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Agriculture and Agricultural Science Procedia 6 (2015) 704 - 711
"ST26733", International Conference "Agriculture for Life, Life for Agriculture"
DEA applicability in assessment of agriculture efficiency on areas with similar geographically patterns
Elena Tomaa, Carina Dobrea, Ion Donaa, Elena Cofasa*
University of Agricultural Sciences and Veterinary Medicine Bucharest, 59 Marasti, 11464, Bucharest, Romania
Abstract
Data envelopment analysis (DEA) is a non-parametric research technique based on a mathematical optimization method. Since was first developed in '78, the method is used in various sectors of economy and at different levels (companies, counties, regions, etc.). Our purpose is to apply DEA at regional level by using various inputs and outputs to analyse the performance of agriculture practiced in plain, hill and mountain areas. Thirty-six counties were classified into three categories based on their geographical main characteristics, respectively: group I - with 50-100% plain areas (20 counties); group II - with 50-80% hill areas (8 counties); group III - with 50-80% mountain areas (8 counties). For these groups were computed, under input-oriented option, CRS and VRS technical scores from which we calculated scale efficiencies. This empirical research shows that exists clear differences of performance between areas with similar geographical characteristics in terms of production factors (work, land and mechanization) allocation and outputs. Our results show that there are only 14 counties (5 in plain areas, 5 in hill areas and 4 in mountain areas) completely achieving DEA efficiency and operate at their optimal scale. In conclusion, in majority of areas the overall efficiency of agriculture is not reached, these regions needing to decrease the input levels (especially work hours that are too high compared with productivity) or to increase the output levels (production value) through a better use of fix capital and higher yields.
© 2015 Publishedby Elsevier B.V. This isan open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the University of Agronomic Sciences and Veterinary Medicine Bucharest Keywords: agriculture; data envelopment analysis; technical efficiency; scale efficiency
1. Introduction
DEA approach is a well-known technique utilized to evaluate the efficiency for peer units compared to the best practice frontier. This method is widely used by researches to analyse the performance of agricultural sector starting
* Toma Elena. Tel: +4-021-318-2564, Fax: +4-021-318-2888, Mobile: +4-072-333-1395 E-mail address: elenatoma2001@yahoo.com
2210-7843 © 2015 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the University of Agronomic Sciences and Veterinary Medicine Bucharest doi:10.1016/j.aaspro.2015.08.127
from different inputs and outputs. Taking in account that there is no need for a production function relation between inputs and outputs the possibilities of research are various. There are studies at regional level which analyse the production efficiency (Huang and Hu, 2006), productivity (Aldaz and Millan, 2003) (Zhou and Fawen, 2005), land use (Yuan et al, 2009) or irrigation use (Diaz et al, 2004), etc.
However, in agriculture, is very important the selection process of inputs because the outputs (production value, work productivity, etc.) depend upon these input consumption. If an area can obtain the current level of output with lower inputs then there can be assumed to be implemented a sustainable development of agriculture (Dalgaard, 2001). Also we consider that is very important to select 'units' with similar characteristics in terms of agriculture systems.
The geographical main characteristics are basic elements that imprint a pattern in the type of agriculture practiced in an area. We consider that is not entirely correct to apply a DEA analysis to areas that are so different from agricultural practice point of view, so in this paper we propose a classification of areas based on their main geographical characteristics.
2. Materials and methods
2.1. Data Envelopment Analysis
Since the DEA models were first developed, this method of converting multiple inputs into multiple outputs was used to evaluate the performance of business firms, regions, etc. and especially for modelling operational processes in performance evaluations (Cooper, 2011).
Data envelopment analyse is a non-parametric research technique, a mathematical optimization method based on a sequence of simple linear programs, used to evaluate technical efficiencies of "Decision Making Units" (DMU). DEA models can be input-oriented (objective: minimizing inputs while maintaining the same level of outputs) or output oriented (objective: increasing outputs with the same level of inputs) (Malana and Malano, 2006). Due to the specificity of agriculture sector which rely on a limited inputs, an input-orientated model is more appropriate. So our main objective was to measure efficiency under presumption that a DMU can produce the same amount of output by using a smaller quantity of inputs. Because each DMU use varying quantity of inputs to produce different levels of output, the method compare each DMU with the most efficient DMU.
For this type of analysis, in 1978 was created CCR model under the assumption of constant returns to scale (CRS) (Charnes et al., 1978) which estimates the gross efficiency of a DMU (Ramanathan, 2003) and in 1984, the researches were completed by the BCC model which takes in account the assumption of variable returns to scale (VRS) (Banker, 1984) and measures pure technical efficiency.
The models use the following notations: 'n' number of DMUs to be evaluated; each DMU have m inputs and produces s outputs; a DMUj consumes xij of input i and produces y^ of output r; ^ - the weights assigned by the linear program, 0 - the efficiency calculated; si and sr are the input and output slacks; s is a non-Archimedean element defined to be smaller than any positive real number (Markovits-Somogyi, 2011) (Vukelic, 2013). CRS input-orientated programming:
subject to:
^Xj jAj + St = 0xio ,i = 1,2
XpS^S? >0, j = 1,2, ...,n
VRS input-orientated programming:
Min 8 + £
subject to:
XijAj + St = 8xl0 ,i = l,2...,m
7 — 1
yr0,r = 1,2 ...,s
1; = 1
Aj-.Sf >0, j = l,2,...,n
The CCR model permits to obtain the technical efficiency (TE) and BCC model to calculate the pure technical efficiency score (PTE). Based on these scores we can measure the scale efficiency (SE) which reflects the potential productivity that can be gained by achieving an optimum size of a DMU [1]:
TE (3)
SE = -
For the analysis, we used MaxDEA 6.3 Beta free software, which permits the compilation of data under our option, respectively CRS (TE), VRS (PTE) and SE in an input-oriented model.
2.2. Data base construction
The Romanians territory comprises a particular pattern of distribution of reliefs 'forms. With the Carpathian Mountains in the middle surrounding the central area of the country, the plain areas are distributed on east, south and west counties. Based on these geographical characteristics and soil types (according to National Research and Development Institute for Soil Science, Agrochemistry and Environment Bucharest) the counties can be grouped into three categories, each of them with specific patterns for agriculture activities: (I) Plain 50-100%; (II) Hill 5080%; (III) Mountain 50-80%. We classified and described them based on these patterns in Table 1:
Table 1. County types based on their main relief form
_Type_Share of vegetal production(%)_Intervals of share of cereals surfaces (%)_Average size of farms -ha/farm-
BR (I) _682_60-65_7.63
CL 75.8 65-70 5.32
CT 74.8 65-70 11.21
GR 78.0 65-70 3.20
IF 74.2 55-60 1.92
IL 79.4 60-65 5.69
TR 76.2 65-70 4.84
BT 70.0 50-55 3.26
DJ 77.7 70-75 3.63
GL 78.2 65-70 3.60
IS 76.1 60-65 2.52
OT 76.3 75-80 3.01
TL 74.7 60-65 7.58
TM 67.2 75-80 3.45
AG 68.6 75-80 1.99
AR 74.3 70-75 6.31
Type Share of vegetal production(%) Intervals of share of cereals surfaces (%) Average size of farms -ha/farm-
BH 67.9 70-75 4.03
BZ 71.2 60-65 2.86
DB 74.1 70-75 1.60
SM 70.2 70-75 3.99
BC (II) 62.7 65-70 1.83
CJ 60.0 60-65 3.52
GJ 64.8 85-90 2.24
MS 64.2 60-65 3.30
SB 55.3 45-50 4.79
SJ 68.0 55-60 2.96
VL 59.5 80-85 1.58
VS 64.8 65-70 3.41
AB (III) 55.8 55-60 3.96
BN 54.4 50-55 3.62
BV 56.8 40-45 5.14
CS 61.5 60-65 6.07
CV 74.9 45-50 4.40
HD 60.1 60-65 3.97
HR 60.8 40-45 4.96
MM 53.3 40-45 2.40
Source: National Research and Development Institute for Soil Science, Agro chemistry and Environment Bucharest; National Institute of Statistics (Romania) - Tempo Online (2013)
The main characteristic of Romanian agriculture is the preponderance of vegetal production, from which the majority is assured by cereals. In hill and mountain areas, the cereals cover a smaller area but and almost 30-40% of areas are covered by fodder and meadows. The differences inside each group regarding average size of farms are very high and if we take in consideration the reduction of labor force in agriculture (Cofas, 2013) our research regarding the evaluation of the degree in which the production factors (land, work hours and mechanical assets) combination relate with the outputs (value of agricultural production) to assure performance is justified.
We constructed our database from the data offered by National Institute of Statistic -Agricultural Census Survey from 2002 and 2010. The main characteristics of variables in 2002 and 2010 are presented in table 2:
Table 2. Variables - descriptive statistics
Land (ha) Work (hours) Mechanical assets (number) Production Value (thou RON)
Plain areas (20 counties)
Minimum 103206 8173550 4758 473955
Maximum 703609 29629716 30317 1804029
Mean 392291 17708039 13335 981485
Std. Deviation 131908 5387054 6714 347456
Minimum 61987 4607874 3717 485169
Maximum 660738 22694715 29317 2562624
Mean 380723 15372168 13688 1308088
Std. Deviation 126796 4548975 6615 428544
Hill areas (8 counties)
Minimum 214486 7716270 5214 503451
Maximum 405579 22276083 13134 1386623
Mean 302258 16680596 8208 904022
Std. Deviation 78639 4655251 3181 338626
Minimum 188871 5504884 6365 547783
Maximum 374464 15602144 13884 1346958
Mean 271644 10891775 8928 834616
Std. Deviation 74119 3118526 2696 254997
Land (ha) Work (hours) Mechanical assets (number) Production Value (thou RON)
Mountain areas (8 counties)
Minimum 171102 8760664 6795 686152
Maximum 399335 20583846 12666 836448
Mean 270469 12830222 9896 777207
Std. Deviation 66996 3773797 2024 53619
Minimum 180148 4834122 5589 546541
Maximum 381386 11745847 12659 866493
Mean 273756 7791706 9482 709049
Std. Deviation 67153 2308231 2499 122464
Source: Own calculation
3. Results and discussions
3.1. Agriculture efficiency in plain areas
The scores of total technical efficiency (CRS) of counties from plain areas are presented in Table 3. It shows that the majorities of counties (70%) had an increasing score between 2002 and 2010, and that in 2010 almost all had a score over 0.5. Actually, if we analyse the frequency of scores 'distribution for 2010 (Table 4), we can observe that 35% of counties reach an efficiency level between 0.7-0.9. There are also 45% of counties that have outstanding performance efficiency (score value of 0.9-1). If we calculate the rate of technical efficiency under variable return to scale (VRS) we can see that 25% of counties in 2010 are identified as technically efficient and operating at the best practice. The increase of efficiency can be observed from the mean values calculated which reached values higher with 6.2% for CRS and with 2.2% for VRS (Table 5).
Table 3. TE, PTE and SE scores - plain areas - 2002 and 2010
DMU Technical Pure Scale RTS Technical Pure Technical Scale RTS SE
Efficiency Technical Efficiency Efficiency Efficiency Efficiency Variation
Score(CRS) Efficiency Score(VRS) Score Score(CRS) Score(VRS) Score (%)
2002 2010 2010/2002
01 0.769937 0.774488 0.994123 IRS 0.679194 0.69029 0.983924 IRS 99.0
02 0.943549 0.965453 0.977312 IRS 0.921326 0.933324 0.987145 IRS 101.0
03 0.800576 0.802224 0.997947 IRS 0.944138 0.956391 0.987188 IRS 98.9
04 0.712728 0.727537 0.979645 IRS 0.769937 0.774488 0.994123 IRS 101.5
05 1 1 1 CRS 0.922997 0.939586 0.982344 IRS 98.2
06 0.795546 0.799078 0.99558 IRS 0.881355 0.890614 0.989603 IRS 99.4
07 0.469187 0.47346 0.990976 IRS 0.943549 0.965453 0.977312 IRS 98.6
08 0.922997 0.939586 0.982344 IRS 0.800576 0.802224 0.997947 IRS 101.6
09 0.691023 0.692119 0.998416 IRS 1 1 1 CRS 100.2
10 1 1 1 CRS 0.691023 0.692119 0.998416 IRS 99.8
11 1 1 1 CRS 1 1 1 CRS 100.0
12 0.713236 0.71808 0.993255 IRS 0.712728 0.727537 0.979645 IRS 98.6
13 0.659825 0.71364 0.924591 IRS 1 1 1 CRS 108.2
14 1 1 1 CRS 0.795546 0.799078 0.99558 IRS 99.6
15 0.679194 0.69029 0.983924 IRS 1 1 1 CRS 101.6
16 0.921326 0.933324 0.987145 IRS 0.713236 0.71808 0.993255 IRS 100.6
17 0.944138 0.956391 0.987188 IRS 0.807558 0.829071 0.974052 IRS 98.7
18 0.881355 0.890614 0.989603 IRS 0.659825 0.71364 0.924591 IRS 93.4
19 1 1 1 CRS 1 1 1 CRS 100.0
20 0.807558 0.829071 0.974052 IRS 0.469187 0.47346 0.990976 IRS 101.7
Table 4. Efficiency distribution on score intervals in 2002 and 2010
Scores intervals 2002 2010
CRS TE VRS PTE CRS TE VRS PTE
<0.5 10.0 5.0 5.0 5.0
0.5-0.7 25.0 20.0 15.0 10.0
0.7-0.9 15.0 25.0 35.0 40.0
0.9-1 30.0 10.0 20.0 20.0
1 20.0 40.0 25.0 25.0
Source: Own calculation
Table 5. Mean efficiency measures in 2002 and 2010 2002 2010 Variation (%)
CRS - TE 0.787 0.836 106.2
VRS -PTE 0.827 0.845 102.2
Scale efficiency - SE 0.939 0.988 105.2
Source: Own calculation
The scale efficiency indicates that 75% of counties operate at an average of 0.988 score. This means that these counties could increase their technical efficiency by continuing to increase their inputs. Only 25% are operating at their optimal scale.
3.2. Agriculture efficiency in hill areas
The scores of total technical efficiency (CRS) of counties from hill areas (Table 6) show that the majorities of counties (62.5%) had also an increasing score between 2002 and 2010, and that in 2010 all had a score over 0.7. The frequency of scores from 2010 (Table 7) shows that 50% of counties reach an efficiency level between 0.7-0.9. There are also 50% of counties that have outstanding performance efficiency (score value of 0.9-1). The scores of efficiency under variable return to scale (VRS) prove that 37.5% of counties in 2010 are identified as technically efficient and operating at the best practice. The mean values calculate for the eight counties are higher with 3.4% for CRS and lower with 4.8% for VRS (Table 8).
Table 6. TE, PTE and SE scores - plain areas - 2002 and 2010
DMU Technical Pure Scale RTS Technical Pure Technical Scale RTS SE
Efficiency Score(CRS) Technical Efficiency Score(VRS) Efficiency Score Efficiency Score(CRS) Efficiency Score(VRS) Efficiency Score Variation (%)
2002 2010 2010/2002
01 1 1 1 CRS 1 1 1 CRS 100.0
02 1 1 1 CRS 0.835212 0.863052 0.967743 IRS 96.8
03 0.524631 1 0.524631 IRS 0.714609 0.882601 0.809663 IRS 154.3
04 0.966262 0.984722 0.981253 DRS 1 1 1 CRS 101.9
05 1 1 1 CRS 0.900326 1 0.900326 IRS 90.0
06 0.787751 1 0.787751 IRS 0.832121 1 0.832121 IRS 105.6
07 0.634304 1 0.634304 IRS 1 1 1 CRS 157.7
08 0.887295 0.891412 0.995382 DRS 0.74873 0.748752 0.999971 IRS 100.5
Source: Own calculation.
Table 7. Efficiency distribution on score intervals in 2002 and 2010
Scores intervals 2002 2010
CRS TE VRS PTE CRS TE VRS PTE
0.5-0.7 25.0 0 0 0
0.7-0.9 25.0 12.5 50.0 37.5
0.9-1 12.5 0 12.5 0
1 37.5 87.5 37.5 62.5
Table 8. Mean efficiency measures in 2002 and 2010
2002 2010 Variation (%)
CRS - TE 0.850 0.879 103.4
VRS -PTE 0.985 0.937 95.2
Scale efficiency - SE 0.865 0.939 108.5
Source: Own calculation.
The scale efficiency indicates that 62.5% of counties operate at an average of 0.939 score. was increasing with 8.5% and 62.5% of the counties are operating below their optimal scale. can affirm that, in hill areas, 62.5% could increase their technical efficiency by continuing to and almost 37.5% are operating at their optimal scale.
3.3. Agriculture efficiency in mountain areas
In mountain areas, 62.5% of counties show an increasing technical efficiency (Table 9). The scores calculated under constant return to scale (CRS) show that the majorities of counties had a score over 0.6. Compared with other counties, with plain and hill forms of relief, 50% of counties from mountain areas have high efficiency (score of 0.9-1), but their number decrease face to 2002 (from 62.5%) (Table 10).
However, even if the number of efficient counties decreased, the CRS and VRS average scores increased with 6.4% and respectively 5.2 (Table 11).
The scale efficiency indicates that 50% of counties operate at optimal scale, 37.5% operate under optimal scale and 12.5% operate above their optimal scale.
Table 9. TE, PTE and SE scores - plain areas - 2002 and 2010
DMU Technical Pure Scale RTS Efficiency Technical Efficiency Score(CRS) Efficiency Score _Score(VRS)_
2002 2010 2010/2002
01 1 1 1 CRS 1 1 1 CRS 100.0
02 1 1 1 CRS 0.835212 0.863052 0.967743 IRS 96.8
03 0.524631 1 0.524631 IRS 0.714609 0.882601 0.809663 IRS 154.3
04 0.966262 0.984722 0.981253 DRS 1 1 1 CRS 101.9
05 1 1 1 CRS 0.900326 1 0.900326 IRS 90.0
06 0.787751 1 0.787751 IRS 0.832121 1 0.832121 IRS 105.6
07 0.634304 1 0.634304 IRS 1 1 1 CRS 157.7
08 0.887295 0.891412 0.995382 DRS 0.74873 0.748752 0.999971 IRS 100.5
Source: Own calculation
Table 10. Efficiency distribution on score intervals in 2002 and 2010
Scores 2002 2010
intervals CRS TE VRS PTE CRS TE VRS PTE
0.5-0.7 0 0 12.5 0
0.7-0.9 37.5 25.0 37.5 37.5
0.9-1 12.5 25.0 25.0 25.0
1 50.0 50.0 25.0 37.5
Source: Own calculation
Table 11. Mean efficiency measures in 2002 and 2010
2002 2010 Variation (%)
CRS - TE 0.864 0.919 106.4
VRS -PTE 0.911 0.958 105.2
Scale efficiency - SE 0.947 0.959 101.2
The scale efficiency In this situation, we increase their inputs
Technical Pure Technical Scale RTS SE
Efficiency Efficiency Efficiency Variation
Score(CRS) Score(VRS) Score (%)
4. Results
The presented analyse comprise the data regarding the land use, work hours and level of mechanization from 36 counties that are grouped in three categories based on their predominant form of relief. As we can see from table 12, in 2010, the most technically efficient counties (CRS and VRS) are from mountain areas (with 50-80% mountain areas and around 75% cultivated area with cereals, fodder and meadows).
Table 12. Technical and scale efficiency situation on relief groups
_Category_2002_2010
CRS TE Plain 0.787 0.836
Hill 0.850 0.879
Mountain 0.864 0.919
VRS TE Plain 0.827 0.845
Hill 0.985 0.937
Mountain 0.911 0.958
SE Plain 0.939 0.988
Hill 0.865 0.939
Mountain 0.947 0.959
Source: Own calculation.
5. Conclusions
Our analyse shows that there are only 14 counties (5 in plain areas, 5 in hill areas and 4 in mountain areas) completely achieving DEA efficiency and operate at their optimal scale. The other counties need to change their input combination to reach a higher efficiency by decreasing especially the working hours (that are too high compared with productivity) or by increase the output levels (production value) through a better use of fix capital and higher yields. The results confirm the utility of using DEA models in the assessment of agriculture in areas with similar geographical patterns. But the method can be applied for other sectors too, like tourism or industry, due to more and more available software (like MaxDEA, DEA Frontier, PIM-DEAsoft, etc). The assessment of technical and scale efficiency at regional level remains in this way a real opportunity for future research in the field.
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