An empirical depreciation model for agricultural tractors in Spain

Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria (INIA)
Spanish Journal of Agricultural Research 2007 5(2), 130-141
Available online at www.inia.es/sjar
ISSN: 1695-971-X
An empirical depreciation model for agricultural tractors in Spain
M. L. Fenollosa Ribera and N. Guadalajara Olmeda*
Centro de Ingeniería Económica. Edificio 7j (ADE). Universidad Politécnica de Valencia.
Camino de Vera, s/n. 46071 Valencia. Spain
Abstract
This work analyses the market value of second hand agricultural tractors in Spain for the period 1999-2002, with
the aims of obtaining the most appropriate valuation models (through the use of ordinary least squares regression) and
proposing an empirical model that estimates the true depreciation of these vehicles. Differences in tractor depreciation
were studied in terms of the three horsepower groups normally employed (< 60, 60-90, > 90 hp), as well as in terms
of a new power classification (< 80, 80-133 and > 133 hp) that appears to better reflect the influence of horsepower on
the change in market value. The results show tractor depreciation to be exponential, with larger, more powerful tractors
depreciating more quickly than smaller machines.
Additional key words: agricultural machinery, Box-Cox models, power groups, remaining value.
Resumen
Modelos empíricos de amortización de tractores agrícolas en España
En el presente trabajo se analiza el valor de mercado de los tractores agrícolas de segunda mano en España, durante
el periodo 1999-2002, con el fin de obtener, por métodos de regresión mínimos cuadrados, los modelos de valoración
más apropiados y proponer un método empírico de amortización que estime la depreciación real. Asimismo, se estu-
dian diferencias de comportamiento de los tractores según los tres grupos de potencia utilizados normalmente en el
mercado ( <60, 60-90, > 90 CV) y se propone una nueva clasificación de potencias (< 80, 80-133, > 133 CV) que re-
fleja mejor los cambios del valor. Se demuestra que la depreciación es de tipo exponencial y mayor en los tractores
de mayor tamaño o potencia que en los pequeños.
Palabras clave adicionales: grupos de potencias, maquinaria agrícola, modelos Box-Cox, valor residual.
Introduction
Argentina]. However, the depreciation in the value
of farm machinery (the consequence of its use and the
The mechanization of agriculture has led to remarkable
passage of time) is without doubt more diff icult to
advances in the competitiveness of agricultural products,
understand. It is now common for business managers
reducing the costs of their production and increasing
to use theoretical models to try to estimate this. However,
the prof its enjoyed by farmers. Manual labour costs
rather than rely on such theory-based models, it would
have been gradually (although greatly) reduced, but
be better to take into account the change in the real market
machinery costs have increased, particularly those
price of these vehicles.
associated with fuel and lubricants, insurance, housing/
Theoretical models of depreciation can be classified
storage, maintenance, repairs and the depreciation rate.
into three main groups depending on the weight assig-
These last three components are often confused by
ned to each year of usage: linear, increasing or decreasing.
managers, who frequently, yet erroneously, understand
In Spain, only certain methods of determining the
them to be synonymous. Maintenance and repair cost
theoretical depreciation are officially accepted with a
are relatively easy to obtain and a number of studies
view to f iscal effects, but these models cannot gua-
in this area have been published [e.g., see Frank (2003),
rantee a true reflection of the depreciation suffered.
who studied these costs in combine harvesters in
In the USA, several authors have studied the depre-
ciation of the value of farm machinery using the
* Corresponding author: nguadala@omp.upv.es
«present value method» (Audsley and Wheeler, 1978;
Received: 22-08-06; Accepted: 30-03-07.
Musser et al., 1986). Other American authors (see below)

---

Depreciation of tractors in Spain
131
have sought to estimate the value of used machinery
Hansen and Lee (1991), Cross and Perry (1995), and
and thus determine its true depreciation. This has in-
Unterschultz and Mumey (1996) used information
volved the use of economic regression methods, which
from manufactures’ catalogues and concessionaires.
are well developed in the USA due to the large amount
All of these authors used the regression method to esti-
of information available. For example, Peacock and
mate the remaining value of machinery, taking into
Brake (1970), McNeill (1979), Leatham and Baker
account variables such as age and technical characte-
(1981), Reid and Bradford (1983), Perry et al. (1990),
ristics. Table 1 provides a brief summary of these im-
Table 1. Previous studies reporting equipment depreciation functions
Author
Data
Variables
Function
Peacock and Brake (1970)
Age
V = 65.6 – 4.1 * X
ASAE (1979)
Age
V = 68 * (0.923) X
McNeill (1979)
32
Age and state
V = e – 4299 – 0.0436*Age + 0.0691* State
Leatham and Baker (1981)
1,454
Age, power, motor
Ct = ?o * ?1 At * It ?2 * C0 * e?1
type, traction and
manufacturer
Reid and Bradforf (1983)
411
Age, power,
V = 368.7 * (X) – 0.273 * (hp) – 0.242 * (NF) –
manufacturer,
– 0.305 * (MX) – 0.121 * (MY) 0.263 * (T1) –
increasing usage and
– 0.621 * (T2) – 0.205
technological changes
Weersink and Stauber
Combined exponential
(1988)
Perry et al.(1990)
1,030
Age, power,
Box-Cox
manufacturer, usage,
care and
macroeconomic
variables
Hansen and Lee (1991)
1,612
Age, year of
1988
10
1985
manufacture, and
LP =
T
? LP + G
? LD + V
? LB
tgv
t
t
g
g
y
y
purchase year
t =1960
g=1
y=1917
Cross and Perry (1995)
Age, usage,
Box-Cox
manufacturer, care,
type of auction, region
and macroeconomic
variables
Unterschultz and Mumey
2,265
Age, manufacturer
Ratified by Hansen and Lee model
(1996)
Combine
3,202
Tractor
Cross and Perry (1996)
Age, usage,
Box-Cox (double square root)
manufacturer, care and
macroeconomic
variables
Dumler et al. (2003)
Age, inspection year,
Compares depreciation methods by regression.
power, manufacturer
and depreciation
method
Wu and Perry (2004)
Age, production year,
Box-Cox (for different machines)
manufacturer and other
After Fenollosa (2006).

---

132
M. L. Fenollosa and N. Guadalajara Olmeda / Span J Agric Res (2007) 5(2), 130-141
portant studies. The first concentrated mainly on trac-
Unknown age
520
tors and involved the use of linear models, but with
time they evolved and expanded to other types of
> 20 years
8,726
machinery and the use of more sophisticated, non-
linear models.
16-20 years
3,101
Cooper (1994) conducted similar studies in England,
11-15 years
3,189
using econometric models. In Spain, such studies have
only been performed by Arias (2001) and Guadalajara
6-10 years
3,652
(2002), and both were based on information obtained
from a second hand marketing publication «Marketing
3-5 years
1,838
Ocasión de Maquinaria Agrícola (MOMA)». The first
0-2 years
1,104
of these studies dealt with the depreciation in the value
of tractors using data corresponding to the last six
months of 1997. The main conclusions were that de-
Figure 1. Total number of tractor title changes in 2003 in Spain,
grouped by vehicle age. Source: ANSEMAT and MAPA data.
preciation was most intense during the first year, and
worse for four-wheel rather than two-wheel drive tractors.
The second study estimated depreciation in tractors in
1994 there were only 789,747. The second hand tractor
Spain and Italy during the years 2000 and 2001. In both
market in Spain is very important. Figure 1 shows the
countries the power, traction, and age of the machines
number of title changes in 2003 by machine age, and
were the most influential variables. It was also shown
draws attention to the fact that tractors over 20 years
that the life of a tractor in Spain is longer – in fact almost
old account for the largest number of transactions.
double that of a tractor in Italy.
Spain’s agricultural tractor population is therefore
Two promotions/legislations dating from 2005 have
largely obsolete. The average age of a working trac-
lent support towards making use of the real depreciation
tor is 16 years, and nearly one third (31.7%) are over
in the value of agricultural machinery in Spain: the
20 years old.
Plan Renove promoted by the Spanish Ministry of
The main aim of the present study was to determine
Agriculture, Fisheries and Food (MAPA), and the
the behaviour of the market value of second hand
introduction of the International Accounting Standards
agricultural tractors in Spain, and to obtain models that
(IAS). The Plan Renove provides a series of subsidies
estimate their value over their lifespan with respect to
for the renovation of Spain’s tractors; this is managed
their horsepower. This study shows that traditional
by the Autonomous Regions of Spain and supported
horsepower grouping appears to have no influence on
by the Asociación Nacional del Sector de Maquinaria
second hand value; a more suitable horsepower classi-
Agrícola y Tractores (ANSEMAT). The IAS system
fication is therefore proposed.
was introduced to better reflect the true market value
of farm equipment etc. The value set is meant to be the
most probable market price obtainable on a theoretical
Data sources
day of sale. It is recommended that this value be deter-
mined by an independent expert.
The source of information used for obtaining the
Information regarding the situation of agricultural
market price of used tractors was the MOMA cata-
machinery in Spain is provided by two official sources:
logue. The MOMA acts as an intermediary, buying and
the MAPA [for example in the publication «Análisis
selling tractors, and publishes lists of prices each se-
del parque de tractores agrícolas» (1996), and the
mester. In the present study, seven catalogues were
Registro Oficial de Maquinaria Agrícola en España
used, dating from December 1999 to December 2002.
(ROMA)], and a private source, the ANSEMAT. Both
A matrix was then created with 12,570 observations
sources recognize the importance of agricultural tractors
and with the 42 variables shown in Table 2. The first
in the farm machinery family, a consequence of their
two variables, the price the MOMA paid for a tractor,
major presence in the sector and their rising retail
and the MOMA sale price (values homogenised to
price.
2001 figures to avoid the effect of inflation), are the
In 2002 there were 946,053 tractors in Spain (73.57%
variables the proposed model hopes to explain. Two
of all agricultural machines in the country), while in
models were constructed, one to explain the MOMA

---

Depreciation of tractors in Spain
133
Table 2. Variables in the used tractor database
Number
Variable
Type
Variable significance
1
Vp
Quantitative
Purchase list price, in euros
2
V
Quantitative
Sale list price, in euros
3
Year
Quantitative
The homologation year; varies between 1973 and 1995
4
Appraisal year
Quantitative
The publication year of the guide or appraisal year of the tractor; varies bet-
ween 1999 and 2002
5
Semester
Binary
Semester of the year; takes the value of 0 if the first semester, 1 if the se-
cond semester
6
Age
Quantitative
Difference between the appraisal year (in the guide) and the homologation
year. Values available from 4 to 29 years
7
Power
Quantitative
Power, in hp; varies from 13 to 263
8
Cylinder
Quantitative
Number of cylinders; 1-8
9
Cil.turb
Binary
Indicates if the motor has turbo or not; 1 if yes, 0 if no
10
Traction
Binary
Type of traction; takes value of 0 if two-wheel drive and 1 if four-wheel drive
11
Wheel/chain
Binary
Takes value of 0 if tractor uses chains and 1 if uses wheel
12
Standard version
Binary
Takes value of 1 if standard version, 0 if not
13
Vers. fruit
Binary
Takes value of 1 if fruit version, 0 if not
14
Vers. vine
Binary
Takes value of 1 if vine version, 0 if not
15
Vers. art
Binary
Takes value of 1 if articulate version, 0 if not
16
Vers. rigid
Binary
Takes value of 1 if rigid version, 0 if not
17
Cabin
Binary
Takes value of 1 if there is a cabin, 0 if not
18
Air. cond
Binary
Takes value of 1 if air conditioned, 0 if not
19
Other charact.
Binary
Takes value of 1 if other special features are present, 0 if not
20
Manufacturer 1
Binary
Manufacturer: Agria
21
Manufacturer 2
Binary
Manufacturer: Antonio Carraro
22
Manufacturer 3
Binary
Manufacturer: Avto
23
Manufacturer 4
Binary
Manufacturer: Belarus
24
Manufacturer 5
Binary
Manufacturer: Case Internacional
25
Manufacturer 6
Binary
Manufacturer: Deutz
26
Manufacturer 7
Binary
Manufacturer: Deutz-Fahr
27
Manufacturer 8
Binary
Manufacturer: Ebro
28
Manufacturer 9
Binary
Manufacturer: Fendt
29
Manufacturer 10
Binary
Manufacturer: Fiat
30
Manufacturer 11
Binary
Manufacturer: Fiatagri
31
Manufacturer 12
Binary
Manufacturer: Ford
32
Manufacturer 13
Binary
Manufacturer: International
33
Manufacturer 14
Binary
Manufacturer: John Deere
34
Manufacturer 15
Binary
Manufacturer: Kubota
35
Manufacturer 16
Binary
Manufacturer: Lamborghini
36
Manufacturer 17
Binary
Manufacturer: Landini
37
Manufacturer 18
Binary
Manufacturer: Massey Ferguson
38
Manufacturer 19
Binary
Manufacturer: Pasquali
39
Manufacturer 20
Binary
Manufacturer: Renault
40
Manufacturer 21
Binary
Manufacturer: Same
41
Manufacturer 22
Binary
Manufacturer: UTB
42
Manufacturer 23
Binary
Manufacturer: Zetor
Source: Own elaboration.
purchase price, and one to explain the sale price. How-
the tractor is sold new), the appraisal year (or the year
ever, these models were very similar, and only the latter
when the catalogue was published), the publication
is therefore presented. The f irst four explanatory
semester, and finally the age of the tractor (estimated
variables are of a temporal nature: the homologa-
as the difference between the appraisal and homolo-
tion year (which is supposed to coincide with the year
gation years).

---

134
M. L. Fenollosa and N. Guadalajara Olmeda / Span J Agric Res (2007) 5(2), 130-141
A second group of variables refers to the mechani-
where k = constant, Va = value of a tractor model with
1
cal characteristics of the tractors: power (hp), number
an age of a1 years, and Va = value of a tractor model
2
of cylinders, and whether the engine has turbo capa-
with an age of a2 years (a2 > a1).
bility.
For multivariate techniques to be used, the data and
In a third group, the locomotive characteristics
the relationships between the variables must be normally
of the machine are taken into account: whether the
distributed, homocedastic, and linear. Following the
tractor is two-wheel or four-wheel drive, and whether
same method as other authors (see Table 1), Box-Cox
it has wheels or tracks. The model (standard, fruit,
transformations (Box and Cox, 1964) were performed
vineyard, articulated or rigid) is also taken into
for each variable (dependent and independent). This
account.
allows the use of functional forms ranging from geo-
The fourth group of variables refers to safety and
metrical to Cobb-Douglas forms to be obtained. All
comfort (the existence of a cabin, air-conditioning,
Box-Cox transformations were performed using the
wide or thin wheels, f ield of vision, old or modern
equation below [3]:
front, etc.).
Finally the tractor manufacturer appears as a dummy
? y? ?1
?
? ? 0
or binary variable; this has also been taken into account
Y (?) = ? ?
[3]
in other studies (for references see Table 1).
?ln y
? = 0
The number of hours of use of the tractors was a
?
further variable employed by some authors in their
When ? = 1, the variable retains its original form;
models, e.g., Perry et al. (1990), but this information
when ? = 0, a logarithmic transformation is performed.
was not available for the present study.
Consequently, the proposed model can now be repre-
sented by expression [4]:
Methodology
V * = b + b ? year * +b ? appraisalyear * +b ? semester +
0
1
2
3
+ b ?age *+b ? power * +b ?cylinder * +b ?cil turb +
4
5
6
7
Ordinary least squares (OLS) regression was used
+ b ?traction + b ?wheelchain + b ?cabin +
[4]
to obtain the depreciation model, and cluster analysis
8
9
10
to identify the new horsepower groups.
+b ?air cond + b ?other charac + c ?version
?
+
11
12
i
The relationship between the absolute remaining
+
d ?company
?
value, V, and the explanatory variables (Table 2) was
i
obtained with the general model shown below [1]:
in which the quantitative variables may be transformed
V = b + b ? year + b ? appraisalyear + b ? semester+
into equation [5]:
0
1
2
3
+ b ? age + b ? power + b
+
4
5
? cylinder + b ? cil turb
6
7
year* = year? ? 1 ;
+ b ?traction + b ? wheelchain + b ? cabin +
[1]
8
9
10
?
+b ? air cond + b ? other charac +
c ? version
?
+
11
12
i
appraisalyear* = appraisalyear? ? 1 ;
+
d ? companies
? i
?
[5]
where b0, b1, ……, bn represent the regression coeffi-
age* = age? ? 1 ; power* = power? ?1 ;
cients of the explanatory variables.
?
?
It was not possible to obtain the monetary values of
tractors under four years of age; the catalogue contai-
cylinder* = cylinder? ? 1 ; V * = V ? ? 1
?
?
ned no data for these years. However, using the follo-
wing expression, it was possible to obtain relative
Once the corresponding models were obtained,
monetary values for any year of usage between 4 and
the adherence to normality, homocedasticity and
29 years:
linearity was checked by means of residual analysis.
Cluster analysis (Peña, 2002) was then used to group
V
?
a
b age(a ) + k
1
= 4
1
[2]
elements or variables into homogeneous classes de-
V
b ? age(a ) + k
a
4
2
2
pending in the similarities between them.

---

Depreciation of tractors in Spain
135
General depreciation model
Tractor power, age, type of traction, the presence or
not of air-conditioning, and the manufacturer together
The model1 constructed is of the linear-logarithmic
explained 89.8% of the value of the used tractors. Power
type; Table 3 shows the results obtained with this
alone explained 47.73% of the value, while power and
model.
age together explained 73.4%. The variables semester
Figure 2 shows that, in the model, the requirements
and appraisal year were not included in the proposed
of linearity, normality and homocedasticity were
model; these factors did not seem to influence tractor
adhered to since no clear tendency was seen in the
value during the period 1999-2002. Neither were the
dispersion between the predicted typified values and
variables number of cylinders, turbo-capability, tractor
the typified values of the residuals.
version, the presence of a cabin, etc. (see Table 2) taken
Table 3. Econometric estimates of variables in remaining value equation
Standard
Non-standard coefficients
coefficients
Model
t
Sig.
B
Typ error
Beta
Constant
5.601
0.037
150.534
0.000
Ln. Power
0.720
0.005
0.528
132.851
0.000
Age
–0.048
0.000
–0.415
–122.128
0.000
Traction
0.249
0.004
0.215
68.660
0.000
Air. Cond
0.116
0.006
0.068
18.629
0.000
Manufact 1
0.766
0.031
0.188
24.416
0.000
Manufact 2
0.895
0.034
0.154
26.452
0.000
Manufact 4
0.165
0.035
0.024
4.660
0.000
Manufact 5
0.965
0.030
0.340
31.986
0.000
Manufact 6
0.959
0.031
0.235
30.660
0.000
Manufact 7
1.001
0.030
0.386
33.306
0.000
Manufact 8
0.741
0.030
0.261
24.651
0.000
Manufact 9
1.391
0.030
0.486
46.200
0.000
Manufact 10
1.001
0.030
0.509
33.930
0.000
Manufact 11
1.291
0.046
0.108
28.041
0.000
Manufact 12
0.929
0.030
0.400
31.186
0.000
Manufact 13
0.965
0.031
0.243
31.054
0.000
Manufact 14
1.196
0.029
0.691
40.615
0.000
Manufact 15
0.787
0.031
0.253
25.704
0.000
Manufact 16
0.988
0.030
0.422
33.254
0.000
Manufact 17
1.027
0.031
0.273
33.124
0.000
Manufact 18
1.043
0.030
0.537
35.268
0.000
Manufact 19
0.881
0.032
0.197
27.481
0.000
Manufact 20
0.927
0.030
0.382
31.080
0.000
Manufact 21
0.835
0.029
0.441
28.381
0.000
Manufact 23
0.459
0.033
0.086
13.981
0.000
Manufact 24
0.400
0.031
0.111
13.040
0.000
Dependent variable: Ln V.
Summary of the model
R
R squared
Adjusted R squared
Typical error of estimation
0.948
0.898
0.898
0.18460
1 The number of observations, 12,570, was very large and though the number of considered variables, 42, was also high, the number
of freedom degrees is more than sufficient for the statistical tests to be trustworthy. The fact that 35 of the variables were dummy
suggests there may have been a bias in colinearity and in the matrix calculations since many columns had zeros.

---

136
M. L. Fenollosa and N. Guadalajara Olmeda / Span J Agric Res (2007) 5(2), 130-141
Histogram (Ln VDF)
P-P normal (Ln VDF)
Dispersion graph (Ln VDF)
4,000
1
6
4
3,000
0.8
2
0
2,000
0.5
–2
equency
Fr
–4
1,000
0.3
–6
–8
0
0
–10
–9.5 –7.5 –5.5 –3.5 –1.5 0.5
2.5
4.5
0
0.3
0.5
0.8
1
–6
–4
–2
0
2
4
Residual regresion
Accumulated probability
Predicted value
Figure 2. Histogram, P-P normal and dispersion graphs (residuals and predicted values).
into account due to their high correlation with horse-
Expression [6] can be used to estimate the percen-
power; their inclusion would have generated an undesi-
tage value of the tractor with respect to its value at 4
rable multicolinearity effect. The model allows some
years. Figure 3 shows the change in the remaining value
clear conclusions to be drawn: greater horsepower,
with respect to the value at 4 years.
four-wheel drive, and the presence of air-conditioning
To attempt to determine the change in a tractor’s
increases the price of used tractors, and age reduces it.
value over its entire life, information was collected on
When there is equality across these factors, the manu-
showroom prices2. This allowed the remaining value
facturer affects the price; Avto tractors (Manufacturer 3)
of a 4 year-old tractor to be determined as a percentage
were the cheapest, and Fendt tractors (Manufacturer 9)
of its showroom price. Table 4 shows the percentages
the most expensive.
obtained (column 2) for tractors made by the seven main
The value that a tractor can demand over its life
manufacturers. In the third column, the table shows the
since its fourth year is shown by expression [6].
same for 29 year-old tractors calculated using equation
[6]. Thus, a 4 year-old tractor maintains 56.16% of its
Va1 = e?0.048*a1 + k ; V
(a ?a )
2
1
a
= V * e?0.048*
[6]
showroom value, and 16.78% of this when it has reached
a
2
1
V
e?0.048*a2 + k
a
the age of 29 years. In other words, during the f irst
2
four years of a tractor’s life, its value depreciates by
43.84%; during the following 25 years it falls by a further
39.38%.
100
90
Table 4. Average percentage of the remaining value com-
80
pared with the new value (seven manufacturers)
70
60
Manufacturer
4 years old
29 years old
50
40
Lamborghini
56.46%
16.87%
30
Deutz 51.46%
15.38%
Remaining value (%) 20
Case
46.39%
13.86%
10
John Deere
62.24%
18.60%
0
Same
47.12%
14.08%
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Massey Ferguson
66.88%
19.99%
Age (years)
Landini
62.60%
18.71%
Figure 3. Remaining value by year with respect to value in the
Average
56.16%
16.78%
fourth year.
2 For new tractors, data was compiled from the MOMA web page.

---

Depreciation of tractors in Spain
137
100
Models of depreciation
90
by power group
80
70
Since horsepower was the variable that most influenced
60
tractor value (explaining 47.73%), a model of deprecia-
50
40
tion by power group was sought (as undertaken by
Perry et al., 1990; Arias, 2001; Guadalajara, 2002) in
30
Remaninig value (%) 20
order to invest the variable age with more influence,
10
and to identify any differences in depreciation be-
0
haviour between tractors of different horsepo-
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
wer. Based on the work of Arias (2001), three groups
Age (years)
of tractors were identif ied: small (? 60 hp, about
Figure 4. Remaining value by year.
28.8% of all tractors considered), medium (60-90 hp;
41.8%) and large (> 90 hp; 29.35%). Table 5 shows the
Consequently, assuming an average value of 56.16%
coeff icients used in the depreciation model in each
of the showroom price when a tractor is four years old,
group.
the original Figure 3 can be expanded to include the first
The most influential variable in all groups was age,
four years of tractor life. Figure 4 shows the remaining
followed by power and manufacturer in the case of the
value over the entire life span.
smaller tractors. The type of traction did not influence
Table 5. Econometric estimate of remaining value equation variables with respect to power groups
Dependent variable: Ln V
Small tractors
Medium tractors
Large tractors
Constant
5.7127
5.2629
6.7270
Ln Power
0.6430
0.7915
0.5554
Age
–0.0410
–0.0455
–0.0583
Traction
0.2459
0.2883
Air. Cond
0.1291
0.1076
Manufacturer: Agria
0.9972
0.5046
Manufacturer: Antonio Carraro
1.2262
Manufacturer: Avto
0.2911
0.2939
–0.1432
Manufacturer: Belarus
1.1922
0.8927
0.7707
Manufacturer: Case Internacional
1.3463
0.9613
0.7583
Manufacturer: Deutz
1.1956
1.0253
0.7292
Manufacturer: Deutz-Fahr
0.7440
0.7326
0.5656
Manufacturer: Ebro
1.7066
1.3803
1.1211
Manufacturer: Fendt
1.1526
1.0088
0.8133
Manufacturer: Fiat
1.0755
Manufacturer: Fiatagri
0.9963
0.9700
0.6917
Manufacturer: Ford
1.0119
0.9381
0.8029
Manufacturer: Internacional
1.2645
1.2675
0.9848
Manufacturer: John Deere
1.0356
0.7944
0.4288
Manufacturer: Kubota
1.2028
1.0378
0.6864
Manufacturer: Lamborghini
1.2509
1.0057
0.7941
Manufacturer: Landini
1.0792
1.0541
0.7784
Manufacturer: Massey Ferguson
1.1204
Manufacturer: Pasquali
1.0692
0.9284
0.7357
Manufacturer: Renault
1.0230
0.8477
0.5977
Manufacturer: Same
0.7131
0.2711
0.1600
Manufacturer: UTB
0.3735
0.4622
0.3545
Adj. R2
79.00%
86.60%
88.00%

---

138
M. L. Fenollosa and N. Guadalajara Olmeda / Span J Agric Res (2007) 5(2), 130-141
the value of the small tractors, nor did the presence of
A proposed classification
air-conditioning; the smallest tractors do not have
of tractors by power group;
sufficient power to run air-conditioning or four-wheel
drive systems.
effect on depreciation
In the other two groups, the type of traction and
the presence of air-conditioning were more influential
The above grouping of tractors by horsepower is that
on the price than the power of the machines them-
most commonly used. However, in terms of tractor de-
selves.
preciation, this may not be the most adequate. Figure 5,
Thus, more powerful tractors suffer greater de-
for example, shows the depreciation curves of small
p r e c i a t i o n t h a n t h o s e o f t h e o t h e r g r o u p s ; t h e
and medium tractors to be very similar. Cluster analysis
coefficient of the age variable is greater. In fact, even
was therefore used to obtain a different power classifi-
though the mean age of tractors in the three groups
cation3 that worked better with the depreciation model.
was 16 years, the most common age for large tractors
Table 6 shows the results obtained with the central
was 11 years, while the medium tractors had a mean
values for each cluster and the number of observations.
age of 15 years and the small tractors a mean age of
The resultant classif ication was: small tractors (13-
23 years.
79 hp), medium tractors (80-133 hp), and large tractors
Starting with the coeff icients for the variable
(134-263 hp). According to this new classification, the
«age» in each category (Table 5) and applying an
number of small tractors represented 62.66% of the
expression equivalent to [2], the change in value of a
total observations, medium tractors 31.52%, and large
tractor by power group from its fourth year is repre-
tractors 5.82%. Econometric models were obtained for
sented by:
each of these new tractor group (Table 7).
In general, with the new cluster classification the
— Small tractors: V
(a ?a )
2
1
a
= V * e?0.041*
[7]
a
model better reflected the influence of horsepower on
2
1
the change in market value. In small tractors, traction
— Medium tractors: V
(a ?a )
2
1
[8]
became a more important variable since, under the new
= V * e?0.0455*
a
a
2
1
rating, these have more power and therefore more
— Large tractors: V
(a ?a )
2
1
a
= V * e?0.0583*
[9]
chances of having four-wheel drive. This classification
a
2
1
is similar to that used by Cross and Perry (1996) (< 80,
See Figure 5 for a graphical representation.
80-150, > 150 hp) and Wu and Perry (2004) (< 80, 81-
120, 121-145, > 145 hp).
With respect to medium tractors, a number of va-
100
riables, such as air conditioning, were no longer impor-
90
tant. With respect to the larger tractors, the variables
80
important in their depreciation remained the same.
70
The coefficient of the variable age did not vary in
60
the new group of small tractors (–0.041), but it increased
50
40
in the corresponding groups of medium (–0.0569
30
instead of –0.0455) and large tractors (–0.0687 instead
Remaining value (%) 20
10
Table 6. Cluster analysis for defining the three horsepower
0
groups
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Age (years)
Centre conglomerate groups
Small tractor (P ? 60 hp)
1
2
3
Medium tractor (60 hp < P < 90 hp)
Large tractor (P ? 90 hp)
Power
100
167
59
Number of observations
Figure 5. Remaining value by year for different tractors sizes
in each group
3,963
731
7,876
with respect to value in the fourth year.
3 A further cluster classification was obtained with four groups: small tractors (? 57 hp), medium tractors (> 7 to ? 87 hp), large tractors
(> 87 to < 138 hp), and extra large tractors (? 138 hp). However, this did not provide any advantage over the use of three groups.

---

Depreciation of tractors in Spain
139
Table 7. Econometric estimate of remaining value equation variables by cluster analysis-defined horsepower groups
Dependent variable: Ln V
Small tractors
Medium tractors
Large tractors
Constant
5.1394
10.2678
5.7399
Ln. Power
0.7911
0.7805
Age
–0.0410
–0.0569
–0.0687
Traction 0.2473
0.2859
0.3464
Air. cond
0.2462
Manufacturer: Agria
0.8497
Manufacturer: Antonio Carraro
1.0159
Manufacturer: Avto
0.2390
–0.2362
Manufacturer: Belarus
0.9921
–0.1823
0.7548
Manufacturer: Case Internacional
0.9808
–0.1689
0.6262
Manufacturer: Deutz
1.0863
–0.2431
0.4226
Manufacturer: Deutz–Fahr
0.7252
–0.3759
0.4492
Manufacturer: Ebro
1.4678
0.1574
1.0494
Manufacturer: Fendt
1.0694
–0.2142
0.7789
Manufacturer: Fiat
0.7377
Manufacturer: Fiatagri
1.0248
–0.3340
0.4972
Manufacturer: Ford
0.9793
–0.1886
0.8647
Manufacturer: Internacional
1.2503
0.8154
Manufacturer: John Deere
0.8947
–0.5341
0.2059
Manufacturer: Kubota
1.0562
–0.2281
0.3761
Manufacturer: Lamborghini
1.0968
–0.1984
Manufacturer: Landini
1.0873
–0.1192
0.4751
Manufacturer: Massey Ferguson
0.9768
Manufacturer: Pasquali
0.9979
–0.3362
0.6932
Manufacturer: Renault
0.8866
–0.4047
0.3271
Manufacturer: Same
0.5493
–1.0346
Manufacturer: UTB
0.4011
–0.7242
0.4739
Adj. R2
86.98%
84.22%
93.46%
100
of –0.0583). Thus, the new classif ication obtained
90
greater differences in depreciation.
Analogously, using these coefficients and applying
80
expression [2], the change in value with age for each
70
power group is represented by:
60
— Small tractors (P < 80 hp):
50
V
(a ?a )
2
1
a
= V * e?0.041*
[10]
a
40
2
1
30
— Medium tractors (80 hp ? P ? 133 hp):
Remaninig value (%) 20
V
(a ?a )
2
1
a
= V * e?0.0569*
[11]
a
2
1
10
— Large tractors (P > 133 hp):
0
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
V
(a ?a )
2
1
[12]
= V * e?0.0687*
a
a
2
1
Age (years)
See Figure 6 for a graphical representation.
Small tractor (P ? 80 hp)
Medium tractor (80 hp < P < 133 hp)
Large tractor (P ? 133 hp)
Conclusions
Figure 6. Remaining value by year for cluster analysis-defined
tractor sizes with respect to value in the fourth year.
The following conclusions can be drawn:

---