Measurıng the Effıcıency of Resource Allocatıon ın Turkısh Economy Usıng Data Envelopment Analysıs[1]
Esra Alp[2]
Abstract
The study aims to analyze the efficiency of resource allocation for industrial and service sectors in Turkish economy. It focuses on allocation of fixed resources and costs across the sectors as decision making units and setting targets for outputs simultaneously. Data envelopment analysis is being used for allocating inputs and setting targets for outputs. Data includes fixed capital investments, foreign direct investments, cost of employes as inputs and sectoral gdp, production volumes, turnovers and added values as outputs. Findings show that fixed resources and costs allocation across the sectors doesn't provide efficiency condition for Mining and quarrying, Manufacturing, Information and communication, Human health and social work activities sectors during 2009-2014 period. Therefore funds transfer needs to be reviewed. As the most productive sector manufacturing industry which is more likely to contribute to sustainable economic growth, has to be stimulated for more investments.
Keywords: Resource Allocation, Data Envelopment Analysis, Efficiency, Target Setting
Jel Codes: C14, D29.
- Introduction
Farell’s (1957) study was the first research on production efficiency measurement and study of Charnes, Cooper, and Rhodes (1978), introduced a non-parametric technique, data envelopment analysis (DEA) to evaluate relative efficiency of homogeneous decision making units (DMUs). This model is known as CCR model in DEA literature. The CCR model captures both technical and scale inefficiencies. Banker et al. (1984) proposed a new model (called BCC model) that extends the traditional CCR model by separating technical efficiency and scale efficiency (Bi et al., 2011).
As Lozano and Villa (2004) stated, in traditional DEA models, to analyze each DMU’s relative performance, they are each separately projected onto the efficient frontier. When carrying out a resource allocation analysis it would project the units onto the efficient frontier as in conventional DEA but in a joint manner instead of separately. They call their approach centralized or intraorganizational resource allocation because it assumes that all DMUs are under the control of a centralized DM. Hence, conventional DEA models do not take into account aggregate input consumption and aggregate output production, different approaches arised in a joint manner in last two decades. Following various attempts proposing centralized DMU approach, with input orientation Golany et al. (1993), output oriented model Golany and Tamir (1995), goal programming model (GoDEA) for centralized planning Athanassopoulos (1995), and other alternative methods presented by Fare et al. (1997), Cook and Kress (1999), Kumar and Sinha (1999), Beasley (2003), Korhonen and Syrjänen (2004); Lozano and Villa (2004) proposed a general centralized resource allocation model, at the same time that looked for the efficiency of the individual operating units, aimed at a global objective of minimizing total input consumption (or maximizing total output production). Centralized resource allocation model (CRA-BCC) had been extended through several studies Lozano and Villa (2005), Asmild et al. (2009), Noura et al. (2010), Bi et al. (2011), Yu et al. (2013), Fang (2013), Du et al. (2014). The idea behind this new model is to globally reduce the total use of inputs or globally augment the production of all outputs. Thereby a central management in charge of all the DMUs can optimize the resource utilization of all DMUs across the total entity, contrarily to traditional DEA models, that optimize the functioning of each DMU separately (Asmild et al., 2009).
In this study, all decision making units are being assumed to manage under the control of a central unit. Decision making units are industrial and service sectors[3] in Turkish economy. The central unit that is supposed to be responsible for the decisions of resource allocation across sectors can be thought of as government or a ministry etc. Data includes 2009-2014 period for input variables; employes cost, foreign direct investments, fixed capital investments and output variables; GDP, production volumes, turnovers and value added per sector[4]. The rest of this study is organized as following: Section 2 provides mathematical background of traditional DEA models, in section 3 centralized DEA model is being introduced, section 4 presents the emprical analysis results and section 5 gives conclusion remarks.
- Background of Traditional DEA Models
Suppose that there are n DMUs producing the same set of s outputs by consuming the same set of m inputs (Du et al., 2014). The performance of each DMU is characterized by a production process of m inputs (xij: i = 1,...,m) to yields s outputs (yrj: r = 1,...,s). The efficiency measure for DMUo is defined as following (Amirteimoori and Tabar, 2010):
and are positive. When estimating the DEA efficiency of DMUo, we solve the following DEA model (Charnes et al., 1978):
for all r, i,
means a non- archimedean construct defined to be smaller than any positive real number. To eliminate this linear fractional programming problem by reducing it to a non-ratio format (Charnes and Cooper (1962). After transformation as below:
And let , then we can express (1) as:
for all and .
DMUs efficiency ratios changes between “0” and “1” . DMUo is being considered efficient relatively if the ratio receives a score of “1”. BCC model was introduced by Banker et al. (1984) as an input oriented type of DEA under the assumption of variable returns to scale. It can be written in the form as below (Kocisova, 2014):
is technical efficiency of DMUq, is produced amounts of output of DMUq, is consumed amounts of input of DMUq; is produced amounts of output of DMUj , is consumed amounts of input of DMUj , is weight assigned to the DMUj in input oriented BCC model.
- Centralized Resource Allocation Model
When considering a central decision unit exists in charge of allocation problem for all DMUs, then cost minimization by reducing total inputs at the same output levels or target setting for outputs become possible. The input-oriented DEA model termed as BCC model which is stated above in equation (3) can be used for measuring technical and cost efficiencies under the assumption of variable returns to scale. To measure cost efficiency of each DMUs (Coelli et al., 2005):
In equation (4), wiq; is a vector of input prices of DMUq, x*iq; is the cost minimising vector of input quantities for DMUq and yrq; is the output levels. The overall cost efficiency (CEq) is defined as the ratio of minimum cost of producing the outputs to observed cost of producing the outputs for the DMUq (Coelli et al., 2005):
The overall cost efficiency can be expressed as a product of technical and allocative efficiency measures. Therefore, the allocative efficiency of the DMUq can be calculated as ratio of overall cost efficiency (CEq) to input-oriented technical efficiency (TEq).
DEA also can be used to set “input minimisation” or “output maximisation” targets for inefficient DMUs based upon their position relative to the efficient frontier (Beasley, 2003). Assume a set A of n DMUs all using m inputs to produce r outputs. The set A can be divided into the subset E of p efficient points and the complementary subset I of q = n − p inefficient points, by initially considering for instance an additive DEA model. The first (radial) phase of the input oriented radial CRA-BCC proposed by Lozano and Villa (2004) had been reformulated by Asmild et al. (2009) as below:
The CRA-BCC model as is shown above has m + r + n restrictions (m inputs, r outputs and n DMUs). Furthermore, this model has been extended with a second stage model that incorporates the non-radial slacks by Lozana and Villa (2004) along the lines of Ali and Seiford (1999) as expressed in Asmild et al. (2009).
- Emprical Analysis and Results
This section provides the results of emprical analysis based upon the data of industry and service sectors between 2009-2014 period. Inputs are being considered as fixed costs or reources and after calculating technical, cost and allocative efficiencies, output maximization targets are reviewed. Table 1 shows inputs and outputs determined for DMUs.
Table 1. Inputs and Outputs
Output 1 / Output 2 / Output 3 / Output 4 / Input 1 / Input 2 / Input 3GDP / Production Volumes / Turnovers / Added Values / Cost of Employes / Foreign Direct Investments / Fixed Capital Investments
As it can be seen from tables 2, 3 and 4, Mining and quarrying and Information and communication sectors that are numbered as respectively (1) and (9) have inefficient scores at both technical, cost and allocative efficiencies for each year during 2009-2014 period. Another significant point is that the sectors which are numbered as (2), (3), (10) and (11) don’t achieve cost and allocative efficiencies for each year despite they have technical efficiencies. Graphic 1. shows change in allocative and cost efficiencies[5] of these sectors by years. Manufacturing and Real Estate sectors’ efficiency scores tend to be more unsteady.
[ insert Table 2 about here ]
[ insert Table 3 about here ]
[ insert Table 4 about here ]
Graphic 1. Allocative and Cost Efficiencies
Output targets for sectors which are not efficient technically under variable returns to scale assumption can be seen from Table 5. Results show that (1) Mining and quarrying, (9) Information and communication and (14) Human health and social work activities sectors are not efficient technically in each year except in year 2010 for sector as numbered (9). According to results, number of inefficient sectors have increased in year 2012 and 2013 but in year 2014 only numbered as (1), (9) and (14) sectors maintain inefficiency.
[ insert Table 5 about here ]
- Conclusion Remarks
It becomes very significant to allocate fixed resources when they are bounded. Especially for emerging economies like Turkey, optimal resource allocation problem becomes more essential for sustainable growth. In centralized DEA models it is assumed that a central unit exists and it is in charge of allocating resources across decison making units. With regard to nature of costs and resources a central unit can both manage input minimization at same output levels or output maximization by using same levels of inputs.
In this study fixed costs are considered as employes cost, foreign direct investments and fixed capital investments. Inherently these inputs are not controlled by sectors and fluctuate according to market conditions and macroeconomic policies. Thus output targets are being reviewed while inputs resume at initial levels. Also in addition to technical efficiency, allocative and cost efficiencies are being calculated. Findings show that despite having efficient scores for technical efficency, Manufacturing and Real Estate sectors come to the fore in allocative and cost inefficient scores. Manufacturing industry as the most productive and exporter sector in Turkish economy needs to be reviewed in respect to reallocation costs and resources by a central unit. Another considerable result is efficiency scores of sectors numbered as (1), (9) and (14). These three sectors don’t have technical, cost and allocative efficiencies from year 2009 to year 2014. It reveals the need for a further analysis of these sectors to become efficient units.
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[1] This is a preliminary draft. Comments welcome, but do not cite, quote or circulate without permission of author. All unreported results to save space are available from the author upon request.
[2] PhD Candidate and Res. Asst. Recep Tayyip Erdoğan University, Department of Banking and Finance, ,
[3] Service sectors doesnt involve “Financial and insurance activities” and “Public administration and defence; compulsory social cecurity” sectors because of imperfect data.
[4] Data is obtained from Turkish Statistical Institue and sectors are classified according to Nace Rev.2. industrial classification. All data is TL-denominated.
[5] Allocative efficiency is equal to cost efficiency technical efficiency ratio therefore when a sector is technically efficient and have a score of “1” then allocative and cost efficiency scores become equal.