Output Orientated Efficiency Measurement Concepts
wise-linear convex isoquant, constructed such that no observed point lies to the left or below it see Figure 6. Second, a parametric function, such as Cobb-
Douglas form, fitted to the data, also such that no observed point lies to the left or below it. The below efficiency measures are defined in the context of CRTS
technology.
Source: Coelli, Rao, Battese, 1998
The piece-wise linear form of the non-parametric in DEA model cause a few difficulties in efficiency measurement. This appears because of the section of the
piece-wise linear frontiers which run parallel to axis see Figure 7 which do not occur in most parametric functions. Figure 7 illustrates the problem, where the
firm using combinations of inputs, point C and D are the two efficient firms, which define the frontier. Point A and B are inefficient firms.
T he technical efficiency of firm A and B are 0A΄0A and 0B΄0B,
respectively Farrell, 1957. However, the question whether the point A΄ is
efficient because at that point the input x
2
used can be reduced by the amount CA΄
and still produce output in the same amount. Excess in the use of inputs is known as input slack input excess. To provide an accurate indication of technical
Figure 7 Piece-wise Linear Convex Unit Isoquant S
S΄ x
1
y x
2
y
efficiency of a firm in DEA analysis is required reports of both the Farrell measure of technical eff
iciency θ and any non-zero input or output slacks. While, Koopmans 1951 in Coelli, Rao, Battese, 1998 defined that the firm is
only technically efficient if it operates on the frontier and furthermore that all associated slacks are zero.
Source: Coelli, Rao, Battese, 1998 S
S΄
x
1
y x
2
y A
A΄ B΄
B
D C
Figure 8 Efficiency Measurement and Input Slack
4 METHOD
This chapter is divided into three sections. First describes about information of data description. This includes type of data, data sources, data collection
method, and etc. Second describes about data processing and analyzing. It consists of description of processing data, analyzing data, model used, and variable used.
The last section describes about comparative test that used to compare efficiency score of two sub-districts.
4.1
Data Description
This study was conducted in Gekbrong and Warungkondang Cianjur Regency, West Java Province. Determination of location research was
purposively done because West Java Province is the biggest rice producer than the others and Cianjur Regency is one of the regencies in West Java, which is produce
rice. Data collection was conducted in May 2012. Data used in this study were
primary data in the form of cross section data and also secondary data. Primary data were obtained from direct observation in the field, direct interview, and
filling of the questionnaire. Secondary data were obtained from books, journals, reports, and literatures relevant to this research such as data from the Statistics
Indonesia, Statistics Indonesia of West Java, Ministry of Agriculture, Directorate General of Marketing and Processing of Agriculture, and the other related
institution. Sample was determined purposively. This study used 94 rice millers, which
was 44 rice millers in Gekbrong and 50 rice millers in Warungkondang. Technology used of all rice millers was similar. Thus, the occurrence of errors in
the calculation and bias assumption can be minimized. This study did not have a definite sample framework. Balai Pengembangan
Budidaya Tanaman Pangan dan Hortikultura Development Center of Food Crops and Horticulture did not have list of rice miller. This study coincided with
a survey being conducted by Statistics Indonesia about the number of rice milling. However, in order to address this limitation, this study used rice miller list from
memory of extension officer which is native who understand conditions in the site. This study also got information about existence of the rice miller from
society, owner of the rice miller visited, and so on. Then, this list was used as a guide to found rice miller in the field. Based on
field survey, there were 44 rice millers in Gekbrong. This number was insufficient to determine the efficiency of rice milling industry. In order to get more accurate
results, this study was expanded to neighboring sub-district. Purposively, Warungkondang selected as the study site by the main reason that Gekbrong was
part of this sub-district before regional expansion occurred. Thus, it was suspected that both sub-districts have similar characteristics of rice miller.
Similar to Gekbrong, this study also did not have a clear sample framework. So, sampling was done same way as in Gekbrong. Due to some limitations such as
materials, time, and field conditions, this study only used 50 rice millers in Warungkondang.