate
both models, and the remaining 10% of all observations were used to calculate the MAPE
values. Data were randomly chosen for each data set.
The MAPE values in each data set will be presented in Chapter 4 and the fitness of
both models will be compared.
36
CHAPTER 4
EMPIRICAL RESULTS
The preceding chapters provide the theoretical basis for this study, as well as a
literature review of related work. In this chapter, the statistical results of each
depreciation model will be presented. This includes (1) the discussion of data
characteristics, (2) the explanation and analysis 'of regression results, and (3) a
comparison of B-C (Box-Cox) and A-E (Additive-Exponential).
Farm equipment will be placed in one of the following four categories for this
analysis: (a) Tractors, (b) Harvest equipment (combines, cotton pickers, swathers,
mowers and conditioners), (c) Tillage and planting equipment (Planters, disks, plows and
drills) and (d) Other equipment (Spreaders, skid steer loaders, mixers and trucks). The
statistical analysis will be developed based on this division.
4.1 TRACTORS
Tractors are widely used in a variety of agricultural operations, such as heavy and
light tillage, planting, spraying, and harvesting operations. Tractors also play a supporting
role on farms such as moving heavy objects or operating stationary pto-driven equipment.
In essence, they serve as a portable source of power in carrying out most mechanized
farming operations.
Tractors, depending on their sizes, are usually assigned different operation jobs. For
example, very small tractors, with 10 to 30 HP (horsepower), are usually used to perform
spraying in a smaller row spacing; while large tractors, with more than 300 HP, are used
for faster performance in very heavy ripping and tillage operations.
Four-wheel drive is another factor that differentiates tractors. Two-wheel drive
tractors have been the industry standard, but four-wheel drive is common for very large
tractors and as an option on many smaller tractors.
37
Each tractor reported in the Hot Line booklet was included in the data set,
provided (a) the tractor had more than 30 HP, (b) it had been manufactured since 1971,
and (c) the sale listed the number of hours the tractor had been used. The resulting data
set, containing 7363 sales, was then divided into five categories: (a) Less than 80 HP, (b)
80 to 120 HP, (c) greater than 120 HP, with FWD (four-wheel drive), (d) 120 to 145 HP,
without FWD and (e) greater than 145 HP without FWD.
4.1.1
Tractors With Less Than 80 Horsepower
4.1.1.1 Data Description
The data set for tractors with less than
80
Horsepower
(HP)
contained
730
observations, of which 657 observations were
used in the estimation process and 73 were
used to test predictive ability. Table 4.1 shows
the average, standard deviation, minimum and
maximum value of HPY (hours per year), RIR
(real interest rate), RNFI (real net farm
interest), RV (remaining value) and Age.
Table 4.2 lists the distribution of dummy
John Deere Four Wheel Drive
Tractors-MFWD 5320 55 HP
variables included in both B-C and A-E
models. Manufacturers John Deere (30.41%) and Ford (22.47%) accounted for over half
of tractors in this type. Two major auction types were represented: Farmer Retirement
and Consignment (40.27% and 39.59%). The majority of tractors were in either Good
(56.7 1%) or Excellent (27.53%) condition, and 68.50% of tractors had front loaders, a
common accessory on small tractor.
38
Table 4.1 - Summary statistics for tractors with less than 80 HP (Sample size:
730)
Variables
HPY
RIR
RNFI
RV
AGE
Mean
233.0433
1.060424
39.97748
0.372825
12.37534
Standard
Deviation
191.1931
0.01025
9.477037
0.186023
6.620328
Minimum
4.222222
1.0494
18.732
0.019163
Maximum
2075.2
1.0916
54.9
1.313416
0
27
Table 4.2 - Frequency statistics for tractors with less than 80 HP (Sample size: 730)
Frequency
MANUFACTURERS
CASE
41
CASEIH
26
FORD
164
DEERE
222
IH
137
MF
54
WHITE
20
OTHER
107
EQUIPMENT CONDITION
EX
201
GOOD
414
FAIR
100
POOR
15
AUCTION TYPE
FARMRET
294
BANKRUPT
37
CONSIGN
289
DEALER
30
UNKNOWN
80
OTHERS
W/LDR
W/OLDR
4.1.1.2 Models Estimation
500
230
Percent (%)
5.61
3.56
22.47
30.41
18.77
7.40
2.74
14.66
27.53
56.71
13.70
2.05
40.27
5.07
39.59
4.11
10.96
68.50
31.50
Table 4.3 - Regression coefficients and t-statistics for tractors with less than 80
39
HP
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
CASEIH
0.32 103
CASE
-0.17068
FORD
0.062715
DEERE
0.195 15
MF
0.18403
WHITE
-0.034606
IH
-0.0083966
MANUFACTURER *AGE
CAGE (CASE*AGE) 0.023255
FAGE(FORD*AGE) 0.022891
DAGE(DEERE*AGE) 0.024563
IAGE(IH*AGE)
0.0243 05
MAGE(MF*AGE)
-0.0026475
CIAGE(CASEIH*AGE) -0.053148
WAGE(WHTTE* AGE) 0.016006
CONDITION
GOOD
-0.056156
FAIR
-0.12027
POOR
-0.2524
AUCTION TYPE
FARMRET
0.050333
BANKRUPT
0.011856
DEALER
0.019376
OTHERS
RNFI
0.010402
RIR
2.1039
LDR
0.15794
HPY
-0.036317
CONSTANT
-2.8228
AGE
-0.095653
B-C TRANSFORMATION
RV
AGE
HPY
B-C R-SQUARE
B-C ADJUSTED R-SQUARE
A-E
COEFFICIENTS
T-RATIO
2.117**
-1.227
0.7056
2.188**
1.753*
-0.2299
-0.07951
0.27473
-0.52622
-0.12645
0.095703
-0.32138
0.055225
-0.4157
-1.2244
-0.44338
0.34418
-1.1007
0.19809
-0.83067
0.7895
0.5 165
0.040355
0.032884
0.031185
0.039029
0.018892
-0.03551
0.03857
1.0554
1.0523
0.9415
1.2196
0.61398
-0.53678
0.88626
2.809**
..4333***
..4595***
-0.15756
-0.20528
-0.47342
_5.9761***
4.7808***
3.6276***
2.959***
0.052704
0.055915
0.053999
1.9955**
1.1905
0.96572
0.01525 1
-1.35 14
10.636* * *
0.9 185
0.9846
0.9335
-0.0997 1
-1.102
0 .3 24 6
0.4848
9393***
2.167***
5Ø4***
7.946***
2.666***
3.917***
0.4
0.6
0.19
0.6653
0.6520
Note: *** Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
0.28123
-0.00025
1.5457
-0.07083
0.543 84
6.299***
6.5349***
-4.1018 * * *
3.2068***
1.9259*
40
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.3. FARMRET was the only significant auction type variable
in both estimations, as were all condition variables and variables RNFI, RIR, LDR, HPY,
AGE and CONSTANT. The Age-Manufacturer cross product variables were insignificant
in both models. Manufacturer type variables CASEIH, DEERE and MF were only
significant in the B-C estimation, but insignificant in the A-B.
The B-C transformations estimated for RV, AGE and HPY were 0.60, 0.19 and 0.4,
respectively. This indicates that the depreciation pattern for tractors with HP less than 80
might approximate the Sum-of-the-year's digits functional form. The R2 and adjusted R2
values in the B-C model indicate a good fit for the data set.
4.1.1.3 Comparison Between Models
Table 4.4 compares the log-likelihood values, as well as the predictive abilities
(MAPE) of both models. Both models exhibited very similar predictive abilities (0.28 for
B-C and 0.29 for A-E).
Table 4.4 - Comparison of B-C and A-E models for tractors with less than 80 HP
SAMPLE SIZE (90%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
B-C
A-E
657
595.378
657
548.0432
73
73
0.2859425
0.2908550
A simplified version of the B-C and A-E equations is provided in Table 4.5, and
these equations are shown graphically in Figure 4.1. To simplify these equations, it was
assumed that the tractor was manufactured by John Deere, in Good condition, without
loader, and sold at a Farmer Retirement auction. Variables RNFI, RIR and HPY were set
at their average levels. This graph shows that the two equations exhibited similar
depreciation patterns after the first few years. Before this, the remaining value estimated
by the B-C model was higher than that of the A-E estimation.
41
Table 4.5 - Comparison of estimated functional forms of the B-C and A-E
models for tractors with less than 80 HP
B-C
RV=-0.l 18517*(AGE**O.6)O.2154
A-E
RV=0.61200.01476*AGE
Figure 4.1 - Comparison of depreciation patterns of the B-C and A-E models for
tractors with less than 80 HP
4.1.2
Tractors With 80-120 Horsepower
4.1.2.1 Data Description
The data set for tractors with 80-120 HP
contained 1578 observations, of which 1420
observations were used in the estimation
process and 158 were used to test predictive
I
ability. Table 4.6 shows the average, standard
deviation, minimum and maximum value of
HPY, RIR, RNFI, RV and Age. Table 4.7 lists
the distribution of dummy variables included in
John Deere Two Wheel Drive
Tractor-MFW 7405 105 HP
42
both B-C and A-E models. Manufacturer John Deere accounted for nearly half
(48.29%) of the 80 to 120 HP tractor sales recorded. Two major auction types were
represented: Farmer Retirement and Consignment (44.93% and 32.38%). More than half
of the tractors were in Good condition (61.22%). In this data set, only 0.3 percent of these
tractors were equipped with loaders, so this attribute was not included in either model.
4.1.2.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-B (Equation 3.7) models
are summarized in Table 4.8. All condition variables were significant; FARMRET was
the only significant variable for both models, as were RNFI and HPY. All the
manufacturer and the Age-Manufacturer cross product variables were insignificant in
both models. Auction type variable BANKRUPT and RIR were also significant in the AE estimation, while DEALER and AGE were only significant in the B-C regression.
The B-C transformations estimated for RV, AGE and HPY were 0.11, 0.13 and
-
0.2, respectively. This indicates that the depreciation pattern for tractors with 80-120 HP
might approximate the Cobb-Douglas functional form. The R2 and adjusted R2 values in
the B-C model indicate a fairly good fit for the data set.
Table 4.6 - Summary statistics for 80-120 HP tractors (Sample size: 1578)
Variables
RV
AGE
HPY
Mean
0.314382
14.77376
283.4131
MR
1.059811
RNFI
40.60289
Standard
Deviation
0.175091
5.900691
155.2437
0.009652
9.082187
Minimum
0.01879
Maximum
3.52279
0
28
13.636
1.0494
18.732
2344
1.0916
54.9
43
Table 4.7 - Frequency statistics for 80-120 HP tractors (Sample size: 1578)
Frequency
MANUFACTURERS
AC
78
CASE
165
CASEIH
32
FORD
96
DEERE
762
IH
293
MF
67
WHTTE
79
OTHER
6
EQUIPMENT CONDITION
EX
326
GOOD
FAIR
POOR
AUCTION TYPE
FARMRET
BANKRUPT
CONSIGN
DEALER
UNKNOWN
OTHERS
W/LDR
W/OLDR
966
262
24
709
78
511
117
163
5
1573
Percent (%)
4.94
10.46
2.03
6.08
48.29
18.57
4.25
5.01
0.38
20.66
61.22
16.60
1.52
44.93
4.94
32.38
7.41
10.33
0.32
99.68
44
Table 4.8 - Regression coefficients and t-statistics for 80-120 HP tractors
VARIABLES
B-C
T-RATIO
COEFFICENTS
MANUFACTURER
AC
0.013521
CASEIH
0.43 179
CASE
0.44555
FORD
0.3275 1
DEERE
0.23307
MF
-0.28256
WHITE
0.12102
III
-0.11424
MANUFACTURER *AGE
AAGE(AC*AGE)
-0.020441
CAGE (CASE*AGE) -0.11263
FAGE(FORD*AGE) -0.022208
DAGE(DEERE*AGE) 0.10742
IAGE(IH*AGE)
0.069026
MAGE(MF*AGE)
0.10728
CIAGE(CASEIH*AGE) -0.067
WAGE(WHITE*AGE) -0.010962
CONDITION
GOOD
-0.065822
FAIR
-0.17292
POOR
-0.37457
AUCTION TYPE
FARMIRET
0.089588
BANKRUPT
0.0066858
DEALER
0.05 1446
OTHERS
RNFI
0.0090745
MR
0.44064
LDR
0.20644
HPY
-0.55065
AGE
-0.3 8673
CONSTANT
0.74273
B-C TRANSFORMATION
RV
0.11
AGE
0.14
HPY
-0.2
B-C R-SQUARE
0.6293
B-C ADJUSTED R-SQUARE
0.6221
A-E
COEFFICIENTS
1-RATIO
0.02986
0.8839
1.042
0.7738
0.5739
-0.6
0.2707
-0.273
-0.1467
0.74434
-0.2 1703
0.9384 1
0.022 122
0.26743
0.46752
-0.24295
-0.03363
-0.13019
0.030394
0.45197
0.7289
-0.36403
-0.05101
-0.19112
-0. 1482
0.003492
-0.00151
-0.00885
-0.00374
0.008766
0.014766
-0.06995
0.003471
0.1105
-0.04275
-0.3362
-0.12509
0.26418
0.44925
-1.1382
0.10875
_2.5395**
_6.825***
6.823***
-0.06778
-0.18727
-0.47462
6.061***
0.2123
1.952*
0.10861
0.10415
0.048214
4.4915***
2.21 57***
1.1263
9.274***
0.5063
9.2923***
..77443***
..9759***
0.0 11322
-1.2753
0. 16894
-0.000 18
_3.153***
0.724
-0.02924
1.0182
-0.8693
-0.1713
0.8699
0. 5442
0.7522
-0.3707
-0.08112
3 .369"
1.433
Note: *** Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
4.730l***
-3.7605 * * *
1.2 102
2.9499***
-0.9963
1.595
45
4.1.2.3 Comparison Between Models
Table 4.9 compares the log-likelihood values, as well as the predictive abilities
(MAPE) of both models. The A-E model exhibited less error in its predictive ability (0.32
for B-C and 0.25 for A-E).
Figure 4.2 illustrates the depreciation patterns for those two models. The graph
represents the tractor that was manufactured by Deere, in Good condition and sold at a
Farmer Retirement auction. Variables RNFI, RIR and HPY were set at their average
levels. Remaining Values for both models were essentially the same after year 7. Before
this, the remaining value estimated by the B-C model was much higher than that of the
A-B model.
Table 4.9 - Comparison of B-C and A-E models for 80-120 HP tractors
SAMPLE SIZE (90%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
B-C
1420
A-E
1420
1661.99
1018.196
158
158
0.3191844
0.2474764
Figure 4.2 - Comparison of depreciation patterns of the B-C and A-B models for 80120 HP tractors
0.8
0.6
A-E
0.4
-3E- B-C
0.2 0
1
I
I
4
7
F
10
13
16
AGE
{
I
f
I
I
1
19 22 25
46
4.1.3
120+ HP Tractors With FWD
4.1.3.1 Data Description
The data set for 120+ HP contained 870 observations,
of which 783 observations were used in the estimation
process and 87 were used to test predictive ability. Table
4.10 shows the average, standard deviation, minimum and
maximum value of HPY (hours per year), RIR (real interest
rate), RNFI (real net farm interest), RV (remaining value)
4.1.3.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.12. The condition variables FAIR and POOR, the auction type
variables FARMRET and DEALER, and RNFI, RIR, HPY, AGE and CONSTANT were
significant in both models. Manufacturer variables CASE, FORD, and DEERE were
significant in the A-E model, while MF and IH were significant in the B-C regression.
The corresponding Age-Manufacturer cross product variables CAGE, FAGE, and DAGE
were significant in the A-E model, while MAGE was only significant in the B-C model.
GOOD and BANKRRUPT were other dummy variables significantly affecting the RV in
the A-E estimation.
47
Table 4.10 - Summary statistics for 120+ HP tractors with FWD (Sample size:
870)
Variables
RV
AGE
HPY
RIR
RNFI
Mean
0.231199
12.93678
342.5924
1.059892
42.86469
Standard
Deviation
0.164619
5.866321
181.3562
0.008734
7.979999
Minimum
0.01291
Maximum
0.96427
28
1715
0
15.95
1.0494
18.732
1.0916
54.9
Table 4.11 - Frequency statistics for 120+ HP tractors with FWD (Sample size:
870)
Frequency
MANUFACTURERS
AC
13
CASE
140
CASEIH
62
FORD
7
DEERE
387
IH
132
MF
WHITE
26
19
OTHER
84
EQUIPMENT CONDITION
EX
137
GOOD
FAIR
POOR
AUCTION TYPE
FARMRET
BANKRUPT
CONSIGN
DEALER
UNKNOWN
OTHERS
W/LDR
W/OLDR
Percent (%)
1.49
16.09
7.13
0.80
44.48
15.17
2.99
2.18
9.66
15.75
510
209
58.62
24.02
14
1.61
285
56
285
32.76
6.44
32.76
151
17.36
10.69
93
0
870
0
100
The B-C transformations estimated for RV, AGE and HPY were 0.4, 0.51 and 0.7,
respectively. This indicates that the depreciation pattern for 120+ HP tractors with FWD
48
might approximate the Double Square Root functional form. The R2 and adjusted R2
values in the B-C model indicate a good fit for the data set.
Table 4.12 - Regression coefficients and t-statistics for 120+ HP tractors with FWD
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
CASEIH
CASE
FORD
DEERE
MF
WHITE
0.016816
-0.14692
0.1075
0.11034
-0.58624
-0.1791
In
-0.24446
MANUFACTURER *AGE
CIAGE (CASEIH*AGE) -0.0032629
CAGE (CASE*AGE) 0.00 10927
FAGE (FORD*AGE) -0.023689
DAGE (DEERE*AGE) -0.0 10963
MAGE (MF*AGE)
0.06 1595
WAGE (W}HTE*AGE) -0.0003 7243
IAGE (IH*AGE)
0.00772 17
A-E
COEFFICIENTS
T-RATIO
-0.0062445
0.25141
0.27587
0.25955
-0.11687
0.017216
-0.010974
-0.06914
2.7367***
2.2273**
3.3561***
-0.73408
0.12844
-0.13061
-0.55671
2.9161***
-0.6 196
1.882*
-0.0036143
-0.025971
-0.016603
-0.015031
0.0034051
-0.0 1247
-0.003 744
0.3926
-0.0035872
0. 1916
-0.12188
-0.30058
-0.52856
0.143
-1.048
0.7302
1.023
-2.738 * * *
-0.9903
2.066* *
-0. 1322
0.04378
-0.7924
l.8289*
0.38282
-0.48639
-0.6646
CONDITION
GOOD
FAIR
POOR
AUCTION TYPE
FARMRET
BANKRUPT
DEALER
-0.0032207
-0.089398
-0.17127
0.10551
0.027432
0.043936
4.246***
-3.08 * * *
7.946***
1.144
5.9366***
1.9226*
2.716* * *
0.15854
0.11553
0.13594
6.1484***
2.2629**
4.0062***
9.524***
0.0 10765
6.73 3 * * *
-0.46888
-0.00011781
-0.011501
0.38882
7.16 15***
_3.0454***
2.0322**
_2.2185**
3.9432***
OTHERS
RNFI
0.0081578
RIR
5.0488
HPY
-0.0014557
AGE
-0.14298
CONSTANT
-6.0192
B-C TRANSFORMATION
RV
AGE
HPY
B-C R-SQUARE
B-C ADJUSTED R-SQUARE
6.698***
8.233***
0.4
0.51
0.7
0.8214
0.8157
Note: *** Significant in 99% confidence level;
** Significant in 95% confidence level; and
49
* Significant in 90% confidence level.
4.1.3.3 Comparison Between Models
Table 4.13 compares the log-likelihood values, as well as the predictive abilities
(MAPE) of both models. The two models exhibited very similar predictive abilities (0.54
for B-C and 0.52 for A-E), but A-E has less predictive error in the MAPE test.
Figure 4.3 provides a graphical summary of the two RV models. The values in the
graphs were calculated assuming the tractor was manufactured by John Deere,
maintained in Good condition, and sold at a Farmer Retirement auction. Variables RNFI,
RIR and HPY were set at their average levels. The two models generated somewhat
different depreciation patterns, particularly before year 4 and after year 18. Despite these
different patterns, both models generated nearly the same MAPE values.
Table 4.13 - Comparison of B-C and A-B models for 120+ HP tractors with FWD
A-E
783
B-C
783
1130.03
87
SAMPLE SIZE (90%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
879.7261
87
0.5209504
0.5364960
Figure 4.3 - Comparison of depreciation patterns of the B-C and A-E models for
120+ HP tractors with FWD
1
0.8
-A E
-*- BC
0.2
0
I
1
5
9
If]
13
AGE
17
21
50
4.1.4
120-145 HP Tractors Without FWD
4.1.4.1 Data Description
The data set for 120-145 HP tractors without
FWD contained 2124 observations, of which 1912
observations were used in the estimation process
and 212 were used to test predictive ability. Table
4.14
shows
the average,
standard
deviation,
minimum and maximum value of HPY (hours per
year), RIR (real interest rate), RNFI (real net farm
interest), RV (remaining value) and Age for these
tractors. Table 4.15 lists the distribution of dummy
variables included in both B-C and A-E models.
John Deere Two Wheel Drive
Tractor - MFWD 7710 135HP
John Deere was dominant in this data set, with
nearly 60 percent of all observations. Farmer Retirements represented almost half of all
auction sales (45% and 31.17%). Most tractors in this type were in Good condition
(60.40%). Few tractors were equipped with loaders, so this attribute was omitted in both
models.
4.1.4.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.16. All condition variables and auction type variables
FARMRET and DEALER were significant in both models, as were RNFI, AGE, HPY
and CONSTANT. RIR and manufacturer variables FORD and DEERE were significant
in the B-C estimation, while Ill and MF were significant in the A-E regression.
51
The B-C transformations estimated for RV, HPY and AGE were 0.61, 0.52 and
0.49, respectively, very close to a Double Square Root functional form. The R2 and
adjusted R2 values in the B-C model indicate a fairly good fit for the data set.
Table 4.14 - Summary statistics for 120-145 HP tractors (Sample size: 2124)
Variables
RV
HPY
Mean
0.318692
325.3804
MR
1.06055
RNFI
AGE
40.17029
13.86535
Standard
Deviation
0.151373
174.3881
0.009957
9.162109
5.514572
Minimum
0.03027
1.25
1.0494
18.732
Maximum
0.89136
3100
1.0916
54.9
0
27
Table 4.15 - Frequency statistics for 120-145 HP tractors (Sample size: 2124)
Frequency
MANUFACTURERS
AC
84
CASE
98
CASEIH
33
FORD
68
DEERE
1218
IH
495
MF
85
WHITE
35
OTHER
8
EQUIPMENT CONDITION
EX
432
GOOD
1283
FAIR
366
POOR
43
AUCTION TYPE
FARMRET
956
BANKRUPT
106
CONSIGN
662
DEALER
171
UNKNOWN
229
OTHERS
W/LDR
W/OLDR
6
2118
Percent (%)
3.95
4.61
1.55
3.20
57.34
23.31
4.00
1.65
0.38
20.34
60.40
17.23
2.02
45.01
4.99
31.17
8.05
10.78
0.28
99.72
52
Table 4.16 - Regression coefficients and t-statistics for 120-145 HP tractors
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
CASEI}i
0.49296
FORD
0.18044
DEERE
0.2 1653
IH
-0.05295
MF
0.0057898
WHITE
-0.045901
MANUFACTURER *AGE
CIAGE (CASEIH*AGE) -0.08457 1
FAGE (FORD*AGE) -0.022986
DAGE (DEERE*AGE) 0.011295
IAGE (IEI*AGE)
MAGE (MF*AGE)
0.0 10902
-0.013803
WAGE (WHITE*AGE) 0.0030092
CONDITION
GOOD
FAIR
POOR
AUCTION TYPE
FARIvIRET
BANKRUPT
DEALER
-0.047785
-0.09632
-0.17593
0.7034
1.757*
2.357**
-0.56 1
0.053 11
-0.3542
-0.5043
-1.131
0.6238
0.5906
-0.664
0. 1213
6.342***
9.469***
8.221***
A-E
COEFFICIENTS
T-RATIO
0.11965
0.036243
0.081346
-0.12621
-0.1292
-0.11876
0.33991
0.57519
1.332
2.1625**
l.8487*
-1.5163
-0.010548
-0.0012733
-0.2851
0.003 1938
0.0078634
0.0062194
0.0067357
0.76213
1.8609*
1.2305
1.1211
-0.10599
-0.20852
-0.56208
8.2726***
10.502***
6.5564***
-0.2613 1
0.035071
-0.0028 176
0.028527
6.005***
-0.2287
2.789***
0.049177
-0.046725
0.054211
4.1336***
-1.6427
RNFI
0.0073983
RIR
0.75197
HPY
-0.003 8097
AGE
-0.098748
CONSTANT
-1.4105
B-C TRANSFORMATION
RV
AGE
HPY
B-C R-SQUARE
B-C ADJUSTED R-SQUARE
18.44***
2.287**
12.73***
5.486***
0.012375
-0.14114
-0.0002521
-0.017019
0.43509
19.636***
-1.3357
8.2799***
2.71 14***
OTHERS
-3.851 * * *
0.61
0.49
0.53
0.7597
0.7569
Note: *** Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
.37957***
59994***
53
4.1.4.3 Comparison Between Models
Table 4.17 compares the log-likelihood values, as well as the predictive abilities
(MAPE) of both models. In this case, the B-C model exhibited less predictive error by
using the MAPE test.
Both models are summarized graphically in Figure 4.4, assuming the tractor was
manufactured by John Deere, in Good condition and sold at a Farmer Retirement auction.
Variables RNFI, RIR and HPY were set at their average levels. This graph shows that the
two models estimated very similar depreciation patterns throughout the useful lives of
tractors, especially from the fifth year to the 22nd year.
Table 4.17 - Comparison of B-C and A-E models for 120-145 HP tractors
SAMPLE SIZE (90%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
B-C
1912
A-E
1912
2354.15
212
2213.867
212
0.3775409
0.299073 1
Figure 4.4 - Comparison of depreciation patterns of the B-C and A-E models for
120-145 HP tractors without FWD
A-E
06
-*- B-C
0.2
I
1
I
T
I
I
TI
I
I
I
T
I
r
1
T
I
I
I
F
I
F
I
I
U
1
t
4 710131619222528
AGE
4.1.5
54
Tractors With 145+ HP
4.1.5.1 Data Description
The data set for tractors with tractors with 145+
HP contained 2050 observations, of which 1845
observations were used in the estimation process and
205 were used to test predictive ability. Table 4.18
shows the average, standard deviation, minimum and
maximum value of HPY (hours per year), RJR (real
John Deere Four Wheel Drive
Tractor- MFWD 7810 15OHP
interest rate), RNFI (real net farm interest), RV
(remaining value) and Age. Table 4.19 lists the distribution of dummy variables included
in both B-C and A-E models. John Deere represented half (52.63%) of all sales. Farmer
Retirement and Consignment each represented about one-third of sales (34.78% and
33.80%). Most tractors were in either Good (59.27%) or Excellent (20.29%) condition.
Few tractors were equipped with loaders, so this attribute was omitted in both models.
4.1.5.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.20. All condition and auction type variables were significant
in both models, as were while variables RNFI, RIR and HPY. All the Age-Manufacturer
cross product variables were insignificant in both estimations. CASEIH, DEERE and
FORD were significant manufacturer dummy variables in the A-E estimation, while AGE
and CONSTANT were only significant in the B-C model.
55
Table 4.18 - Summary statistics for 145+ HP tractors (Sample size: 2050)
Variables
RV
HPY
RIR
RNFI
AGE
Mean
0.317644
384.9655
1.05981
42.23705
11.96195
Standard
Deviation
0.196172
283.0771
0.009466
8.369522
5.749405
Minimum
0.01485
2.333
1.0494
18.732
0
Maximum
0.982
4864
1.0916
54.9
26
Table 4.19 - Frequency statistics for 145+ HP tractors (Sample size: 2050)
Frequency
MANUFACTURERS
AC
110
CASE
229
CASEIH
157
FORD
23
DEERE
1079
III
395
MF
WHITE
OTHER
36
15
6
Percent (%)
5.37
11.17
7.66
1.12
52.63
19.27
0.73
1.76
0.29
EQUIPMENT CONDITI416ON
EX
GOOD
FAIR
POOR
AUCTION TYPE
FARMRET
BANKRUPT
CONSIGN
DEALER
UNKNOWN
OTHERS
W/LDR
W/OLDR
416
1215
20.29
59.27
364
55
17.76
713
108
693
34.78
5.27
33.80
12.98
13.17
266
270
6
2044
2.68
0.29
99.71
The B-C transformations estimated for RV, HPY and AGE were 0.59, 0.42 and
0.42, respectively. This indicates that the depreciation pattern for tractors in this type
might approximate the Double Square Root functional form. The R and adjusted R2
values were the highest among the five tractor models estimated.
56
Table 4.20 - Regression coefficients and t-statistics for 145+ HP tractors
VARIABLES
B-C
COEFFICENTS
T-RATIO
A-E
COEFFICIENTS
T-RATIO
MANUFACTURER
CASE1}1
0.03111
CASE
-0.31832
FORD
0.13838
DEERE
0.14478
MF
-0.11654
WHITE
-0.12289
IH
-0.19612
MANUFACTURER *AGE
CIAGE (CASEIH*AGE) 0.04058
CAGE (CASE*AGE)
0.057353
FAGE (FORD*AGE) -0.009288
DAGE (DEERE*AGE) 0.033702
MAGE (MF*AGE)
0.002247
WAGE (WHITE*AGE) 0.03 3228
IAGE(IH*AGE)
0.049737
0.114
-1.153
0.4983
0.5328
-0.3988
-0.4345
-0.719
0.975
-0.03009
0.98992
1.1241
0.50027
0.35813
0.17993
1.744*
-0.05273
1.7332*
2.015**
0.86379
0.56522
0.31826
0.6962
0.9807
-0.1554
0.5866
0.03632
0.5574
0.8624
-0.06049
-0.00398
-0.06174
-0.04274
-0.04033
-1.6409
-0.10491
-1.5942
-1.1946
-1.0667
-0.49064
-0.28217
3.132***
6.273***
8.282***
-0.08273
-0.20636
-0.54821
-0.0 197
-0.01012
CONDITION
GOOD
-0.027464
FAIR
-0.070581
POOR
-0.1743
AUCTION TYPE
FARMRET
0.065183
BANKRUPT
0.036868
DEALER
0.069344
OTHERS
RNFI
0.0071854
RIR
2.2848
HPY
-0.0068361
AGE
-0.17052
CONSTANT
-2.8823
B-C TRANSFORMATION
RV
AGE
HPY
B-CR-SQUARE
B-C ADJUSTED R-SQUARE
5.8821***
8.6847***
54997***
9.096***
2.62***
73Ø7***
0.10375
0.059699
0.13582
7.3724***
2.0452**
8.177***
15.72***
5.919***
13.61***
2.97***
5.889***
0.012054
-1.4517
-0.00015
-0.03076
0.94157
15.82***
15.295***
6.7772***
-0.85801
1.6413
0.59
0.42
0.42
0.8248
0.8225
Note: *** Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
57
4.1.5.3 Comparison Between Models
Table 4.21 compares the log-likelihood values, as well as the predictive abilities
(MAPE) of both models. The B-C model exhibited a slightly lower predictive value.
Both models are summarized graphically in Figure 4.5, assuming the tractor was
manufactured by John Deere, in Good condition and sold at a Farmer Retirement auction.
Variables RNFI, RIR and HPY were set at their average levels. This graph shows that the
two models estimated similar depreciation patterns from the fifth to the 19th year.
Table 4.21 - Comparison of B-C and A-E models for 145+ HP tractors
B-C
SAMPLE SIZE (90%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
1845
2149.65
205
0.3009953
A-E
1845
1820.745
205
0.3201986
Figure 4.5 - Comparison of depreciation patterns of the B-C and A-B models for
145+ HP tractors
58
4.2 HARVESTING EQUIPMENT
Machinery and equipment in this category are more specialized than tractors, since
they are manufactured for harvest purposes, and often are limited to a small number of
crops.
Depreciation models for eight types of harvest equipment are reported in this
section: Combines, Corn Headers, Cotton Harvesters, Swathers, Balers, Forage
Harvesters, Mower Conditioners and Mower Cutters. This is the first attempt to estimate
models for Corn Headers and Cotton Harvesters. Mower Conditioners and Mower
Cutters were combined by Cross and Perry (1995), prior to being used to estimate an RV
equation.
4.2.1
Combines
4.2.1.1 Data Description
The data set for Combines contained 2522
observations, of which 2270 were used in the
estimation process and 249 were used to test
predictive ability. Table 4.22 shows the average,
standard deviation, minimum and maximum value
of HPY (hours per year), RIR (real interest rate),
RNFI (real net farm interest), RV (remaining
value) and Age. Table 4.23 lists the distribution of
2300 Series AXIAL-FLOW®
Combine
dummy variables included in both B-C and A-E models. John Deere dominated this data
set, with nearly 65 percent of all observations. Farmer Retirement and Consignment were
most common (36.12% and 32.00%). Most Combines were in Good condition (61.38%).
59
Table 4.22 - Summary statistics for Combines (Sample size: 2522)
Variables
RV
AGE
HPY
RIR
RNFI
Mean
0.214838
12.97145
198.842
1.060865
42.7806
Standard
Deviation
0.166196
5.888086
130.8556
0.008635
8.028032
Minimum
0.00727
Maximum
0.91027
0
28
8.824
1.0494
21.3178
2636.45
1.0916
54.9
Table 4.23 - Frequency statistics for Combines (Sample size: 2522)
Frequency
MANUFACTURERS
AC
179
CASEIH
108
DEERE
1637
IH
333
MF
164
WHITE
18
NH
75
OTHER
8
EQUIPMENT CONDITI398ON
EX
398
GOOD
1548
FAIR
516
POOR
60
AUCTION TYPE
FARMRET
911
BANKRUPT
147
CONSIGN
807
DEALER
654
UNKNOWN
3
Percent (%)
7.10
4.28
64.91
13.20
6.50
0.71
2.97
0.32
15.78
61.38
20.46
2.38
36.12
5.83
32.00
25.93
0.12
4.2.1.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.24. All condition variables and auction type variables
FARMERET and DEALER were significant, as were RIR, RNFI, HPY and
CONSTANT. All the Age-Manufacturer cross product variables and most manufacturer
variables were insignificant in both models. WHITE and AGE were only significant in
the B-C estimation.
60
The B-C transformations estimated for RV, HPY and AGE were 0.51, 0.15 and
0.7, respectively. The R2 and adjusted R2 values in the B-C indicate a very good fit for
the data set.
Table 4.24 - Regression coefficients and t-statistics for Combines
VARIABLES
MANUFACTURER
AC
CASEIH
DEERE
MF
WHITE
B-C
COEFFICENTS
-0.20183
0.00031166
-0.028831
-0.37576
-0.5084
III
-0.11168
NH
-0.090015
MANUFACTURER *AGE
AAGE(AC*AGE)
0.053516
CJAGE (CASEIH*AGE) 0.04632
DAGE(DEERE*AQE) 0.048982
MAGE(MF*AGE)
0.064746
WAGE(W}iITE*AGE) 0.082674
IAGE(1}I*AGE)
NAGE(NH*AGE)
0.049706
0.026963
T-RATIO
A-E
COEFFICIENTS
T-RATIO
-0.7872
0.00121
-0.1132
-1.455
l.835*
-0.4357
-0.3463
-0.010113
0.021026
0.0097725
-0.036001
-0.039265
-0.0069368
-0.0058579
-0.29288
0.60612
0.28481
-1.0511
-1.0526
-0.20144
-0.1691
0.9611
0.8236
0.882
1.16
1.438
0.8928
0.481
0.0021409
-0.00014378
0.0014042
0.003527
0.0037938
0.002082
0.0014225
0.48932
-0.032553
0.32218
0.81184
0.84076
0.479
0.32496
6.785***
7.966***
-0.16129
-0.33018
-0.6756
11.928***
11.088***
6.7941***
CONDITION
GOOD
FAIR
POOR
AUCTION TYPE
FARMRFT
BANKRUPT
DEALER
-0.061823
-0.095863
-0.1954
0.061082
4.5618E-06
0.026389
7454***
7.736***
0.0003353
3.216***
0.067188
-0.0011026
0.073026
3.8344***
-0.035797
4.6566***
14.78***
5.649***
5.223***
2.853***
12.98***
0.010387
12.586***
11.116***
2.5208***
-1.3432
8.0051***
OTHERS
RNFI
0.0070628
RIR
2.2244
CONSTANT
-2.5888
AGE
-0.15843
HPY
-0.043644
B-C TRANSFORMATION
RV
HPY
AGE
B-CR-SQUARE
B-C ADJUSTED R-SQUARE
0.51
0.15
0.7
0.8199
0.8 179
1.358
0.089499
-0.0058849
-0.00028596
61
Note: *** Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
4.2.1.3 Comparison Between Models
Table 4.25 provides a comparison of the log-likelihood values, as well as the
predictive abilities (MAPE) of both models. The B-C model had a much lower predictive
error (0.44 for B-C and 1.42 for A-E).
Both models are summarized graphically in Figure 4.6, assuming the combine
equipment was manufactured by John Deere, in Good condition and sold at a Farmer
Retirement auction. Variables RNFI and RJR were set at their average levels. This graph
shows that both models presented very similar depreciation patterns, although the RV
estimated by the A-E model was slightly higher than that of the B-C estimation before the
sixth year of the useful lives of Combines.
Table 4.25 - Comparison of B-C and A-E models for Combines
B-C
2270
3158.25
249
0.4374688
SAMPLE SIZE (90%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
A-E
2270
2652.520
249
1.417796
Figure 4.6 - Comparison of depreciation patterns of the B-C and A-E models for
Combine
1
0.8
0.6
-*---A E
0.4
-*- B C
0.2
0
1
3
5
7
9 11 13 15 17 19 21 23
AGE
62
4.2.2
Corn Headers
4.2.2.1 Data Description
The data set for Corn Headers contained 196
observations, of which 176 were used in the
estimation process and 20 were used to test
predictive ability. Table 4.26 shows the average,
standard deviation, minimum and maximum value
of RIR (real interest rate), RNFI (real net farm
interest), RV (remaining value) and Age. Table 4.27
Case IH 2212
Corn Header and Combine
lists the distribution of dummy variables included in both B-C and A-E models. John
Deere dominated this data set, with nearly 66.32% of all observations. Farmer Retirement
represented the most common auction type (57.65%). Most Corn Headers sold were in
either Good or Excellent condition.
4.2.2.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.28. FARMRET, CASE, FAIR and RNFI were significant
variable in both models, while all the Age-Manufacturer cross product variables were
insignificant in both estimations. AGE was only significant in the B-C model, while RIR
was only significant in the A-E estimation.
The B-C transformations estimated for RV and AGE were 0.26 and 0.99,
respectively. This indicates that the depreciation pattern for Corn Headers might
approximate the Geometric functional form. The R2 and adjusted R2 values in the B-C
indicate a fairly good fit for the data set.
63
Table 4.26 - Summary statistics for Corn Headers (Sample size: 196)
Variables
RV
AGE
RIR
RNFI
Mean
0.331729
8.219388
1.061755
39.94594
Standard
Deviation
0.141418
4.381527
0.009296
8.624975
Minimum
0.01572
Maximum
0.81813
1
18
1.0494
21.3178
1.0916
54.9
Table 4.27 - Frequency statistics for Corn Headers (Sample size: 196)
Frequency
MANUFACTURERS
AC
11
CASE
19
DEERE
131
IH
23
MF
7
OTHER
5
EQUIPMENT CONDITION
EX
60
GOOD
118
FAIR
17
POOR
1
AUCTION TYPE
FARMRET
113
BANKRUPT
34
CONSIGN
8
DEALER
41
Percent (%)
5.61
9.69
66.33
11.73
3.57
2.55
30.61
59.69
8.67
0.51
57.65
17.35
4.08
20.92
64
Table 4.28 - Regression coefficients and t-statistics for Corn Headers
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
AC
0.13158
CASE
0.2231
DEERE
0.15623
IH
0.097986
MF
0.064938
MANUFACTURER *AGE
AAGE (AC*AGE)
-0.026295
CAGE(CASE*AGE) -0.002794
DAGE(DEERE*AGE) 0.010249
IAGE(IH*AGE)
-0.005596
MAGE(MF*AGE)
0.003676
CONDITION
GOOD
-0.030351
FAIR
-0.0652 1
POOR
-0.10214
AUCTION TYPE
FARMRET
0.063643
BANKRUPT
0.036238
DEALER
0.051126
OTHERS
RNFI
0.002524
RIR
-0.90531
CONSTANT
0.25489
AGE
-0.096059
B-C TRANSFORMATION
RV
AGE
B-C R-SQUARE
B-C ADJUSTED R-SQUARE
Note:
0.740045
1.9 1174*
1.4560 11
0.688 104
0.328967
-0.374786
-0.0485 17
0. 19683 1
-0.092063
0.049033
A-E
COEFFICIENTS
T-RATIO
-0.14838
0.87714
0.40091
-0.01717
-0.41071
0.057631
0.008187
0.062646
0.054629
0.088427
-0.89337
1.6647*
1.6035
-0.14703
-1.2851
1.4851
0.37933
1.476
1.388
1.5233
-1.46907 1
-2.214261 **
-0.995517
-0.07829
-0.20454
-0.523 13
-1.4309
2.3531**
-0.84167
1.65 1778*
0.876372
1.245457
0.20252
0.10051
0.16998
1.7997*
0.82281
1.4194
1.972188**
-0.805436
0.209441
1.88684*
0.005584
-1.6758
1.7639
-0.13801
1.852*
0.26
0.99
0.5976
0.5486
Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
2.813***
1.6396
-1.6121
65
4.2.2.3 Comparison Between Models
Table 4.29 provides a comparison of the log-likelihood values, as well as the
predictive abilities (MAPE) of both models. The two models exhibited very similar
predictive abilities (0.26 for B-C and 0.27 for A-E)
Both models are summarized graphically in Figure 4.7, assuming the tractor was
manufactured by John Deere, in Good condition and sold at a Farmer Retirement auction.
Variables RNFI and RIR were set at their average levels. This graph shows that the two
models estimated very similar depreciation patterns, although before the fourth year of
the useful lives of tractors, the B-C model estimated higher the remaining values than the
A-E model did.
Table 4.29 - Comparison of B-C and A-E models for Corn Headers
SAMPLE SIZE (9 0%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
B-C
176
A-E
176
171.689
20
0.2598430
168.1836
20
0.266928
Figure 4.7 - Comparison of depreciation patterns of the B-C and A-E models for
Corn Headers
66
4.2.3
Cotton Harvesters
4.2.3.1 Data Description
The data set for Cotton Harvesters
contained
75
observations,
which are
summarized in Tables 4.30 and 4.31. Table
4.30 shows the average, standard deviation,
4
minimum and maximum value of RIR (real
interest rate), RNFI (real net farm interest),
RV (remaining value) and Age. Table 4.31
lists the distribution of dummy variables
included in both B-C and A-E models. John
2555 EXPRESS® Cotton Pickers
Deere dominated this data set, with nearly 61.33% of all observations. Three main
auction types were represented: Farmer Retirement, Bankrupt and Consignment (37.33%,
29.33% and 29.33%). Most Cotton Harvesters were in Good condition.
4.2.3.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.28. GOOD and POOR were significant condition variables,
RNFI was also significant in both models. Manufacturer variables AC and DEERE, Age-
Manufacturer cross product variables AAGE and CAGE, and AGE and constant were
other significant variables in the B-C model, while auction type variables BANKRUPT
and DEALER were only significant in the A-E estimation.
The B-C transformations estimated for RV and AGE were 1.85 and 0.41,
respectively. The R2 and adjusted R2 in the B-C indicate a very good fit for the data set.
67
Table 4.30 - Summary statistics for Cotton Harvesters (Sample size: 75)
Variables
RV
RIR
RNFI
AGE
Mean
0.129709
1.063507
47.02217
16.65333
Standard
Deviation
0.108386
0.00677
6.733099
5.617283
Minimum
0.00715
1.0539
23.529
Maximum
0.48802
1.0916
54.9
3
25
Table 4.31 - Frequency statistics for Cotton Harvesters (Sample size: 75)
Frequency
MANUFACTURERS
Percent (%)
AC
ii
CASE
7
DEERE
46
IH
11
EQUIPMENT CONDITION
EX
3
GOOD
49
FAIR
10
POOR
13
AUCTION TYPE
FARMRET
28
BANKRUPT
22
CONSIGN
22
DEALER
3
14.67
9.33
61.33
14.67
4.00
65.33
13.33
17.33
37.33
29.33
29.33
4.00
68
Table 4.32 - Regression coefficients and t-statistics for Cotton Harvesters
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
AC
l.921448*
-0.50707
CASE
0.69437
1.4 10748
1.77924*
DEERE
0.27169
MANUFACTURER *AGE
1.864201*
AAGE(AC*AGE)
0.003604
CAGE (CASE*AGE) -0.032124
1.779723*
DAGE(DEERE*AGE) -0.000923
-0.819432
CONDITION
GOOD
-0.33 14
-2.07644 1 **
FAIR
-0.14002
-0.798745
POOR
3.028746***
-0.5 1943
AUCTION TYPE
FARMRET
-0.008676
-0. 140406
BANKRUPT
0.048527
0.743823
DEALER
0.09909 1
0.57278
OTHERS
RNFI
0.018917
2. 593 857***
RIR
9.026
1.468359
1.663904*
CONSTANT
-11.243
4.394366***
AGE
-0.00468
B-C TRANSFORMATION
RV
1.85
AGE
0.41
B-C R-SQUARE
0.8059
B-C ADJUSTED R-SQUARE
0.7566
COMPARISON OF LOG-LIKELIHOOD VAL UES
SAMPLE SIZE (100%)
75
Log-likelihood Value
224.885
Note: *** Significant in 99% confidence level;
* * Significant in 95% confidence level; and
* Significant in 90% confidence level.
A-E
COEFFICIENTS
T-RATIO
-0.86695
0.23025
0.7983
-0. 18884
0.053527
0. 10052
0.0094143
-0.015387
-0.0033585
0.79623
-0.49984
-0.35681
0.022995
-1.0068
2.7788***
0.17736
-0.635 15
3 .4824***
0.13567
0.30997
2.965***
0.4 1604
2.102* *
0.023532
-0.73731
0.28979
-0.011985
4.564***
-0.96407
1.1896
-1.1428
1.2301
75
205.4697
69
4.2.3.3 Comparison Between Models
Because the cotton harvester data set contained fewer than 100 observations, no
attempt was made to reserve observations for a MAPE test of predictive ability.
Both models are summarized graphically in Figure 4.8, assuming the Cotton
Harvester was manufactured by John Deere, in Good condition and sold at a Farmer
Retirement auction. Variables RNFI and RIR were set at their average levels. This graph
shows somewhat different depreciation pattern with other type of farm equipments. The
Box-Cox function generated a slight backward "S" relationship that was generally lower
than the A-E results. Nevertheless, RV estimates were similar for both models.
Figure 4.8 - Comparison of depreciation patterns of the B-C and A-E models for
Cotton Harvesters
70
4.2.4
Swathers
4.2.4.1 Data Description
The data set for Swathers contained 187
observations, of which 168 were used in the
estimation process and 19 were used to test
predictive ability. Table 4.33 shows the
average, standard deviation, minimum and
maximum value of RIR (real interest rate),
RNFI (real net farm interest), RV (remaining
value)
and
Age.
Table
4.34
lists
the
Self-Propelled Swather
distribution of dummy variables included in
both B-C and A-E models. Versatile and Deere dominated the Swather data set, but great
diversity existed in this category. FARMRET represented the most common auction type
(66.84%). Most Swathers were in either Good or fair condition.
4.2.4.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.35. The condition dummy variables GOOD and FAIR were
significant in both models. In the B-C estimation, all manufacturer variables, except
CASE; the age-manufacturer cross product variables DAGE, FAGE and VAGE; all
condition variables and RNFI were significant. RIR and RNFI were also significant in the
A-E estimation.
Table 4.33 - Summary statistics for Swathers (Sample size: 187)
Variables
RV
RIR
RNFI
AGE
Mean
0.213453
1.061477
38.92
13.29947
Standard
Deviation
0.1459
0.011034
9.332707
5.504265
Minimum
0.01747
1.0494
21.3178
2
71
Maximum
0.76922
1.0916
54.9
24
Table 4.34 - Frequency statistics for Swathers (Sample size: 187)
Frequency
MANUFACTURERS
CASE
6
DEERE
45
IH
26
MF
11
NH
14
HT
25
VS
53
OTHER
7
EQUIPMENT CONDITION
EX
24
GOOD
113
FAIR
49
POOR
1
AUCTION TYPE
FARMRET
125
BANKRUPT
32
CONSIGN
15
DEALER
10
UNKNOWN
5
Percent (%)
3.21
24.06
13.90
5.88
7.49
13.37
28.34
3.74
12.83
60.43
26.20
0.53
66.84
17.11
8.02
5.35
2.67
The B-C transformations estimated for RV and AGE were 0.18 and 1.22,
respectively. This indicates that the depreciation pattern for Swathers might approximate
the Geometric functional form. The R2 and adjusted R2 in the B-C suggest a reasonably
good fit.
72
Table 4.35 - Regression coefficients and t-statistics for Swathers
B-C
VARIABLES
COEFFICENTS T-RATIO
MANUFACTURER
CASE
0.68147
DEERE
1.3131
IH
1.1186
MF
0.98553
NH
1.3877
HT
1.257
VS
1.4653
MANUFACTURER *AGE
CAGE(CASEE*AGE) 0.011254
DAGE(DEERE*AGE) -0.062351
A-E
COEFFICIENTS T-RATIO
0.9206
2.88***
2.267**
1.904*
2.805***
2.673***
2.933***
2.7918
2.6477
2.1867
3.3092
2.7626
2.8707
1.4609
1.4818
1.5237
0.1133
2.301**
-1.276
-1.475
-1.924
2.099**
2.227**
-0.051988
-0.17334
-0.13072
-0.1396
-0.18167
-0.16917
-0.16397
-1.0092
-1.4547
-1.3757
-1.3714
-1.3844
-1.4184
-1.4559
4.7254***
5.1231***
0.87767
1.7551
1.5381
1.518
1.481
1.4481
IAGE (I}j*AGE)
MAGE(MF*AGE)
NAGE(NH*AGE)
HAGE(HT*AGE)
VAGE(VS*AGE)
CONDITION
-0.037225
-0.046554
-0.056173
-0.057867
-0.062046
GOOD
FAIR
POOR
AUCTION TYPE
FARMRET
BANKRUPT
DEALER
-0.24291
-0.54305
-0.82535
2.314**
1.951*
-0.40537
-0.79489
-1.2057
0.059619
-0.064259
0.063707
0.5386
-0.4879
0.3374
0.12399
0.15328
-0.079485
0.77199
0.8429
0.30686
2.258**
-0.1653
-0.3946
0.9489
0.016124
-2.1444
-0.041483
0.070492
3.685***
3.2211***
0.20135
1.3359
4544***
OTHERS
RNFI
0.011788
RIR
-0.65293
CONSTANT
-1.687
AGE
0.02535
B-C TRANSFORMATION
RV
AGE
B-C R-SQUARE
B-C ADJUSTED R-SQUARE
Note:
0.18
1.22
0.5453
0.4727
Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
73
4.2.4.3 Comparison Between Models
Table 4.36 provides a comparison of the log-likelihood values, as well as the
predictive abilities (MAPE) of both models. The two models exhibited very similar
predictive abilities (0.42 for B-C and 0.44 for A-E).
Both models are summarized graphically in Figure 4.9, assuming the swather was
manufactured by Versatile, in Good condition and sold at a Farmer Retirement auction.
Variables RNFI and RIR were set at their average levels. This graph shows that the A-E
model estimated higher remaining values than the B-C model from the fifth to the
eighteenth year of the useful lives of Swathers. Beyond, the B-C model estimated higher
remaining values than the A-B model did.
Table 4.36 - Comparison of B-C and A-E models for Swathers
SAMPLE SIZE (90%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
B-C
168
A-E
168
177.656
144.9859
19
19
0. 442 092 6
0.4249221
Figure 4.9 - Comparison of depreciation patterns of the B-C and A-E models for
Swathers
I
0.8
>0.6
A-E
0.4
B-C
0.2
0
1
3
5
7
9
11 13 15 17 19 21 23
AGE
74
4.2.5
Balers
CASE IH Round Balers
CASE IH 8500 Series
Square Balers
4.2.5.1 Data Description
The data set for Balers contained 330 observations, of which 297 were used in the
estimation process and 33 were used to test predictive ability. Two major manufacturers
were represented in the data set: DEERE (John-Deere, 3 9.7%) and NH (New Holland,
26.67%). More than half of Balers were sold at Farmer Retirement auctions (60.30%).
Most Balers were in either Good (52.42%) or Excellent (32.73%) condition.
4.2.5.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.39. DEERE was the only significant manufacturer variable in
both models; FARMRET was the only significant variable among the various auction
types; Condition variables GOOD and FAIR were also significant; The Age-
Manufacturer cross product variables DAGE and HAGE were significant in both model,
as were the RNFI and CONSTANT variables. The manufacturer dummy variables
75
CASE, HT, III and NET, condition variable POOR, and the Age-Manufacturer cross
product variable IAGE were also significant in the B-C estimation.
Table 4.37 - Summary statistics for Balers (Sample size: 330)
Variables
RV
AGE
RIR
RNFI
Mean
0.355978
7.49697
1.061683
38.57529
Standard
Deviation
0.181153
4.884843
0.010673
8.921517
Minimum
0.01041
1
1.0494
21.3178
Maximum
0.97454
28
1.0916
54.9
Table 4.38 - Frequency statistics for Balers (Sample size: 330)
Frequency
MANUFACTURERS
CASE
22
DEERE
131
IH
13
MF
17
NH
88
HT
36
OTHER
23
EQUIPMENT CONDITION
EX
108
GOOD
173
PAW
41
POOR
6
UNKNOWN
2
AUCTION TYPE
FARMRET
199
BANKRUPT
75
CONSIGN
40
DEALER
6
UNKNOWN
10
Percent (%)
6.67
39.70
3.94
5.15
26.67
10.91
6.97
32.73
52.42
12.42
1.82
0.006
60.30
22.73
12.12
1.82
3.03
The B-C transformations estimated for RV and AGE were 0.173 and
0.7,
respectively. This indicates that the depreciation pattern for Baler might approximate the
Geometric or Double Square Root functional forms. The R2 and adjusted R2 in the B-C
indicate a fairly good fit for the data set.
76
Table 4.39 - Regression coefficients and t-statistics for Balers
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
CASE
0.24217
DEERE
0.40691
MF
0.10667
HT
0.36301
IH
0.64555
NH
0.25708
MANUFACTURER *AGE
CAGE (CASE*AGE)
-0.032469
DAGE(DEERE*AGE)
-0.079904
MAGE(MF*AGE)
0.0 1499
HAGE(HT*AGE)
-0.13891
IAGE(IH*AGE)
-0.25007
NAGE(NH*AGE)
-0.059158
CONDITION
GOOD
-0.098975
FAIR
-0.084744
POOR
-0.22034
AUCTION TYPE
FARMRET
0.086767
BANKRUPT
0.0 10756
DEALER
-0.022957
OTHERS
RNFI
0.004521
RIR
1.9548
CONSTANT
-3.0247
AGE
-0.053669
B-C TRANSFORMATION
RV
AGE
B-C R-SQUARE
B-C ADJUSTED R-SQUARE
Note:
2.1 68039**
4.53 0283 ***
0.5 17063
3.517539***
2.01 1059**
A-E
COEFFICIENTS
T-RATIO
0. 13452
1.264 1669
0.20492
0.04963
2.699853***
0.11284
1.8322604*
0.3106729
1.495277
0.7540283
1.2747402
-0.542234
-0.0 18443
-1.119726
-1 .969049**
0. 178729
-0.020485
-0.00889
-0.027511
-0.029029
-0.016465
-2.068795 * *
2.939272***
_2.189755**
-1.4 19338
-4.25 1503
-2.499823 **
_1.825518*
3.082309***
0.329534
-0.3 10776
3.11 1493***
1.642689
2.335676**
-1.4568 13
0.173
0.7
0.5689
0.536
Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
0. 153 55
0. 13945
-0. 19765
-0.15493
-0.46095
0. 193 14
0.075227
0.05726
0.006745
-0.22625
0.3387
-0.0 1069
-0.52 1274
1.984348**
-1.468 187
1.866124*
_4.525576***
2.355383**
-1.150706
3.4280542***
1.0841031
0.343450 1
3.3138449***
-0.543178
2.0916445**
-1.175294
77
4.2.5.3 Comparison Between Models
Table 4.40 provides a comparison of the log-likelihood values, as well as the
predictive abilities (MAPE) of both models. The A-E model exhibited less error in its
predictive ability (1.05 for B-C and 0.77 for A-E).
Both models are summarized graphically in Figure 4.10, assuming the baler was
manufactured by John Deere, in Good condition and sold at a Farmer Retirement auction.
Variables RNFI and RIR were set at their average levels. This graph shows that the RV
estimated by the A-B model was slightly higher than that of the B-C estimation from the
fourth year to the eleventh year of the useful lives of Balers. Beyond this, the B-C model
estimated higher remaining values than the A-E model did.
Table 4.40 - Comparison of B-C and A-E models for Balers
SAMPLE SIZE (90%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
B-C
A-B
297
224.885
297
205.4697
33
1.0537
33
0.7721
Figure 4.10 - Comparison of depreciation patterns of the B-C and A-E models for
Baler
78
4.2.6
Forage Harvesters
4.2.6.1 Data Description
The data set for Forage Harvesters
contained
76
observations
and
is
I if
i
summarized in Tables 4.41 and 4.42. Table
4.43 shows the average, standard deviation,
minimum and maximum value of RIR (real
New Holland Forage Harvester
interest rate), RNFI (real net farm interest),
RV (remaining value) and Age. Table 4.44 lists the distribution of dummy variables
included in both B-C and A-E models. Two main manufacturers, DEERE and NH,
accounted for three-fourths of all sales. The most common auction type (68.42%) was
Farmer Retirement and most Forage Harvesters were in either Good or Excellent
condition.
4.2.6.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.43.
FARMRET was the significant auction type variable; all the Age-Manufacturer
cross product variables were insignificant in both models; and RNFI, RIR and constant
also affected the remaining value significantly. DEERE was a significant variable in the
A-E model and FAIR was significant in the B-C estimation. AGE was also significant in
the B-C estimation.
Table 4.41 - Summary statistics for Forage Harvesters (Sample size: 76)
Variables
RV
RIR
RNFI
AGE
Mean
0.27888
1.063057
36.31089
9.236842
Standard
Deviation
0.205161
0.012412
9.13515
5.281082
Minimum
0.03853
1.0494
21.3178
Maximum
0.92692
1.0916
54.9
0
21
79
Table 4.42 - Frequency statistics for Forage Harvesters (Sample size: 76)
Frequency
Percent (%)
MANUFACTUpRS
DEERE
NH
OTHER
32
24
20
EQUIPMENT CONDITION
EX
21
GOOD
FAIR
POOR
UNKNOWN
AUCTION TYPE
FARMRET
BANKRUPT
CONSIGN
DEALER
UNKNOWN
44
9
1
1
42.12
31.58
26.32
27.63
57.89
11.84
1.32
1.32
6
2
68.42
19.74
7.89
2.63
1
1.32
52
15
The B-C transformations estimated for RV and AGE were 0.09 and 1.42,
respectively. This indicates that the depreciation pattern for Forage-Harvester equipment
might approximate the Geometric functional form. The R2 and adjusted R2 in the B-C
indicate a fairly good fit for the Forage Harvester data set.
Table 4.43 - Regression coefficients and t-statistics for Forage Harvesters
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
DEERE
0.1946
0.9628
NH
-0.095217
-0.444
MANUFACTURER *AGE
DAGE(DEERE*AGE)
0.011077
1.074
NAGE (NH*AGE)
0.0083777
0.7711
CONDITION
GOOD
-0.11456
-1
FAIR
l.875*
-0.30989
POOR
-0.2405
-0.5289
AUCTION TYPE
FARMRET
3.221***
0.51126
BANKRUPT
2.414**
0.45967
DEALER
0.52388
1.55
OTHERS
RNFI
2.383**
0.015869
RIR
2.958***
-14.227
CONSTANT
2.541**
13.348
AGE
5.234***
-0.044048
B-C TRANSFORMATION
RV
0.09
AGE
1.42
B-C R-SQUARE
0.7437
B-C ADJUSTED R-SQUARE
0 .6900
COMPARISON OF LOG-LIKELIHOOD VAL UES
SAMPLE SIZE (100%)
76
Log-likelihood Value
80.4162
Note:
Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
80
A-E
COEFFICIENTS
T-RATJO
2.1048
0.43243
1.7455*
1.4585
-0.051827
0.00698
-1.4017
-0.059004
-0.093483
0.42128
-0.5404
-0.46017
0.22711
0.56758
0.52743
0.51155
1.8531*
1.6379
1.4014
0.017277
-3.4653
5.4462
-0.28433
3.8645***
5.6605***
1.7855*
-1.5456
0.29 153
76
50.59121
81
4.2.6.3 Comparison Between Models
Because the Forage Harvester data set contained fewer than 100 observations, no
attempt was made to reserve observations for a MAPE test of predictive ability.
Both models are summarized graphically in Figure 4.5, assuming the tractor was
manufactured by John Deere, in Good condition and sold at a Farmer Retirement auction.
Both models are summarized graphically in Figure 4.5, assuming the tractor was
manufactured by John Deere, in Good condition and sold at a Farmer Retirement auction.
Variables RNFI and RIR were set at their average levels. This graph shows that the A-E
model estimated higher remaining values than the B-C model did until the 1 sixth year of
the useful lives of Forage Harvesters. After that, the B-C model estimated higher
remaining values than the A-E model did.
Figure 4.11 - Comparison of depreciation patterns of the B-C and A-B models for
Forage Harvesters
1
0.8
>0.6
0.4
0.2
0
1
3
5
7
9
11
AGE
13 15 17 19
82
4.2.7
Mower Conditioners
4.2.7.1 Data Description
The data set for Mower Conditioners contained
217 observations, of which 195 were used in the
estimation process and 22 were used to test predictive
ability. Two main manufacturers, New Holland and
John Deere, accounted for most of data for Mower
Conditioners. The most common auction type was
Farmer Retirement (64.52%) and most Mower
SC414 Deluxe Case IH
Mower Conditioner
Conditioners were in either Good or Excellent condition.
4.2.7.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.46. All auction type variables and all condition variables were
significant in both models, as was RNFI. Manufacturer variable HT and its corresponding
age-manufacturer cross product variable were also significant in the B-C estimation.
AGE was significant in the B-C estimation.
83
Table 4.44 - Summary statistics for Mower Conditioners (Sample size: 217)
Variables
RV
RIR
RNFI
AGE
Mean
0.321531
1.063794
35.74111
7.880184
Standard
Deviation
0.17283
0.011841
9.098077
4.772066
Minimum
0.02633
1.0494
21.3178
Maximum
0.82686
1.0916
54.9
1
23
Table 4.45 - Frequency statistics for Mower Conditioners (Sample size: 217)
Frequency
MANUFACTURERS
DEERE
58
IH
18
NH
88
HT
30
OTHER
23
EQUIPMENT CONDITION
EX
57
GOOD
118
FAIR
30
POOR
10
UNKNOWN
2
AUCTION TYPE
FARMRET
140
BANKRUPT
46
CONSIGN
29
UNKNOWN
2
Percent (%)
26.73
8.29
40.55
13.82
10.60
26.27
54.38
13.82
4.61
0.92
64.52
21.20
13.36
0.92
The B-C transformations estimated for RV and AGE were 0.5 and 0.24,
respectively. This indicates that the depreciation pattern for Mower Conditioners might
approximate the Double Square Root functional form. The R2 and adjusted R2 in the B-C
indicate a good fit for the data set.
Table 4.46 - Regression coefficients and t-statistics for Mower Conditioners
VARIABLES
MANUFACTURER
DEERE
IH
NH
HT
MANUFACTURER *AGE
DAGE (DEERE *AGE)
IAGE (IH*AGE)
NAGE (NH*AGE)
HAGE (HT*AGE)
CONDITION
GOOD
FAIR
POOR
AUCTION TYPE
FARMRET
BANKRUPT
OTHERS
RNFI
B-C
COEFFICENTS
T-RATIO
-0.14299
0.30292
-0.087021
-0.45549
-1.067
A-E
COEFFICIENTS
1-RATIO
-0.0 12073
0.0017 194
-0.83227
0.075707
-0.7335
2.721***
-0.0011518
-0. 10032
-0.03 563 5
-1.1142
0.0526
1.023
-0. 10875
-1.223
1.592
3.053***
0.0011202
-0.0005303
0.001067
0.0043274
0.62091
-0.23779
0.56449
1.1675
-0.13613
-0.3988
-0.67287
2.6098***
0.074846
0.19143
1.123
-0.2 1435
-1 944*
3 .764***
-0.32432
345***
-0.079546
0. 1296
2.685 * * *
0.097925
1.751 *
0.0052997
-1.2274
0.64054
-0.20077
2.29**
-0.6504
CONSTANT
AGE
B-C TRANSFORMATION
RV
AGE
B-C R-SQUARE
B-C ADJUSTED R-SQUA RE
0.3 105
0.5
0.24
0.5766
0.53 85
Note: *** Significant in 99% confidence level;
* * Significant in 95% confidence level; and
* Significant in 90% confidence level.
84
34733***
2.4667***
0.32456
0.20589
3.2658***
1.8274*
0.013 024
4.6205***
0.93102
0.098744
-0.0045234
1.4963
1.4314
-1.3144
85
4.2.7.3 Comparison Between Models
Table 4.47 provides a comparison of the log-likelihood values, as well as the
predictive abilities (MAPE) of both models. The A-E model exhibited less error in its
predictive ability.
Both models are summarized graphically in Figure 4.12, assuming the tractor was
manufactured by New Holland, in Good condition and sold at a Farmer Retirement
auction. Variables RNFI and RIR were set at their average levels. This graph shows that
the A-E model estimated higher remaining values than the B-C model did until the
eleventh year of the useful lives of Mower Conditioners. After that, the B-C model
estimated higher remaining values than the A-E model did.
Table 4.47 - Comparison of B-C and A-E models for Mower Conditioners
SAMPLE SIZE (90%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
B-C
195
A-E
195
157.002
22
0.5237233
140.3572
22
0.3840946
Figure 4.12 - Comparison of depreciation patterns of the B-C and A-E models for
Mower Conditioners
1
0.8
>0.6
A-E
0.4
--- B-C
0.2
0
1
3
5
7
9
11 13 15 17 1921 23
AGE
86
4.2.8
Mower Cutters
4.2.8.1 Data Description
The data set for Mower Cutters
contained
54
observations
and
is
summarized in Tables 4.48 and 4.49.
Table 4.48 shows the average, standard
deviation, minimum and maximum value
of HPY (hours per year), RIR (real interest
rate), RNFI (real net farm interest), RV
(remaining value) and Age. Table 449
CAT NOVA 310 front Mower Cutter
lists the distribution of dummy variables included in both B-C and A-E models.
Manufacturer John Deere dominated this data set, with nearly 55.56% of the all
observations. Farmer Retirement represented the most common auction type (83.33%).
Most Mower Cutters were in either Good or Excellent condition.
4.2.8.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.50. A-E model suggests that FAIR was the only significant
condition variable. FARMRET was the only significant manufacturer type variable and
AGE affected the remaining value significantly in the B-C estimation.
87
Table 4.48 - Summary statistics for Mower Cutters (Sample size: 54)
Variables
RV
RIR
RNFI
AGE
Mean
0.430409
1.061326
39.02359
7.462963
Standard
Deviation
0.177183
0.009043
8.372586
5.060811
Minimum
0.12634
1.0494
21.3178
Maximum
0.89842
1.0916
54.9
1
21
Table 4.49 - Frequency statistics for Mower Cutters (Sample size: 54)
Frequency
MANUFACTURERS
DEERE
30
IH
5
NH
6
BH
6
OTHER
7
EQUIPMENT CONDITION
EX
15
GOOD
32
FAIR
7
AUCTION TYPE
FARMRET
45
BANKRUPT
4
CONSIGN
4
UNKNOWN
5
Percent (%)
55.56
9.26
11.11
11.11
12.96
27.78
59.26
12.96
83.33
7.41
7.41
9.26
The B-C transformations estimated for RV and AGE were 0.55 and 0.12,
respectively. This indicates that the depreciation pattern for Mower Cutters might
approximate the Logarithmic functional form. The R2 and adjusted R2 vales in the B-C
indicate a fair fit for the data set.
88
Table 4.50 - Regression coefficients and t-statistics for Mower Cutters
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
DEERE
-0.2963 2
-0.76
IH
-0.26175
-0.549
NH
-0.31366
-0.671
BH
-0.5381
-1.213
MANUFACTURER *AGE
DAGE (DEERE*AGE) 0.28613
0.8202
IAGE (IH*AGE)
0.22243
0.574
NAGE (NH*AGE)
0.3465
0.9294
BAGE(BH*AGE)
1.213
0.46956
CONDITION
GOOD
0.01 14
0.1675
FAIR
-0.6598
-0.069361
AUCTION TYPE
FARMRET
-0.048637
-0.4828
1.989*
BANKRUPT
-0.2889
OTHERS
RNFI
-0.0038951
-0.9651
RIR
-2.503
-0.6005
CONSTANT
2.987 1
0.6688
1.812*
AGE
-0.61942
B-C TRANSFORMATION
RV
0.55
AGE
-0.12
B-CR-SQUARE
0.6151
B-C ADJUSTED R-SQUARE
0.463 1
COMPARISON OF LOG-LIKELIHOOD VAL UES
SAMPLE SIZE (100%)
54
Log-likelihood Value
Note:
45.1300
Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
A-E
T-RATIO
COEFFICIENTS
-0.15397
-0. 13201
-0. 15593
-0.6556 1
-0.6 112
-0.09997
-0.62302
-0.55403
0.043778
0.037777
0.046259
0.038632
0.66086
0.62969
0.6635
0.64036
-0.054021
-0.65331
2.7969***
-0.3815 1
0.048421
-0. 15476
0.32907
-0.0082261
1.3506
0.35374
-1.6406
1.1358
0.74514
-0.68646
-0.05 1395
-0.73 5 19
54
39.25167
89
4.2.8.3 Comparison Between Models
Because the Mower Cutter data set contained fewer than 100 observations, no
attempt was made to reserve observations for a MAPE test of predictive ability.
Both models are summarized graphically in Figure 4.13, assuming the tractor was
manufactured by John Deere, in Good condition and sold at a Farmer Retirement auction.
Variables RNFI and RIR were set at their average levels. This graph shows that the A-E
model estimated higher remaining values than the B-C model did from the second year to
the eleventh year. Beyond that, the B-C model estimated higher remaining values than
the A-E model did.
Figure 4.13 - Comparison of depreciation patterns of the B-C and A-E models for
Mower Cutters
I
0.8
>0.6
A-E
0.4
B-C
0.2
ii
0
1
I
3
r
1
5
Ti'
I
7
9
I
1
I
Ii
11 13 15 17 19 21
AGE
90
4.3
PLANTING AND TILLAGE EQUIPMENT
The major types of machinery included in the planting and tillage equipment are
planters, disks, plows and drills. This is the first attempt to estimate models for drills.
4.3.1
Planters
4.3.1.1 Data Description
The data set for planters contained
266 observations, of which 239 were used
in the estimation process and 27 were used
to test predictive ability. Table 4.51 shows
the average, standard deviation, minimum
and maximum value of RIR (real interest
rate), RNFI (real net farm interest), RV
(remaining value) and Age. Table 4.52
lists the distribution of dummy variables included in both B-C and A-E models.
Manufacturer John Deere dominated this data set, with nearly 75.56% of all observations.
Farmer Retirements represented the most comnion auction type (71.43%). Most planters
were in either Good or Excellent condition.
4.3.1.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are sunmiarized in Table 4.53. The condition dummy variables GOOD and FAIR and the
91
auction type variable BANKRUPT were significant in both estimations, as was
variable RINFI. DEERE was significant in the B-C model, while RIR was only significant
in the A-E estimation.
Table 4.51 - Summary statistics for Planters (Sample size: 266)
Variables
RV
RIR
RNFI
AGE
Mean
0.428266
1.063736
36.64519
8.161654
Standard
Deviation
0.200442
0.011845
8.699051
4.436576
Minimum
0.03422
1.0494
21.3178
Maximum
0.99079
1.0916
54.9
0
23
Table 4.52 - Frequency statistics for Planters (Sample size: 266)
Frequency
MANUFACTURERS
DEERE
201
III
50
OTHER
15
EQUIPMENT CONDITION
EX
84
GOOD
146
FAIR
31
POOR
1
UNKNOWN
4
AUCTION TYPE
FARMRET
190
BANKRUPT
16
CONSIGN
27
DEALER
16
UNKNOWN
17
Percent (%)
75.56
18.80
5.64
31.58
54.89
11.65
0.38
1.50
71.43
6.02
10.15
6.02
6.39
The B-C transformations estimated for RV and AGE were 0.49 and 0.75,
respectively. This indicates that the depreciation pattern for planters might approximate
the Sum of Year Digits functional form. The R2 and adjusted R2 value in the B-C indicate
a fair fit for the data set.
92
Table 4.53 - Regression coefficients and t-statistics for Planters
VARIABLES
MANUFACTURER
DEERE
IH
MANUFACTURER *AGE
DAGE (DEERE*AGE)
IAGE (IH*AGE)
CONDITION
GOOD
FAIR
POOR
AUCTION TYPE
FARMRET
BANKRUPT
DEALER
OTHERS
RNFI
B-C
COEFFICENTS
T-RATIO
0.3677
0.3212
1.632
0.018853
0.015879
1.1584
1.0459
-0.064867
-0.089925
-1.108
-1.509
-0.0019737
-0.0025134
-0.7772
-0.08578
-0.20935
0.00087078
_2.281**
-0.13865
-0.32231
0.024638
2.977***
_3.7193***
0.14266
0.0052075
-0.131
-0.02286
0. 1203
0.012558
-0.21038
-0.02488 1
0.20475
1.7658*
-0.23442
0.0059792
0.81395
2.3**
0.4602
-0.8968
-0.04667
0.0078187
2.1644
0.035486
-0.00010339
3.1866***
4.6611***
1.4838
-0.043146
CONSTANT
-1.73 82
AGE
-0.0027315
B-C TRANSFORMATION
RV
AGE
B-C R-SQUARE
B-C ADJUSTED R-SQUARE
Note:
l.975**
A-E
T-RATIO
COEFFICIENTS
3.704***
0.003631
1.663*
-0.3054
-0 .98866
0.49
0.75
0.5 117
0.4835
Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
4.3.1.3 Comparison Between Models
Table 4.54 provides a comparison of the log-likelihood values, as well as the
predictive abilities (MAPE) of both models. The two models exhibited very similar
predictive abilities (0.31 for B-C and 0.34 for A-E).
Both models are summarized graphically in Figure 4.14, assuming the planter was
manufactured by John Deere, in Good condition and sold at a Farmer Retirement auction.
93
Variables RNFI and RIR were set at their average levels. This graph shows very
similar deprecation patterns estimated by both models.
Table 4.54 - Comparison of B-C and A-E models for Planters
B-C
SAMPLE SIZE (90%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
239
132.544
27
0.3090279
A-E
239
117.2576
27
0.3389036
Figure 4.14 - Comparison of depreciation patterns of the B-C and A-E models for
Planters
4.3.2
Disks
4.3.2.1 Data Description
The
contained
data
139
set
for
disks
observations, of
which 125 were used in the
estimation process and 14 were
used to test predictive ability.
Table 4.55 shOws the average,
1444 4-Section Flexible Tandem Discs 29' - 40'
94
standard deviation, minimum and maximum value of RIR (real interest rate), RNFI
(real net farm interest), RV (remaining value) and Age. Table 4.56 lists the distribution of
dummy variables included in both B-C and A-E models. John Deere and International
Harvester accounted for more than 80 percent of the total disk sales (43.17% and
38.12%). Farmer Retirement represented the most common auction type (57.55%). Most
disks were in either Good or Excellent condition.
4.3.2.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.60. POOR was the significant condition dummy variable in
both models.
Condition variable EX and Age were only significant in the B-C
estimation, while FARJvIRET was significant manufacturer variable only in the A-E
regression.
Table 4.55 - Summary statistics for Disks (Sample size: 139)
Variables
RV
RIR
RNFI
AGE
Mean
0.271066
1.065774
34.37417
9.302158
Standard
Deviation
0.148178
0.01311
8.112854
4.605691
Minimum
0.02467
1.0494
21.3178
2
Maximum
0.70972
1.0916
54.9
24
The B-C transformations estimated for RV and AGE were 0.21 and 0.5,
respectively. This indicates that the depreciation pattern for disks might approximate the
Double Square Root functional form. The R2 and adjusted R2 values in the B-C indicate
a fair fit for the data set.
95
Table 4.56 - Frequency statistics for Disks (Sample size: 139)
Frequency
MANUFACTURERS
DEERE
60
IH
53
KE
5
OTHER
21
EQUIPMENT CONDITION
EX
41
GOOD
60
FAIR
17
POOR
13
UNKNOWN
8
AUCTION TYPE
FARMRET
80
BANKRUPT
38
CONSIGN
19
DEALER
2
Percent (%)
43.17
38.13
3.60
15.11
29.50
43.17
12.23
9.35
5.76
57.55
27.34
13.67
1.44
4.3.2.3 Comparison Between Models
Table 4.61 provides a comparison of the log-likelihood values, as well as the
predictive abilities (MAPE) of both models. The A-E exhibited less error in its predictive
ability (1.6 for B-C and 1.35 for A-E).
Both models are summarized graphically in Figure 4.15, assuming the disk was
manufactured by John Deere, in Good condition and sold at a Farmer Retirement auction.
Variables RNFI and RIR were set at their average levels. This graph shows that the two
models estimated similar depreciation patterns from the fifth year to the eleventh year of
the useful lives of disks. Beyond this, remaining value estimated by the B-C model was
higher that that of the A-E model, especially in the early and late years.
96
Table 4.57 - Regression coefficients and t-statistics for Disks
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
DEERE
IH
-0.053577
-0.065179
KB
0.62642
MANUFACTURER *AGE
DAGE(DEERE*AGE) 0.0041997
IAGE (IH*AGE)
0.06574
KAGE(KE*AGE)
-0.207 19
CONDITION
EX
0.11892
GOOD
0.0 10467
POOR
-0 .2605
AUCTION TYPE
FARMRET
0.041743
BANKRUPT
-0.03019
OTHERS
RNFI
0.0023887
RIR
-1.4985
CONSTANT
1.079
AGE
-0.23851
B-C TRANSFORMATION
RV
AGE
B-C R-SQUARE
B-C ADJUSTED R-SQUARE
A-E
COEFFICIENTS
T-RATIO
-0.254281
-0.3 14116
0.994791
0.031739
0.094321
0.29899
0.2936349
0.8092056
0.741175
0.05 1791
-0.009365
0.010349
-0.025503
-0.558344
0.486348
-0.695948
1.89062*
0.180466
2.614937***
0. 18462
-0.00 18
1.63 16394
-0.016 137
-0.62333
2.350769**
0.681518
0.24765
0.067395
1.9566248*
0.453228
0.008241
-1.3526
1.1121
-0.05 1372
1.5500404
-0.980785
0.6526791
-0.654963
0.846728
-0.972723
-0.4 1948
0.604734
-0.674089
0.439332
3 .44369w
0.21
0.5
0.4649
0.4021
Note: *** Significant in 99% confidence level;
* * Significant in 95% confidence level; and
* Significant in 90% confidence level.
Table 4.58 - Comparison of B-C and A-E models for Disks
SAMPLE SIZE (100%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
B-C
125
109.5 19
102.6703
14
14
1.60889
1.350507
A-B
125
97
Figure 4.15 - Comparison of depreciation patterns of the B-C and A-E models for
Disks
I
0.8
0.6
-*---A-E
0.4
-*-- BC
0.2
0
(
1
3
5
7
9
11
13
15
17
AGE
4.3.3
Plows
4.3.3.1 Data Description
The data set for plows contained 108
observations, of which 97 were used in the
estimation process and 11 were used to test
predictive ability. Table 4.59 shows the average,
standard deviation, minimum and maximum value
of RIR (real interest rate), RNFI (real net farm
interest), RV (remaining value) and Age. Table
4.60 lists the distribution of dummy variables
included in both B-C and A-E models. John Deere
700 and 800 Trailing
Mold Board Plow
(42.59%) and International Harvester (57.4 1%) dominated the data set in this sample.
Farmer Retirement represented the most common auction type (75%). Most plows were
in Good condition (70.37%).
98
Table 4.59 - Summary statistics for Plows (Sample size: 108)
Variables
RV
RIR
RNFI
AGE
Mean
0.272295
1.067548
33.18449
10.52778
Standard
Deviation
0.126664
0.014938
8.490812
4.163613
Minimum
0.06995
1.0494
23.529
Maximum
0.54527
1.0916
54.9
2
23
4.3.3.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.61. Neither model fit very well, a result that likely arises out
of the abuse that this equipment receivers. No variables in the A-E estimation were
significant, while only Dealer was significant in the B-C model.
The B-C transformations estimated for RV and AGE were 0.52 and 0.25,
respectively. This indicates that the depreciation pattern for plows might approximate the
Double Square Root functional form. The R2 and adjusted R2 values in the B-C indicate a
poor fit for the data set.
Table 4.60 - Frequency statistics for Plows (Sample size: 108)
Frequency
MANUFACTURERS
DEERE
46
IH
62
OTHER
2
EQUIPMENT CONDITION
EX
12
GOOD
76
FAIR
16
POOR
2
UNKNOWN
2
AUCTION TYPE
FARMRET
81
BANKRUPT
5
CONSIGN
15
DEALER
1
UNKNOWN
6
Percent (%)
42.59
57.41
1.85
11.11
70.37
14.81
1.85
1.85
75.00
4.63
13.89
0.93
5.56
99
Table 4.61 - Regression coefficients and t-statistics for Plows
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
DEERE
0.31665
MANUFACTURER *AGE
DAGE (DEERE*AGE)
-0.067719
CONDITION
GOOD
0.097253
FAIR
0.069605
POOR
0.17304
AUCTION TYPE
FARMRET
0.041775
BANKRUPT
0.14421
DEALER
-0.4 1845
OTHERS
RNFI
0.000323 15
MR
0.79326
CONSTANT
-1.7724
AGE
-0.073735
B-C TRANSFORMATION
RV
AGE
B-C R-SQUARE
B-C ADJUSTED R-SQUARE
A-E
COEFFICIENTS
T-RATIO
1.537
0.019462
0.20478
-1.032
-0.0009625
-0.20032
1.176
0.6812
0.9376
0.04557
-0.018668
0.38224
-0.10589
0.38334
0.6171
1.179
0.088047
0.2496
-1.0769
-1.73 *
0. 13385
0.3 197
0.0046201
1.5168
-0.6485
-1.426
0.049 133
-0.00 1116
0.06731
0.75788
1.2 187
-1. 1603
0.49781
0.35441
0.20968
-0.21324
0.52
0.25
0.2186
0.1175
Note: *** Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
4.3.3.3 Comparison Between Models
Table 4.62 provides a comparison of the log-likelihood values, as well as the
predictive abilities (MAPE) of both models. Both models exhibited very similar
predictive abilities (0.43 6 for B-C and 0.43 7 for A-E).
Both models are summarized graphically in Figure 4.16, assuming the plow was
manufactured by International Harvester, in Good condition and sold at a Farmer
Retirement auction. Variables RNFI and RIR were set at their average levels. This graph
100
shows that the A-B model estimated higher remaining value than the A-E model did
14th
from the fourth to the
year in the useful life of plows.
Table 4.62 - Comparison of B-C and A-E models for Plows
SAMPLE SIZE (90%)
Log-likelihood Value
SAMPLE SIZE (10%)
MAPE
B-C
97
A-E
97
78.2884
74.95526
11
11
0.4360396
0.4366988
Figure 4.16 - Comparison of depreciation patterns of the B-C and A-B models for
Plows
I
0.8
RB-C
0.2
0'
1
3
5
7
9
11 13 15 17 19 21
AGE
4.3.4
Drills
4.3.4.1 Data Description
The
data set
for
drills
contained
75
observations and is summarized in Tables 4.63 and
4.64. Table 4.63 shows the average, standard
deviation, minimum and maximum value of RIR
(real interest rate), RNFI (real net farm interest),
107 All Purpose Drill
101
RV (remaining value) and Age. Table 4.64 lists the distribution of dummy variables
included in both B-C and A-B models. John Deere and International Harvester (48.61%
and 50%) contained almost all the observations. Farmer Retirement was the most
common auction type (75%) and most drills were in Good condition.
Table 4.63 - Summary statistics for Drills (Sample size: 72)
Variables
RV
RIR
RNFI
AGE
Mean
0.39478
1.059931
37.7988
10.65278
Standard
Deviation
0.210771
0.009173
7.860633
4.37393
Minimum
0.03397
1.0494
23.529
Maximum
0.94286
1.0916
54.9
3
22
Table 4.64 - Frequency statistics for Drills (Sample size: 72)
Frequency
MANUFACTURERS
DEERE
35
IH
36
OTHER
1
EQUIPMENT CONDITION
EX
12
GOOD
49
FAIR
10
UNKNOWN
1
AUCTION TYPE
FARMRET
54
BANKRUPT
4
CONSIGN
10
UNKNOWN
4
Percent (%)
48.61
50.00
1.39
16.67
68.06
13.89
1.39
75.00
5.56
13.89
5.56
4.3.4.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.65. Although the R2 values were reasonably good, virtually all
variables were insignificant. Only Age in the B-C model was significant.
102
The B-C transformations estimated for RV and AGE were 0.61 and 0.26,
respectively. This indicates that the depreciation pattern for Drills might approximate the
Double Square Root functional form.
Table 4.65 - Regression coefficients and t-statistics for Drills
VARIABLES
B-C
T-RATIO
COEFFICENTS
MANUFACTURER
IH
0.28373
1.248
MANUFACTURER *AGE
IAGE (IH*AGE)
-0.063775
-0.921
CONDITION
GOOD
1.018
0.081276
FAIR
-0.2572
-0.028153
AUCTION TYPE
FARMRET
0.057449
0.8283
BANKRUPT
-0.3 11
-0.041224
OTHERS
RNFI
0.5294
0.0025 197
RIR
1.019
3.7676
CONSTANT
-4.1084
-1.027
6.068***
AGE
-0.26995
B-C TRANSFORMATION
RV
0.61
AGE
0.26
B-C R-SQUARE
0.6065
B-C ADJUSTED R-SQUARE
0.5494
COMPARISON OF LOG-LIKELIHOOD VAL UES
SAMPLE SIZE (100%)
72
42.7578
Log-likelihood Value
Note:
A-E
T-RATIO
COEFFICIENTS
0.18019
0.64701
-0.0090612
-0.50178
0.058108
-0.29327
0.65779
-1.4161
0.13388
-0.039435
1.0777
-0.19815
-0.00365
-0.28006
0.91892
-0.039222
-0.60284
-0.23795
0.75931
-0.75273
72
39.50035
Significant in 99% confidence level;
* * Significant in 95% confidence level; and
* Significant in 90% confidence level.
4.3.4.3 Comparison Between Models
Because the drill data set contained fewer than 100 observations, no attempt was
made to reserve observations for a MAPE test of predictive ability.
103
Both models are summarized graphically in Figure 4.17, assuming the drill was
manufactured by International Harvester, in Good condition and sold at a Farmer
Retirement auction. Variables RNFI and RIR were set at their average levels. This graph
shows that the A-B model estimated a slightly higher remaining value than the B-C
estimation did in the middle years.
Figure 4.17 - Comparison of depreciation patterns of the B-C and A-E models for
Drills
0.8'
0.6
0.4
0.2
0
1
3
5
7
9
11
AGE
13
15
17
19
104
4.4 OTHER MACHINERY
Miscellaneous machinery, including Grinder Mixers, Manure Spreaders, Skid Steer
Loaders and Trucks are examined in this section. This is the first attempt to estimate
models for Grinder Mixers and Trucks.
4.4.1
Grinder Mixers
4.4.1 .1 Data Description
The data set for Grinder Mixers contained 41 observations and is summarized in
Tables 4.66 and 4.67. Table 4.66 shows the average, standard deviation, minimum and
maximum value of RIR (real interest rate),
RNFI (real net farm interest), RV (remaining
value) and Age. Table 4.67 lists the distribution
of dummy variables included in both B-C and
A-E models. Gehi and New Holland contained
more than 60 percent of all observations (31.7%
and 34.14%). Farmer Retirement was the most
common auction type (80.49%) and most
New Holland 355 Grinder Mixer
Grinder Mixers were in either Good or Excellent condition.
4.4.1.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.68. Although the B-C model generated a higher R2, the
number of variables relative to total sample size apparently contributed to problem of
105
variable significance. No variables in the A-B estimation were significant, while only
Age was significant in the B-C model.
The B-C transformations estimated for RV and AGE were 0.07 and 0.38,
respectively. This indicates that the depreciation pattern for Grinder Mixers might
approximate the Geometric functional form.
Table 4.66 - Summary statistics for Grinder Mixers (Sample size: 41)
Variables
RV
Mean
0.359532
MR
1.0593
RNFI
AGE
39.27008
8.878049
Standard
Deviation Minimum
0.21601
0.05002
0.008238
1.0494
9.045413
21.3178
5.710495
1
Maximum
0.86599
1.0916
54.9
25
Table 4.67 - Frequency statistics for Grinder Mixers (Sample size: 41)
Frequency
MANUFACTURERS
GE
13
NH
14
OTHER
14
EQUIPMENT CONDITION
EX
11
GOOD
23
FAIR
6
POOR
1
AUCTION TYPE
FARMRET
33
BANKRUPT
6
CONSIGN
1
DEALER
1
Percent (%)
31.71
34.15
34.15
26.83
56.10
14.63
2.44
80.49
14.63
2.44
2.44
106
Table 4.68 - Regression coefficients and t-statistics for Grinder Mixers
VARIABLES
MANUFACTURER
GE
B-C
COEFFICENTS
T-RATIO
A-E
COEFFICIENTS
T-RATIO
0.12418
0.303 1
-0.00200 17
-0.03 8947
NH
MANUFACTURER *AGE
GAGE (GE*AGE)
NAGE (NH*AGE)
CONDITION
-0.147 15
-0.3653
-0.026504
-0.24559
-0.11956
0.012626
-1.121
0. 1029
-0.0011142
-0.00034523
-0.17009
-0.062908
GOOD
FAIR
POOR
AUCTION TYPE
FARMRET
BANKRUPT
DEALER
0.062178
-0.45145
-1.5511
0.3738
-1.644
-3.41
0.087267
-0.47726
-1.7533
0.77606
-1.3207
-0.76935
0.090368
-0.6637
0.30647
0.2 156
0.33055
1.03 14
-1.429
0.5442
-0.4267 1
0.26567
-0.99565
0.66827
0.57
0.8442
-0.885
-0.0022189
0.68121
0.24082
-0.0087656
-0.37391
0.20523
0.27927
-0.27684
OTHERS
RNFI
0.0053479
RIR
8.5 173
CONSTANT
-9.6805
AGE
-0. 16434
B-C TRANSFORMATION
RV
0.07
AGE
0.38
B-C R-SQUARE
0.783 7
B-C ADJUSTED R-SQUARE
0.6796
COMPARISON OF LOG-LIKELIHOOD VALUE
SAMPLE SIZE (100%)
41
Log-likelihood Value
l.7l7*
37.8209
41
25.91851
Note: *** Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
4.4.1.3 Comparison Between Models
Because the Grinder Mixer data set contained fewer than 100 observations, no
attempt was made to reserve observations for a MAPE test of predictive ability.
Both models are summarized graphically in Figure 4.18, assuming the grinder
mixer was manufactured by New Holland, in Good condition and sold at a Farmer
107
Retirement auction. Variables RNFI and RIR were set at their average levels. This
graph shows that the A-E model estimated higher remaining values than the B-C model
did until the ninth year of the useful lives of Grinder Mixers. After that, the B-C model
estimated higher remaining values than the A-E model did.
Figure 4.18 - Comparison of depreciation patterns of the B-C and A-E models for
Grinder Mixers
1
0.8
0.6
0.4
-'*-- B-C
0.2
0
I
1
r
I
I
3
5
7
9
11
13
15
17
19
AGE
4.4.2
Manure Spreaders
4.4.2.1 Data Description
The
data
set for
Manure
Spreaders contained 81 observations
fr
and is summarized in Tables 4.69
and 4.70. Table 4.69 shows the
average,
standard
deviation,
minimum and maximum value of
RIR (real interest rate), RNFI (real
Gehi Scavenger
Manure Spreader
108
net farm interest), RV (remaining value) and Age. Table 4.70 lists the distribution of
dummy variables included in both B-C and A-E models. New Holland and John Deere
contained more than half of all observations (38.27%, 22.22% and 14.81%). Farmer
Retirement was still the most common auction type (62.96%) and most manure spreaders
were in either Good or Excellent condition.
Table 4.69 - Summary statistics for Manure Spreaders (Sample size: 81)
Variables
RV
RIR
RNFI
AGE
Mean
0.441573
1.059315
38.44304
6.012346
Standard
Deviation
0.241694
0.011172
7.792691
4.553828
Minimum
0.02064
23.529
Maximum
0.99058
1.0916
54.9
0
17
1.0494
Table 4.70 - Frequency statistics for Manure Spreaders (Sample size: 81)
Frequency
MANUFACTURERS
DEERE
18
NH
31
OTHER
32
EQUIPMENT CONDITION
EX
31
GOOD
38
FAIR
10
POOR
2
AUCTION TYPE
FARMRET
51
BANKRUPT
13
CONSIGN
13
DEALER
1
UNKNOWN
3
Percent (%)
22.22
38.27
39.50
38.27
46.91
12.35
2.47
62.96
16.05
16.05
1.23
3.70
4.4.2.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-B (Equation 3.7) models
are summarized in Table 4.71. FARMRET was the significant auction type variable, as
109
were the manufacturer variable DEERE and its Age-Manufacturer cross product
variables DAGE. The condition dummy variables POOR and AGE were only significant
in the B-C model, while the condition variable FAIR and auction type variable
CONSIGN were only significant in the A-E estimation.
The B-C transformations estimated for RV and AGE were 0.49 and 0.39,
respectively. This indicates that the depreciation pattern for the manure spreaders might
approximate the Double Square Root functional form. The R2 and adjusted R2 values in
the B-C indicate a fair fit for the data set.
Table 4.71 - Regression coefficients and t-statistics for Manure Spreaders
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
2.703***
DEERE
0.40306
NH
-0.021359
-0.183
MANUFACTURER *AGE
2.507**
DAGE (DEERE*AGE)
-0.1345
NAGE (NH*AGE)
-0.037773
-0.8766
CONDITION
GOOD
0.0973 96
1.20 1
FAIR
-0.11562
-0.9205
-2.731 * * *
POOR
-0.60338
AUCTION TYPE
l.93**
FARMRET
0.29643
BANKRUPT
0.18655
1.094
CONSIGN
0.20708
1.197
OTHERS
RNFI
0.0081995
1.444
RIR
3.2399
0.8 105
CONSTANT
-4.5117
-1.03
AGE
-0.098985
B-C TRANSFORMATION
RV
0.49
AGE
0.39
B-CR-SQUARE
0.5944
B-C ADJUSTED R-SQUARE
0.5 157
COMPARISON OF LOG-LIKELIHOOD VALUE
SAMPLE SIZE (100%)
Log-likelihood Value
A-E
COEFFICIENTS
T-RATIO
0. 16488
0.5 15 15
0.032873
0.34691
-0.025276
-0.5116
-0.46629
-0.0106 13
0.089097
-0.43294
-1.8822
1. 1325
2.0459**
-1.0 166
0.55638
0.4897
0.63937
1.7 147*
0.0086001
-0.58022
1.4437
-0.34161
1.4494
1.836*
0.4 14 1
0.553 11
-0.0097211
-0.53566
81
81
39.0702
30.00273
Note: *** Significant in 99% confidence level;
110
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
4.4.2.3 Comparison Between Models
Because the Forage Harvester data set contained fewer than 100 observations, no
attempt was made to reserve observations for a MAPE test of predictive ability.
Both models are summarized graphically in Figure 4.19, assuming the manure
spreader was manufactured by New Holland, in Good condition and sold at a Farmer
Retirement auction. Variables RNFI and RIR were set at their average levels. This graph
shows that the two models estimated similar depreciation patterns until the ninth year.
After that, the B-C model estimated higher remaining values than the A-E model did.
Figure 4.19 - Comparison of depreciation patterns of the B-C and A-E models for
Manure Spreaders
1
0.8
A-E
*B C
0.2
0l
1 234567891011121314
AGE
4.4.3 Skid Steer Loaders
4.4.3.1 Data Description
The data set for Skid Steer Loaders contained 94 observations and is summarized in
Tables 4.72 and 4.73. Table 4.72 shows the average, standard deviation, minimum and
111
maximum value of HPY (hours per year), RIR (real
interest rate), RNFI (real net farm interest), RV
(remaining value) and Age. Table 4.73 lists the
distribution of dummy variables included in both B-C
and A-E models. Case, Meirose and Gehi contained
more than 80 percent of the all observations (37.23%,
25.53%
and
19.15%).
Farmer
Retirement
and
New Holland Superboom
skid steers
Bankruptcy were the most common auction types
(45.74% and 32.98%). Most skid steer loaders were in
either Good or Excellent condition.
Table 4.72 - Summary statistics for Skid Steer Loaders (Sample size: 94)
Variables
RV
MR
RNFI
HPY
AGE
Mean
0.420553
1.060326
43.08308
1322.553
5.531915
Standard
Deviation Minimum
0.148173
0.10199
0.006202
1.0494
6.874663 29.5678
969.0891
41
3.884632
1
Maximum
0.81299
1.0688
54.9
5000
21
Table 4.73 - Frequency statistics for Skid Steer Loaders (Sample size: 94)
Frequency
MANUFACTURERS
CASE
35
GE
18
MELROSE
24
OTHER
17
EQUIPMENT CONDITION
EX
27
GOOD
53
FAIR
12
UNKNOWN
2
AUCTION TYPE
FARMIRET
BANKRUPT
CONSIGN
DEALER
UNKNOWN
43
31
12
4
4
Percent (%)
37.23
19.15
26.53
18.09
28.72
56.38
12.77
2.13
45.74
32.98
12.77
4.26
4.26
112
4.4.3.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.74. FARMRET was a significant auction type variable for
both models, as were variables RNFI, HPY and AGE. CONSTANT was also significant
in the A-B estimation.
Table 4.74 - Regression coefficients and t-statistics for Skid Steer Loaders
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
CASE
0.022431
0.2379
GE
-0.098627
-1.034
MELROSE
0.0061292
0.06987
MANUFACTURER *AGE
CAGE (CASE*AGE)
0.0027344
0.06069
GAGE (GE*AGE)
0.026073
0.5 176
MAGE (MELROSE*AGE) 0.026268
0.5932
CONDITION
GOOD
-0.024984
-0.626 1
FAIR
-0.023827
-0.4348
AUCTION TYPE
3.729***
FARMRET
0. 14716
BANKRUPT
0.05258
1.097
DEALER
0.07082
0.9095
OTHERS
373***
RNFI
0.0082626
RIR
1. 1267
0.4279
CONSTANT
-1.9704
-0.7083
4.482***
AGE
-0.13995
2.691***
HPY
-0.00033866
B-C TRANSFORMATION
RV
0.7
AGE
0.15
HPY
0.73
B-C R-SQUARE
0.6565
B-C ADJUSTED R-SQUARE
0.5905
COMPARISON OF LOG-LIKELIHOOD VALUE
SAMPLE SIZE (100%)
94
Log-likelihood Value
98.1156
A-E
COEFFICIENTS
T-RATIO
0.0043723
-0.010185
0.0029206
0.36494
-0.66903
0.24287
-0.0011216
-0.00051439
0.000074707
-0.72083
-0.22476
0.052588
-0.070817
-0.12945
-1.2 124
-1.5 197
0.2845
0.11237
0.20662
3 .6347***
0.0 17448
0.85 185
47574***
1.3 502
1.713 1
1.6 155
-0.00322 15
1.809*
1.6799*
-0.000092274
2.9624***
0.098968
94
94.21853
113
Note: *** Significant in 99% confidence level; ** Significant in 95% confidence
level; and * Significant in 90% confidence level.
The B-C transformations estimated for RV, HPY and AGE were 0.7, 0.73 and 0.15,
respectively. This indicates that the depreciation pattern for skid steer loaders might
approximate the Double Square Root functional form. The R2 and adjusted R2 values in
the B-C indicate a good fit for the data set.
4.4.3.3 Comparison Between Models
Because the skid steer loader data set contained fewer than 100 observations, no
attempt was made to reserve observations for a MAPE test of predictive ability.
Both models are summarized graphically in Figure 4.20, assuming the skid steer
loader was manufactured by Case, in Good condition and sold at a Farmer Retirement
auction. Variables RNFI, RIR and HPY were set at their average levels. This graph
shows that the A-E model estimated higher remaining values than the B-C model did
until the seventh year of the useful lives of skid steer loaders. After that, the B-C model
estimated higher remaining values than the A-E model did.
Figure 4.20 - Comparison of depreciation patterns of the B-C and A-E models for
Skid Steer Loaders
11
0.8
A-E
-*- B-C
0.2
0
-
1
I
3
5
7
F
9
F
I
11
AGE
I
F
13 15 17 19
114
4.4.4 Trucks
4.4.4.1 Data Description
Although the Hot Line data
set
contained many observations for heavyduty trucks, list prices were only available
for lighter duty pickup trucks. The data set
for trucks contained 123 observations, of
which 111 were used in the estimation
process and 12 were used to test predictive
ability. Table 4.75 shows the average,
2001 F-iSO SuperCrew 4x4 Ford Truck
standard deviation, minimum and maximum value of MPY (miles per year), RIR (real
interest rate), RNFI (real net farm interest), RV (remaining value) and Age. Table 4.76
lists the distribution of dummy variables included in both B-C and A-E models. Ford and
Chevrolet contained more than 90 percent of all observations (54.47% and 38.21%).
Farmer Retirement and Bankrupt were the most common auction type (3 9.02% and
57.72%). Most trucks were in either Good or Fair conditions (40.65% and 30.08%).
Table 4.75 - Summary statistics for Trucks (Sample size: 123)
Variables
RV
MR
RNFI
MPY
AGE
Mean
0.317241
1.062806
34.84145
9799.864
9.308943
Standard
Deviation
0.245056
0.009601
6.997774
6533.111
4.345961
Minimum Maximum
0.03304
0.98112
1.0494
1.0916
21.3178
54.9
476.62
41666.67
1
22
115
Table 4.76 - Frequency statistics for Trucks (Sample size: 123)
Frequency
MANUFACTURERS
FORD
67
DODGE
8
CHEV
47
OTHER
1
EQUIPMENT CONDITION
EX
18
GOOD
FAIR
POOR
AUCTION TYPE
FARMRET
BANKRUPT
CONSIGN
DEALER
Percent (%)
54.47
6.50
38.21
0.81
14.63
50
37
40.65
30.08
18
14.63
48
3
39.02
57.72
2.44
1
0.81
71
4.4.4.2 Models Estimation
The regression results for the B-C (Equation 3.5) and A-E (Equation 3.7) models
are summarized in Table 4.77. Notice that MPY in this sample is actually miles per year,
instead of hours per year as was the case for tractors, Combines and Skid Steer Loaders
(See Table 5.1).
All condition variables and AGE were significant for both models, while all auction
type variables were insignificant.
All manufacturer type variables and their
corresponding cross product variables were only significant in the A-E estimation, as
were RIR and CONSTANT, while RNFI and MPY were only significant in the B-C
regression. RNFI also had the wrong sign, because the market for these trucks extends
well beyond the farm sector. RNFI was not the best variable to reflect the economy.
The B-C transformations estimated for RV, MPY and AGE were 0.31, 0.04 and
0.21, respectively. This indicates that the depreciation pattern for trucks might
approximate the Cobb-Douglas functional form. The R2 and adjusted R2 values in the BC indicate a fairly good fit for the data set.
116
Table 4.77 - Regression coefficients and t-statistics for Trucks
VARIABLES
B-C
COEFFICENTS
T-RATIO
MANUFACTURER
FORD
0.3539
CHEV
0.060568
MANUFACTURER *AGE
FAGE (FORD*AGE)
-0.054429
CAGE (CHEV*AGE)
0.10932
CONDITION
GOOD
-0.18937
FAIR
-0.5271
POOR
-0.68158
AUCTION TYPE
FARMRET
-0.0044376
BANKRUPT
-0.19254
OTHERS
RNFI
-0.011799
RIR
-4.6721
CONSTANT
6.7394
MPY
-0.10838
AGE
-0.46317
B-C TRANSFORMATION
RV
AGE
MPY
B-C R-SQUARE
B-C ADJUSTED R-SQUARE
A-E
COEFFICIENTS T-RATIO
1.144
0.1941
16.634
16.34
3.4675***
2.7467***
-0.4698
0.9399
-1.1236
-0.90255
3.6503***
2.2465***
2.064**
4.697***
_5.138***
-0.24144
-0.87668
-1.2134
2.4993***
4.9787***
3.3867***
-0.02329
-1.002
-0.13985
-0.40495
-0.35178
-1.0102
2.011**
-1.094
0.0055334
-2.9433
5.7133
-5.6163E-06
13.578
1.177
1.42
2.964***
4.468***
6.670l***
1.9228*
-0.89949
1.9269*
0.31
0.12
0.04
0.7408
0.7060
Note: *** Significant in 99% confidence level;
** Significant in 95% confidence level; and
* Significant in 90% confidence level.
4.4.4.3 Comparison Between Models
Table 4.85 provides a comparison of the log-likelihood values, as well as the
predictive abilities (MAPE) of both models. Nevertheless, the A-E model exhibited lower
error in predictive value (MAPE was 0.40 for B-C and 0.30 for A-E)
Both models are summarized graphically in Figure 4.21, assuming the truck was
manufactured by Ford, in Good condition and sold at a bankrupt auction. Variables
117
RNFI, RIR and MPY were set at their average levels. This graph shows that the
difference between the two models was more obvious compared with other models.
Table 4.78 - Comparison of B-C and A-E models for Trucks
SAMPLE SIZE (10%)
MAPE
SAMPLE SIZE (90%)
Log-likelihood Value
B-C
12
A-E
0.4021756
0.3022057
111
111
91.2347
56.16311
12
Figure 4.21 - Comparison of depreciation patterns of the B-C and A-E models for
Trucks
I
0.8
-IE-B-C
0:2
o L
1
3
5
7
9
AGE
11
13
15
17
118
CHAPTER 5
5.1
CONCLUSIONS AND LIMITATIONS
SUMMARIES AND COMPARISONS
The primary objectives of this study were to (1) update depreciation functions for
farm equipment; (2) estimate functions for several types of equipment not previously
analyzed and (3) compare the predictive abilities of several alternative functional forms,
particularly the Box-Cox and Additive-Exponential. Attention will now be focused on an
overview of the result and the implication they suggest.
5.1.1
Summary of the Data Distribution
The primary data used in this analysis were obtained from auction sales prices
reported monthly by Hot Line Inc. from 1984 to 1999, organized into four major groups:
tractors, harvesting equipment, harvesting and tillage equipment and other equipment
(See Table 5.1).
By far, the largest data sets were for tractors and combines, all of which had over
650 observations. Mower Cutters and Grinder Mixers had only about 50 observations.
The average remaining value by equipment category ranged from 0.12 to 0.44, and
the average age varied from 5.53 to 16.65 years. The average RV value generally
decreased as the average Age increased. For example, the oldest farm machinery, on
average, was Cotton Harvesters, which also had the average lowest remaining value
(0.12). One counter example was Skid Steer Loaders, which was the newest equipment
on average, but which did not have the average highest remaining value. This last result
underscores the fact that age is a primary factor affecting the RV value, but not the only
one. Other variables impacting the average RV are also summarized in Table 5.1. The
average value for HPY ranged from 198.84 to 1322.55, the average RNFI varied from
33.18 to 47.02, and the average RIR fluctuated between 1.059 and 1.067.
Table 5.1 - Summary of Data Distribution -- Average Data and Largest Frequency Data
Type of Farm
Machinery
Tractors
Sample
Size
RV
Average Data for
HPY*
AGE
RNFI
RIR
Largest Frequency for
Manufactures Auction Type
Less than 80 HP
657
80120HP
1420
783
0.372825
0.314382
0.231199
12.37534 233.0433
14.77376 283.4131
12.93678 342.5924
39.97748
40.60289
42.86469
1.060424
1.059811
1.059892
DEERE
DEERE
DEERE
1912
1845
0.318692
0.317644
13.86535
11.96195
325.3804
40.17029
42.23705
1.06055
105981
DEERE
DEERE
FARMRET
FARMRET
FARMRET
CONSIGN
FARMRET
FARMRET
0.214838 12.97145
0.331729 8.219388
0.129709 16.65333
0.213453 13.29947
0.355978 7.49697
0.27888 9.236842
0.321531 7.880184
0.430409 7.462963
198.842
42.7806
39.94594
47.02217
38.92
38.57529
36.31089
35.74111
1.060865
1.061755
1.063507
1.061477
1.061683
1.063057
1.063794
1.061326
DEERE
DEERE
DEERE
DEERE
DEERE
DEERE
NH
DEERE
FARMRET
FARMRET
FARMRET
FARMRET
FARMRET
FARMRET
FARMRET
FARMRET
1.063736
1.065774
1.067548
1.059931
DEERE
DEERE
IH
IH
FARMRET
FARMRET
FARMRET
FARMRET
1.0593
1.059315
NH
NH
CASE
FORD
FARMRET
FARMRET
FARMRET
BANKRUPT
120+ HP wi FWD
120145 wlo FWD
145+ HP wlo FWD
3849655
Harvesting Equipment
Combine
Corn_Header
Cotton Harvester
Swather
Baler
Forage_harvester
Mower Conditioner
Mower Cutter
2510
176
75
168
297
76
195
54
3902359
Planting and Tillage Equipment
Planters
Disks
Plows
Drills
239
125
97
72
0.428266 8.161654
0.271066 9.302158
0.272295 10.52778
0.39478 10.65278
36.64519
34.37417
33.18449
0.359532
0.441573
0.420553
0.317241
39.27008
38.44304
43.08308
34.84145
377988
Other machinery
Grmder Mixer
Manure_Spreader
Skid_Steer_Loader
Truck
*
41
81
94
163
HPY for trucks was not Hours per year, but miles per year.
8.878049
6.012346
5.531915
9.308943
1322.553
9799.864*
1.060326
1.062806
Table 5.2 - Comparison of the Significant Variables in the Box-Cox and Additive-Exponential Models
Type of Farm
Box-Cox
Additive-Exponential
Machinery
MANU
MANU
COND
AUC
OTHERS
MANU MANU COND
AUC
*AGE
Tractors
Less than 80 HP
-G,-F,-P
CI, DR,
MF,
80--i20 HP
120+ HP wI FWD
-MF, -IH,
120-445 w/o FWD
FD, DR
*AGE
-
MG
145+ HP wlo FWD
F
-G,-F,-P
F,D
-F, -P
F, D
-G, -F, -P
F, D
-G, -F, -P
F, B, D
RN, RI, A
-H,L, -CN
RN,-H, -A
RN,RI, -A
-H, -CN
RN,RI, -A
-H, -CN
RN,RI,-A
-H, -CN
CA, FD,
DR
-IH, -MF
-CG, FG
-DG
IG
CI, FD,
DR
-G, -F, -P
F
-G, -F, -P
-G, -F, -P
F, B
F, B, D
-G, -F, -P
F, D
-G, -F, -P
F, B, D
Combine
WH
-G, -F, -P
F, D
RN,RI,-A
-H, -CN
-G, -F, -P
F, D
Corn Header
Cotton Harvester
Swather
CA
-F
-G, -P
-G, -F, -P
F
RN,-A
-F
RN, -C,-A
-G,-P
F
B,D
RN
-G, -F
-G, -F, -P
F
RN, -CN
DR
-F
F,B
RN,-RI,
DR
F, B
CN, -A
RN, -A
-G, -F, -P
-B
-A
-F
RN
-G, -F
-P
Baler
AG,-CG
DR,IH,MF,
NH,HT,VS
CA, DR,
HT,IH, NH
-DG,
-HG-VG
-DG,
-HG -IG
Forage Harvester
Mower Conditioner
Mower Cutter
-HT
HG
-G, -F, -P
-DG,-HG
-NG
RN, -RI, A,
-H, L, CN
RN,-RI, -H
RN,-RI, -A
-H,CN
Harvesting Equipment
-AC
OTHERS
-G, -F
RN, RI, -A
-H, CN
RN, -RI,
-H
RN, RI,
-H, CN
RN, -RI
RN
RN, -RI
F
RN, CN
F
RN,-RI,
CN
F, B
Planting and Tillage Equipment
Planters
Disks
Plows
Drills
DR
-G,-F
-B
E, -P
-
-A
-D
-A
-B
F
RN, RI
Table 5.2 (Continued)
Other Machinery
Grinder Mixer
Manure_Spreader
Skid_Steer_Loader
Truck
-A
DR
-DG
-P
-G, -F, -P
F
-A
F
RN,-H,
-A
-RN, -H, -A
-F
F,C
F
FD, CV
-FG, -CVG
-G, -F, -P
RN,-H,
-
-A, CN
-RI,CN,A
Notations: 1. MANU=Manufacture; MANU*AGE=Manufacture* Age; COND=Conditions; AUC=Auction Type;
AC= Allis-Chalmers; CICaseIH; DR=Deere; MF= Massey-Ferguston; IH= International Harvester; CA=CASE;
FD=FORD; WH=White; NH= New Holland; HT= Hesston; VS= Versatile; CV=CHEV
AG=AC*AGE; CIGCI*Age; DG=DR*Age; MGMF*Age; IG=IH*Age; CAG=CA*Age; FG=FD*Age;
WGWH*Age; NG=NH*Age; HG=HT*Age; VGVS*Age; CVGCHEV*Age
E=Excellent; G=Good; FFair; P=Poor. (In most cases, Excellent is default.)
F= Farmer retirement; C=Consignrnent; BBankrupcy; D=Dealer closeout. (In most cases, Consignment is default.)
RNRNFI; RJRIR; A=Age; H=HPY; L=LDR, CN=Constant
122
Most equipment sold was in good condition. John Deere was the predominant
manufacturer of tractors, combines and most harvest equipment. New Holland was
important in manufacturing hay-harvesting equipment. Most equipment was sold by
consignment or when a farmer was retiring.
5.1.2 Summary of the Significant Variables in the B-C and A-E models
Table 5.2 provides a summary of the significant variables estimated in the Box-Cox
and Additive-Exponential models. The variables significant in both B-C and A-E models
at the 90% confidence level have been highlighted in bold. A negative indicates there was
a negative sign for the estimated coefficient; otherwise, the estimated coefficients were
positive.
Some conclusions regarding these variables can be derived from Table 5.2:
I. Manufacturers:
The manufacturer variables were generally insignificant in tractors in both B-C
and A-E estimations. They were few consistent patterns among these dummy variables
for both B-C and A-E model; and
John Deere variables, when significant, were always positive in sign. Only in one
case (Baler) was Deere positive for both models. In general, manufacturer seemed to
have little impact on the intercept for either model.
II. Manufacturer 'i4 Age:
Manufacturer seemed to have even less impact on the age coefficient than it did
on estimated intercept coefficients; and
Most manufacturer Age variables showed negative coefficients. In essence, this
means a faster rate of depreciation than exists for the default equipment. Again, however,
the general conclusion is that manufacturer makes little difference on the rate of
depreciation.
123
III. Condition:
Condition variables were generally significant in most types of farm machinery,
particularly those where many transactions were used in the data set; and
Condition variables Good, Fair and Poor coefficients were negative in all the
models, and generally become more negative as condition became worse. The average
difference between variables is shown as Figure 5.1. The intuitive knowledge suggests
that the remaining value decreases with reduced care. There was little difference, on
average between excellent and good condition, but moving to fair or poor condition
definitely impacted value.
Figure 5.1 - Average Discount Values for condition variables
0
-0.1
flA7
-0.09385
DB-C
A-E
-0.2
-0.3
-0.28511
-0.4
-0.5
-0.6
-0.7
-0.8 -
B-C
A-E
GOOD
-0.04722
-0.09385
FAIR
-0.1594
-0.28511
POOR
-0.36103
-0.66802
IV. Auction types
Auction type variables were generally significant in most types of farm
machinery; and
The coefficients for farmer retirement were most often significant and were
always positive. Dealer closeouts were significant in about one-third of the models, and
124
were always positive. Bankruptcy coefficients were also significant with the same
frequency as Dealer closeout, but the signs were mixed.
V. RNFI and RIR
Macroeconomic variables RNFI was generally significant in most types of farm
machinery. RIR was less significant than RNFI, but it kept its significance in all the
tractors;
RNFI was positive in all types of machinery, consistent with the prior hypothesis.
A strong agricultural economy does drive up equipment prices; and
RIR was mostly negative in the A-E estimation, but positive in the B-C
estimation. The hypothesis is that increasing real interest rates reflect higher borrowing
costs, which in turn make equipment purchases more expensive. The inconsistent signs
bring the validity of this variable into question.
VI. Age
In the Box-Cox estimation, the Age variable was significant for almost every type
of farm machinery. In the Additive-Exponential estimation, the Age variable was only
significant in tractors and some other machinery such as Skid Steer Loaders and Trucks;
and
The Age coefficient was negative for all B-C models except the under 80 HP
tractors. It is obvious that remaining value declines when the farm equipment becomes
old. The counter intuitive result for the small tractor category can possibly be attributed
to secondary demand for these tractors by hobby farmers.
VII. HPY
HPY was only available for Tractors, Combines, Skid Steer Loaders and Trucks,
but was significant in each type; and
In both B-C and A-E estimations, the coefficients of HPY were negative. Since
HPY measures the degree of using equipment, one may expect RV deceases when UPY
increases.
VIII. LDR
125
LDR only appeared in the Tractors with less than 120 HP. It was significant in the
less than 80 HP tractors, but not 80-120 HP tractors. This shows that the presence of front
loaders significantly increases the value of small tractors, but not that in the mid or large
size tractors.
5.1.3 Comparison of depreciation patterns in each category of farm equipment
To provide an intuitive understanding of the depreciation patterns presented by the
two models, a graphical comparison was provided following the tabular results for each
model.
Figures 5.2-11 provide this comparison from another perspective - comparing the
depreciation patterns for each category of farm equipment estimated by the B-C and A-E
models.
From Figures 5.2 and 5.3, it is not difficult to see that the depreciation pattern for
120+ HP tractors with FWD was generally distinguished from other types of tractors,
which suggests that the presence of FWD does make some difference on the remaining
value of tractors1. The less than 80 HP, 80-120 HP and 120-145 HP w/o FWD tractors
had similar depreciation patterns. Generally, tractors with FWD and tractors with larger
horsepower depreciated more rapidly than tractors without FWD and smaller HP. Several
reasons could contribute to this phenomenon: There are fewer substitutes on farms for
these tractors, so reliability becomes more important. Consequently, their values decline
more rapidly as age and use makes them more prone to breakdowns; and the faster rates
of technology change for these tractors may also speed up the depreciation rate.
For harvesting equipment (See Figures 5.4 and 5.5), Swathers showed the most
rapid depreciation in the early years and Forage Harvesters presented the fastest decrease
in the remaining value in the late life. Mower Cutters have the slowest depreciation rate
in both estimations. The lower salvage values of Swathers and Forage harvesters may be
Unfortunately, little attention was paid to this in previous studies. Most research before categorized
tractors according to the horsepower (See Table 5.4).
126
related with the fact that this equipment is only used for a specific period of time in
forage harvesting, so reliability becomes more important. Alternatively, technology may
be changing more rapidly for this equipment compared with other harvest equipment.
For planting and tillage equipment (See Figures 5.6 and 5.7), disks and plows
showed more rapid rates of depreciation. Drills presented the slowest depreciation rate in
the early life of farm machinery, while planters had the slowest decreasing rate in the
later years. Since disks and plows are used for difficult tasks that cause a lot of wear and
tear, they are more likely to depreciate rapidly early on. This fact may also explain why
fewer variables were found significant for tillage equipment compared with those in other
depreciation functions (See Table 5.2). The results suggest a relatively flat depreciation
pattern in late service life for plows and disks, since the remaining value will keep fairly
stable after being heavily worn during the initial use.
In the other types of equipment (See Figures 5.8 and 5.9), Skid Steer Loaders and
Grinder Mixers showed surprisingly similar depreciation patterns, with the remaining
values declining rapidly in their early years, but comparatively slowly in later years. This
is consistent with the fact that both equipments are heavily used in the agricultural
practice2.
Finally, 120-145 HP tractors, Mower Conditioners, Plows and Trucks were
compared to see how patterns differed between major categories (See Figure 5.10 and
5.11). Mower Conditioners and plows presented very similar depreciation patterns, with
rapid decline in the remaining value in their early life, and exhibited a fairly flat
depreciation pattern thereafter. This can be explained by the similar reason as above:
Both receive heavy use but, with regular maintenance, can last many years. Tractors also
exhibit a stable depreciation pattern, and their remaining values were higher than that of
the other three types. Changes on RV of trucks were most evident, from the highest value
in their early life to the lowest value in their late life.
2
Based on average HPY (Hours per year), Skid Steer Loaders are obviously more used than other types of
machinery: tractors and combines (See Table 5.1).
127
Figure 5.2 - Comparison of the B-C depreciation pattern for tractors
-- Less than
80 HP
0.6
>
.--80-120 HP
120+ HP
0.4
with FWD
-4'---120-145 HP
wlo FWD
0.2
*-145+ HP
wlo FWD
0
1
2 3 4 5 6 7 8 91011121314151617181920212223
Age
Figure 5.3 - Comparison of the A-E depreciation pattern for tractors
128
Figure 5.4 - Comparison of the B-C depreciation pattern for harvesting
equipment
-+- Combines
aCornHeaders
- - CottonHarvesters
x-- Swathers
"Balers
ForageHarvesters
MowerConditioners
1
2345678
9 1011 121314151617181920
- MowerCutters
Age
Figure 5.5 - Comparison of the A-E depreciation pattern for harvesting equipment
1
-4-- Combines
0.8
Headers
-----CottonHarvesters
0.6
-*- Swathers
0.4
-
-'- '-
02
---ForageHarvesters
-+--- MowerConditioners
0
1
3
5
7
9
11
Age
13
15
17
Balers
19
MowerCutters
Figure 5.6 - Comparison of the B-C depreciation pattern for planting and tillage
equipment
1
0.8
>
-.-- Planters
0.6
--Disks
-A--- Plows
0.4
)(-- Drills
0.2
o
1
2
34567
8
9 101112131415161718
Age
Figure 5.7 - Comparison of the A-E depreciation pattern for planting and tillage
equipment
129
130
Figure 5.8 - Comparison of the B-C depreciation pattern for other equipment
Figure 5.9 - Comparison of the A-B depreciation pattern for other equipment
'ManureSpreaders
e-- Skid-SteerLoaders
Figure 5.10 - Comparison of the B-C depreciation pattern for 120-145 HP
131
tractors, Mower-Conditioners, Plows and Trucks
-.--- 120-145 HP
Tractors
MowerConditioners
..--- Plows
Figure 5.11 - Comparison of the A-E depreciation pattern for 120-145 HP tractors,
Mower-Conditioners, Plows and Trucks
I
0.8
-.- 120-145 HP
0.6
Tractors
0.4
-*- Mower-
0.2
--- Plows
Conditioners
0
I
1
3
5
7
9
11
Age
13
-*--- Trucks
I1
I
15
17
19
Table 5.3 - Comparison of the MAPE, R2 and Log-Likelihood Value of the Box-Cox, Additive-Exponential, and Exponential Models.
Type of Farm
Machinery
Tractors
Less than 80 HP
80120HP
120+HPw/FWD
120-445w/oFWD
145+HPw/oFWD
Harvestin' E' u/s meid
Combine
Corn-Header
Cotton-Harvester
Swather
Baler
Forage-Harvester
Mower-Conditioner
Mower-Cutter
B-C
MAPE
EXP
A-E
B-C
R2
EXP
Size
0.6653
0.6293
0.8214
0.7597
0.8248
0.6199
0.6110
0.7713
0.7175
0.7599
657
1420
783
1912
1845
595.38
1661.99
1130.03
2354.15
2149.65
548.04
1018.20
879.73
2213.87
1820.75
0.8199
0.5976
0.8059
0.5453
0.5689
0.7437
0.5766
0.6151
0.7552
0.4266
2273
2652.52
168.18
205.47
144.99
205.47
50.59
140.36
39.25
2510
0.5427
0.5187
0.6676
0.5664
0.5394
3158.25
171.69
224.885
178.749
224.89
80.42
157.00
45.13
0.5190
0.4373
0.2252
0.5576
239
-
0.5117
0.4649
0.2186
0.6065
132.54
109.52
78.29
42.76
0.7841
0.6074
0.6311
0.7085
41
37.82
39.07
98.12
0.267
0.7837
0.5944
0.6565
0.7408
0.286
0.319
0.536
0.299
0.301
0.291
0.247
0.521
0.378
0.320
0.266
0.227
0.514
0.281
0.276
0.437
0.260
1.418
0.267
-
-
0.4249
0.442
0.722
0.433
0.219
0.4255
0.881
1.054
Size
73
158
87
212
205
249
20
19
33
-
-
-
-
0.524
0.384
0.431
22
-
-
-
-
0.326
0.362
0.295
27
1.609
1.351
1.301
14
0.436
0.437
0.426
11
0.75 15
176
75
168
297
76
195
54
Log-Likelihood Value
B-C
A-E
Size
Planting and Ti//age Equipment
Planters
Disks
Plows
Drills
-
125
97
72
657
1420
783
1912
1845
176
75
168
Better
Predicative
Ability
EXP
EXP
EXP
EXP
EXP
EXP
EXP
-
297
EXP
A-E
76
195
A-E
54
-
117.26
102.67
74.96
39.50
239
EXP
EXP
EXP
25.92
30.00
94.22
56.163
41
125
97
72
-
-
r £QU1flfllen
Grinder-Mixer
Manure-Spreader
Skid-Steer-Loader
Truck
0.402
0.302
12
81
94
ill
9 1.235
81
94
ill
EXP
133
5.1.4 Comparison of the B-C and A-E models
It's generally desirable for purposes of consistency to use the same functional form
for all types of farm equipment. No one form dominated in the previous results, so it was
beneficial to summarize all the results and determine which function was generally best.
Both B-C and A-E models were estimated based on the same data set with 90% of
total observations, and MAPEs predicted by both models were based on the same sample
size for the remaining 10% of total observations. The comparison results showed that
although B-C always generated a higher Log-likelihood value, in six cases the MAPE test
favored the A-B model.
In light of this evidence, it is worthwhile to examine the predictive ability of the
Exponential form, another common functional form for farm equipment. Summary
statistics are also provided in Table 5.3. The result suggested that the Exponential model
was superior to the B-C in all but one case. Initially this seems to make no intuitive sense.
If the B-C function can mimic the Exponential, why would it identify a functional
relationship that does not predict RV as well as the Exponential? The answer lies in the
nature of the three measurements.
MAPE was used to measure the predictive ability. This method has been illustrated
in Equation (3.10). Rewriting the Equation 3.10, we have
MAPE
R2
(5.1)
measures the goodness fit for the models and is calculated as follows:
y)2
R2
(yi y)2
(5.2)
We can also obtain a measure of how well the regression line fits data by using:
R2
SSR
SST - SSE
SST
SST
1
SSE
SST
(5 3)
where SST (total sum of squares) = SSR (regression sum of squares) + SSE (error
sum of squares).
134
The Maximum Likelihood Estimators are attractive because of their largesample or asymptotic properties: Consistency, Asymptotic normality, Asymptotic
Efficiency and Invariance (Greene, 1997). The likelihood equation is defined as a
function of the unknown parameter vector, 0:
f(x1 ...x,0)= fTf(x,,0)
For random sampling from a normal distribution, we have:
L(p., a) = I-I (2itcy2 )_1/2 e_E122)11_2
To maximize the log-likelihood value, we obtain the first derivatives from its log
form:
f(x) =lnL(jt,a)= _ln(2)_.lno.2 ------(x _)2
2
3lnL
3j.t
_--(xt)
1
2
and
2c
i
3 in L
2c
2c
(5.4)
i
The unbiased estimators can be obtained from Equation (5.4):
(x
il=x
and
)2
n-I
Consider the sample errors conform to a normal distribution, c-'N(O,
22) we maximize the log-likelihood function for c:
f(c)=_ln(2t)_!lncyI2
2
Since
2
?2),
(where
(5.5)
2c
(2 =SSE, we found that, J(*) increases when SSE decreases. This is
consistent with the fact that higher R2 indicates a lower SSE, which can be concluded
from Equation (5.3). Nevertheless, the MAPE seems to be independent from these two
measures. Rewrite the Equation (5.5) as follows:
f(s) = _-ln(27z)_.lno?2
2cr'2
(5), -y1)2
(5.6)
135
Comparing this equation with Equations (5.1) and (5.2) suggests that, although
those three seem to have some relationship, Equation (5.1) actually differs from other two
by taking the absolute value of the difference between y and 5', while the other two
square this difference.
As the statistical results show, the Box-Cox model generally had a better measure
of fitness (higher R2) than that of the Exponential model, and it also generated higher log-
likelihood values than that of the Additive-Exponential form. However, the predictive
abilities (measured by MAPE) of Exponential and Additive-Exponential forms were
superior to that of the Box-Cox.
The following table provides a general evaluation of the Box-Cox, AdditiveExponential and Exponential models:
Table 5.4 - Summary of the predictive ability, goodness of fit and Log-likelihood
value of the B-C, A-E and EXP models:
N
Functional
orms
Measure'N\
Box-Cox
-
Additive-Exponential
Exponential
RV*=o+X1*+Y
RV* and X are B-C
RVo+j31x1)ExP(f3Y)
transformed variables.
Predictive
Abilities
Goodness of
Fit
Loglikelihood
Value
5.1.5
Comparison With Previous Studies
The final comparison was between the previous studies and this research.
Unfortunately, most previous research focused on estimating models for tractors. Only
Table 5.5 - Comparison of previous studies with this thesis
Type of Farm
Machinery
This thesis (2001)
Transformations on
RV
AGE
Cross's thesis (1991)
Cross & Perry (1996)
Data
Size
Transformations on
0.67
0.63
0.82
0.76
0.82
657
1420
783
1912
1845
0.35
0.44
0.61
0.98
-0.43
0.48
0.68
0.68
421
0.52
0.52
0.83
0.83
0.30
0.30
0.77
0.77
528
489
0.82
0.60
0.81
0.55
0.57
0.74
0.58
0.62
2270
0.53
0.73
R2
RV
R2
AGE HPY
Data
Transformations on
Size
RV
Data
R2
AGE HPY
Size
Tractors
Less than 80 HP
80120 HP
120+HPw/FWD
120-445 w/o FWD
145+HPw/oFWD
0.4
0.11
0.4
0.61
0.59
0.6
0.14
0.51
0.49
0.42
0.19
-0.2
0.7
0.53
0.42
226
0.45
0.76
0.24
-
433
0.24
0.5
-0.03
-
1946
0.43
0.15
0.90
-
866
-
1026
Harvesting Equipment
Combine
Corn_Header
Cotton Harvester
Swather
Baler
Forage_harvester
Mower Conditioner
Mower Cutter
0.51
0.26
1.85
0.18
0.17
0.09
0.5
0.55
0.70
0.99
0.15
-
0.41
1.22
-
0.7
-
1.42
-
0.24
-0.12
176
75
168
0.42
0.72
0.67
0.47
-
-
-
-
-
0.72
0.60
511
108
140
-
-
-
-
-
-
0 29
-0 12
-
-
77
0.63
-0.32
-
-
185
116
-
-
-
297
76
0.31
0.33
0.50
0.74
-
-
195
54
-
-
97
72
0.48
0.58
0.62
0.75
-0.75
2.40
-
-
-
-
-
-
-
-
-
-
-
0.83
-
-
-
-
-
-
-
0.21
0.34
0.90
0.76
-
-
107
181
Plaiztiiig and Tillage Equipment
Planters
Disks
Plows
Drills
0.49
0.75
0.5
0.25
0.26
-
0.51
239
0.21
0.52
0.61
0.46
0.22
125
0.07
0.49
0.7
0.31
0.38
0.39
0.15
0.12
-
0.78
0.59
0.66
41
0.71
111
0.61
0.58
-
-
0.51
0.28
-
129
89
74
0.61
0.5
-
-
0.64
1.21
-
-
94
-
Other machinery
Grinder Mixer
Manure_Spreader
Skid Steer Loader
Truck
-
0.73
0.04
S
2. Cross, Timothy L, PhD thesis, unpublished.
94
-
81
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0.29
-0.4
1.26
-
-
0.36
0.36
-
55
63
-
-
-
-
-
-
-
-
137
previous studies by Cross (1991) and Cross and Perry (1995) were of sufficient
breadth to make this comparison. A comparison of these two studies with this thesis is
summarized
in Table 5.5. Results from this study were consistently close to those generated by Cross
and Perry. In some sense, this result might be expected because the data used by Cross
and Perry were also used in this study. However, the current study has a major increase in
the number of observations used in the estimated process, suggesting the functional form
parameters were fairly stable.
5.2
LIMITATIONS AND FUTURE THOUGHTS
Most of the results seemed to fit well with economic theory and practical intuition.
The study also improved on work in this area from several dimensions. First, this study
utilized more data in the regression estimates. The estimation of the old models,
therefore, became more reliable and accurate, and some new models were created.
Second, a new model, Additive-Exponential model was postulated and estimated. Third,
the comparison of the predictive ability by using the MAPE test was conducted among
models, which provided some new evidences: 1) Although the Box-Cox model excelled
in its goodness of fit and high log-likelihood value, it could not ensure good predictive
ability by MAPE measure; 2) The Exponential model had an overall better predictive
ability but was weak in fitting models to the data; and 3) The Additive-Exponential
model was moderately better for some types of equipment.
However, some limitations also existed in this study. The first problem encountered
was related with data. Although more data were available than the previous studies
(Bayaner and Perry et. al. 1990, Cross and Perry, 1991, 1995), some farm machinery such
as Grinder-Mixers, Mower-Cutters, and Cotton-Harvesters, still had small sample sizes,
prohibiting the use of the MAPE tests. At the same time, some auction sales reported to
Hotline could not provide enough details to describe a hedonic pricing model. The typical
138
missing information included auction type, condition and list price. The observations
without these information were discarded from estimation.
Some heavily used farm machinery such as Plows, Drills and Grinder-Mixers
generated relatively poor fits to the data. This problem complicated the estimation work
and thus resulted in few variables of significance.
It is also worthy to notice that the estimated functional forms were mainly
determined by old equipment, and therefore, cautions should be exercised in applying the
estimated models to new equipment.
This thesis will be useful in selecting a more appropriate depreciation model for
used farm equipment. It would also be helpful for identifying the optimal equipment
replacement patterns in the future research. More attention could be focused on the
exponential and other functional forms to solve the problem of relatively weak predictive
ability exhibited by the Box-Cox model.
139
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