Measurment of Technical efficiency of Ethiopian insurance companies.Technical efficiency

Thesis (M.A.) 2012 74 Pages

Business economics - Investment and Finance


Table of Contents




Index of Tables

Index of Figures

1. Introduction
1.1. Background of the Study
1.2. Statements of Problems
1.3. Objective of the Study
1.4. Significance of the Study
1.5. Scope and Limitation of the Study
1.6. Organization of Paper

2. Related Literature Review
2.1. Theoretical Literature
2.1.1. Concept of Efficiency
2.1.2. Parametric Approach.
2.1.3. Mathematical Programming Methods
2.1.4. Basics of DEA.
2.1.5. DEA and Technical Efficiency
2.1.6. The Constant Return to Scale (CRS) DEA
2.1.7. The Variable Return to Scale (VRS) DEA
2.1.8. Scale Efficiency.
2.1.9. Malmquist Productivity Index
2.1.10. Inputs and Output Determination
2.2. Empirical Literature Review

3. Research Methodology.
3.1. Research Design:
3.2. Data Source and Types
3.3. Sampling Techniques
3.4. Data Analysis
3.5. Specification of Mathematical Model DEA

4. Results and Discussions
4.1. Production Frontier and Efficiency
4.2. The Overall Technical Efficiency Scores and Its Indications
4.3. Peers and Virtual Inputs of Inefficient Insurance Companies..
4.4. Factor which Determine Technical Inefficiency of Insurance Company
4.5. Malmquist Productivity Index of the Insurance Companies
4.6. Productivity Performance of Insurance Industry

5. Conclusion and Recommendation
5.1. Conclusions
5.2. Recommendation


Annex-A: Charts..

Annex-B: Efficiency Results of Insurance Companies from DEAP Software

Annex-C: Inputs and Outputs Categories.


I would like to express my special gratitude to my Principal advisor Assefa Worede (Asst. Prf.) and Co-advisor Dr. S.K. Pandey (Associate Prf.) for their time, comments and professional guidance throughout the paper. My heartfelt appreciation and great thanks goes to Hailemichael Tesfay (Asst. Prf.) for his professional support, useful suggestions and the technical assistance rendered to accomplishment of this study.

My sincere appreciation goes to Ethiopian insurance companies’ staffs for providing me the necessary data; special those individuals cooperate in the data collection.

And also this is a chance to express my gratitude to all my beloved families and my Friends. It is impossible to list all the people who have played a role in the completion of this study. So I want to express my special gratitude to all those who have handover directly or indirectly.

For all, thanks to God!!!


This study was conducted in Ethiopian insurance companies in order to measure the technical efficiency using DEA input oriented approach under both constant and variable return versions and Malmquist index output oriented approach in the period 2006-2010. In the first stage, the relative technical efficiency is estimated with data envelopment analysis (DEA) to establish benchmarking company, then, they are ranked according to their technical efficiency. Mann whiney- U test in the second stage was used to determine the factors affecting efficiency. The concept of efficiency concerns is an insurer’s ability to produce a given set of outputs (such as premiums and investment income) via the use of inputs such as administrative and general expenses and financial capital. The insurance company is said to be technically efficient if it cannot reduce its input usage without some corresponding reduction in outputs, given the current state of production technology in the industry. The technical efficiency of Ethiopian insurance companies during the study period was 86.7%, 97.1% and 84.9% in technical efficiency, pure technical efficiency and scale efficiency, respectively. The productivity change shows Ethiopian insurance companies were quite well in efficiency change rather than technological change. It suggested that it is better to employ advanced technology to be efficient in competitive environment. So it is advisable Ethiopian insurance companies are better-off to follows the best practicing firms in the industry. The economic implications arising from findings were also considered.

Key words : Insurance companies, DEA, Technical efficiency, and Malmquist index


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Index of tables

Table-1: Efficiency Score of Ethiopian Insurance Companies under CRS and VRS

Table-2: Over all Technical Efficiency Score of Ethiopian Insurance Companies

Table-3: Peers of the Inefficient Insurance Companies under BCC Model

Table-4: Result of Inefficient Insurance Companies under BCC Model (VRS)

Table-5: Average Technical Efficiency of Ethiopian Insurance Companies’ 2006-2010

Table-6: The Result of Mann Whitney U-Test

Table-7: Malmquist Index Summary of Insurance Companies in Year

Table-8: Malmquist Index Summary of Insurance Companies in Year

Table-9: Malmquist Index Summary of Insurance Companies in Year 2009

Table-10: Malmquist Index Summary of Insurance Companies in Year 2010

Table-11: Malmquist Index Summary of Firm Means of 2006-2010

Index of figures

Figure-1: Input-Output Observations Over the Time

Figure-2: Malmlquis Index and Productive Change Over the Time



This chapter introduces about the background of the study, the statement of the problem, the objectives of the study, significance of the study, scope of the study and limitation of the study and the organization of the paper.

1.1. Background of the Study

According to the finance-growth nexus theory financial system development promotes economic growth through marginal productivity of capital, efficiency of channeling saving to investment, saving rate and technological innovation (Levine, 1997 as cited in Curak, Lončar & Poposki, 2009). In performing functions of financial system, insurance companies play an important role. Insurance firms are main risk management tool for companies and individuals, through issuing insurance policies; they collect funds and transfer them to deficit economic units for financing real investment. Therefore, according to this theory insurance sector could be one of the factors contributing to economic growth (Curak et al., 2009).

Insurance company provides services, like making the usual risk financing, pooling and transfer, investment, and real services and advice. The efficient operations of such activities by insurance industry could be appropriate to contribute economic development. The concept of efficiency in insurance is concerns an insurer’s ability to produce a given set of outputs (such as premiums and investment income) via the use of inputs such as administrative and sales staff and financial capital. An insurer is said to be technically efficient if it cannot reduce its resource usage without some corresponding reduction in outputs, given the current state of production technology in the industry (Brien, Diacon & Starkey).

Efficiency for insurance companies is of interesting in contemporary economics, considering the increasing risks related to environmental and globalization issues in the world today. Efficiency has been the focus of most research in insurance in the recent past (Barros & Obijiaku, 2007).

Moreover, the increased market competition at the national level has equally placed insurance companies in a competitive environment. Due to these crucial issues, most of the researches on efficiencies of insurance industries and/or companies were done in developed part of the world. Following the implementation of a single European insurance license in 1994, inter-country efficiency studies has started to gain grounds (Brien, Diacon & Starkey, 2002).

More of technical efficiency studies in the insurance industry have been conducted in the developed nations. Further, few studies conducted in developing countries in general and Africa in particular, especially in Ghana and Nigerian insurance market. It appears no earlier studies were conducted in the Ethiopian insurance industry. Hence, to the best of researcher knowledge, this paper is probably the first paper employed DEA to estimate the efficiency of the Ethiopian insurance industry.

The idea behind efficiency measurement is to measure a company’s performance relative to “best practice” frontiers, which are determined by the dominant, i.e., most efficient, companies in the industry. The underlying theory was originally developed by Farrell (1957). Modern frontier efficiency methods, similar to more traditional techniques such as financial ratio analysis, aim at benchmarking firms of an industry against each other. However, these methods are considered superior to other techniques because they integrate different measures of firm performance into a single and thus easily comparable statistic that differentiates between companies based on a sophisticated multidimensional framework (Cummins & Weiss, 2000).

As literature indicates there are two principal types of efficiency methodologies the econometric (parametric) approach and the mathematical programming (non-parametric) approach. The econometric approach is non parametric approach requires the specification of a production, cost, revenue, or profit function as well as assumptions about the error term(s). Its primary advantage is that it allows firms to be off the due to random error as well as inefficiency. However, this methodology is exposed to errors in the specification of the functional form or error term(s). While the mathematical programming approach is a non parametric approach avoids the specification error by imposing somewhat less structure on the optimization problem (Cummins & Zi (1998).

1.2. Statements of Problems

Increasing efficiency in financial institutions is one of the key steps in the direction of economic development of country. Insurance institutions according to the role that the community’s economy can maintain that national wealth and financial indemnity and guarantee supply and large investments in the community and their development and growth of the whole set of economic development will lead the country. In fact, insurance companies, by attracting the premium and additional funds flows, can efficiently use to their investments and could provide economic development (Kazemipour & Saeidy, 2011).

In Ethiopian, insurance sector is dependent on the banking sector for much of its new business (NBE, 2009). Most of the Ethiopian insurance companies have sister banks and it is common for these banks to refer their clients to their sister insurance companies. Their large portion of total income is derived from investments in banks. A World Bank project appraisal document suggested that the balance sheets of Ethiopian insurance companies are over-exposed to and over-concentrated in the banking sector with over 40% of assets exposed to the banking sector.

Although the financial statements of Ethiopian insurance companies reveal that a very limited amount of the sectors’ returns are reinvested in the industry. In an environment where capital is scarce, there is little incentive for shareholders to reinvest dividends in the insurance sector and are instead channeled into the banking sector or other high yielding investments. This makes it difficult for insurance companies to invest in the modernization of its infrastructure, develop innovative products or explore new market opportunities (World Bank project appraisal document, n.d.).

These issues help to raise questions like, is market share affect the technical efficiency of insurance companies? Is the size of companies affecting insurance productivities/efficiency? These questions have been possibly answered in the second stage of efficiency analysis based on the determined technical efficiency scores of each firm with the help of Mann whiney- U test hypothesis.

After establishing the efficiency rankings of the Ethiopian insurance companies, the hypotheses were tested by Mann-Whitney U-test, which tests for differences between the efficiency scores, which is adopted by Grosskopf and Valdamanis, 1987; Brockett and Golany 1996 as cited in Barros & Obijiaku (2007) recommend that Mann-Whitney U-test for the non-parametric analysis of DEA results. It is used here because the efficiency scores might not be fit within a standard normal distribution. The following hypotheses were defined:

Hypothesis 1: Scale of operation of an insurance company positively correlates with its efficiency). As Barros, Barroso and Borges (2005) described this is a common hypothesis in insurance analysis, based on economies of scale. To test this hypothesis, the insurance companies are classified by equity capital (Shareholder funds) and then the sample is also divided into two subsets on this basis.

Hypothesis 2: Market share of an insurance company positively correlates with its efficiency. The work of Bernstein (1999) indicates that market share distinction is another common hypothesis in insurance analysis. To test this hypothesis, the insurance companies are classified according to the estimated market share by gross premium and the sample is divided into two subsets on this basis.

1.3. Objectives of the Study

The objective of the study is to measure technical efficiency of the Ethiopian insurance companies for the period 2006-2010.

1.3.1. Specific objectives :

- To evaluate the overall technical efficiency of Ethiopia insurance companies.

- To identify the sources of inefficiency of the insurance companies.

- To measure the productivity changes of insurance companies during the study period.

- To assess the possible needs for improving the efficiency of the insurance companies.

1.4. Significance of the Study

According to Sabbir (2002) the primary function of insurance is to act as a risk transfer mechanism to provide peace of mind and protect against losses. According to Sabbir, insurance schemes utilize the combination method by persuading a large number of individuals to pool their risks into a large group to minimize overall risk.

However in the developing countries which are characterized as having low-income levels, and lacking access to social security systems, healthcare, and education, sanitation, and employment opportunities, the need for insurance as a risk transfer mechanism is even more imperative (World Bank project appraisal document, n.d.).

Measurement of technical efficiency has important implications for the insurance operators who always working to improve operating performance. For policy makers, an awareness of the determinants of insurance efficiency may help them in designing policies to improve the stability of the financial institution (Kasturi, 2006).

The understanding of the level of inefficiencies and factors that affect the efficiency of insurance companies in the country would enable policy makers to design effective resource utilization strategies so as to improve efficiency operation.

There have been no literature on technical efficiency of insurance company in Ethiopia so this may serve as means of embarking and it will bring possible areas of improvement to the attention of the management of respective insurance companies. Besides, this study could be used as a base for further empirical research on the subject, particularly general insurers. Finally, the outcome of this study is intended to provide relevant evidence for policy makers .

1.5. Scope and Limitations of the Study

This study was limited to the technical efficiency measurement of the insurance companies in Ethiopia, that have an operation experience of a minimum of five year starting 2006 – 2010 by using the Data Envelopment Analysis (DEA). The detail of study is on technical efficiency and on some of efficiency determinant factors, and productivity changes during the study period.

The limitation of this study is started by unavailability of 2011 audited financial statement of Ethiopian Insurance Corporation, due to this short in data availability, the researcher was forced to drop 2011 for all others selected insurance companies. There was also minor confusion on preparation of financial statement from company to company, especially balance sheet. For example, some of the companies include technical provision under equity capital (share holders fund) and other under liability.

Meanwhile, the study is not free from limitations, from technical aspect, methods and sampling errors. As far as data set is concerned, the homogeneity of the insurance companies used in this analysis is questionable, since the researcher used by including only two factors, but there are other factors, which may face different restriction, for example, location of company, bank net working, internal regulation system…etc. In this study the researcher combined life and non life insurance companies which can be with different restrictions. However, in Ethiopia insurance market, the old companies combine these to insurance activities, which make the separation impossible.

The tools used to determine efficiency score (DEA) does not have restriction to bound any factor of inefficiency, it consider this inefficiency whether from scale efficiency or pure technical efficiency. The other limitation from DEA is that, it does not consider any difference between efficient DMUs. If it may considered by super efficiency method it can be avoided. The DEA used in this study, either imposes any functional form on the data or makes any distributional assumptions for the inefficient term or a prior distinction between the relative importance of any combination of inputs and outputs.

1.6. Organization of the Paper

This section peresented the structure of paper in the following chapter wise sequence. The first chapter of this paper is presented about the introduction of the whole study, introduction, statement of the problem, objectives of the study, signifcance of the study and scope.

The emperical and theortical lirarature review about technical efficiency and data envelopment analysis in the context of financial institution, specifically insurance company are presented in the second chapter of the study.

In chapter three presentes, the reseach methololoy of the study: research design, data source and data type, sampling techniquies, description of data and model spesfication. In chapter four the results and interprtation parts of the study that is the significat portion for which the study is conducted. Finally the concllusion and recommendation part are presented in chapter five.



This chapter introduces the relevant literatures on the efficiency, efficiency measurement and Data Envelopment Analysis and its application. Theoretical literatures and empirical findings which are relevant to present study are presented.

2.1. Theoretical Literatures

2.1.1. Concept of Efficiency

In economics, the term cost efficiency refers to the use of resources, so as to maximize the production of goods and services. An economic system is said to be more efficient than another in relative terms if it can offer more goods and services for society without using extra resources. In absolute terms, a situation can be called economically efficient if one cannot make improved without making someone else worse off, no additional output can be obtained without increasing the amount of inputs and production proceeds at the lowest possible per-unit cost.

Efficiency is described as evaluation of the relationship between inputs and outputs in the production process (Alhabshi, Bacha & Ismail, 2011). Efficiency measurement is a technique used to examine the performance of firms by computing the relative efficiency of each firm. Then, individual efficiency score of each firm is compared to the best practice efficient frontiers consisting of the most efficient firms in the industry. It is found the frontier methodologies are superior compare to traditional techniques such as financial ratio (Eling & Luhnen, 2010).

In an article which represents the inception of DEA, Farrell (1957) was motivated by the need for developing better methods and models for evaluating productivity. He argued that while attempts to solve the problem usually produced careful measurements, they were also very restrictive because they failed to combine the measurements of multiple inputs into any satisfactory overall measure of efficiency. Responding to these inadequacies of separate indices of labor productivity, capital productivity, etc., Farrell proposed an activity analysis approach that could more adequately deal with the problem. His measures were intended to be applicable to any productive organization; in his words, ‘… from a workshop to a whole economy’. In the process, he extended the concept of “productivity” to the more general concept of “efficiency”.

The idea of efficiency of a production unit was first introduced by Farell (1957) under the concept of “input oriented measure”. According to Farell, technical efficiency measure is defined by one minus the maximum equi-proportionate reduction in all inputs that still allows continuous production of given outputs.

Technical efficiency is linked to the possibility of avoiding waste by producing as much outputs as the use of input allows it (output oriented measure), or by using as less input as the production target plans it (input oriented measure). This efficiency is measured by comparing observed and optimal values of production, cost, revenue, profit or all that the production system can follow as objective and which is under appropriate quantities and prices constraints. It can analyze technical efficiency, in terms of deviation compared with idealistic production frontier. The literature proposes two approaches for measuring frontier production; the stochastic (parametric) frontier approach and the mathematical programming approach (non- parametric). These approaches are discussed in the following section.

2.1.2. Parametric Approach

The measurement of insurance efficiency is mostly focused on the efficient frontier approach. This has been used widely to assess the efficiency levels as both approaches allow the use of multiple inputs and outputs from a sample of institutions to develop an efficiency frontier and evaluate the efficiency of a decision-making unit (DMU) relative to other DMUs in the sample. The parametric stochastic frontier approach (SFA) which is also known as the Econometric Frontier Approach was developed by Aigner, Lovell and Schmidt (1977). This approach specifies a functional form for cost, profit or production relationship among inputs, outputs, and environmental factors and allows for random error. The SFA deals with the problem that not all deviations from the frontier may be due to inefficiency. Deviations from the benchmark may also occur due to bad (or good) luck or measurement errors. The SFA modifies a standard cost (production) function to allow inefficiencies to be included in the error term. The functions are used to estimate the distance that a firm is from the optimizing envelope.

Another assumption needed in the SFA is to distinguish the inefficiencies from random components of the error terms. The random components include short-term luck which places individual DMU in relatively high or low cost positions and measurement error from excluded explanatory variables, misspecification etc. These two components are separated by assuming that inefficiencies are drawn from asymmetric half-normal distribution, and that random errors are drawn from a symmetric normal distribution. The basic SFA model has the following form:

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The primary advantage of the econometric approach is that it allows firms to be off the due to random error as well as inefficiency. However, this methodology is vulnerable to errors in the specification of the functional form or error term(s).

According to Haron and Tahir (2008), however, it is not possible to decompose individuals’ residuals into inefficiency or random variation; therefore, estimating technical inefficiency by observation is impossible. The second approach is mathematical programming which take some of the advantages over SFA is discussed in the following section.

2.1.3. Mathematical Programming Methods

The non-parametric frontier approach also called mathematical programming approach known as DEA method consist of estimating the frontier by using non-parametric mathematical linear programming. It offers an analysis based on the relative evaluation of the efficiency in an input/output multiple situations, by taking into account each insurance company and measuring its relative efficiency to an envelopment surface made up with the best companies. The main advantage of DEA over SFA is that DEA models do not require a-priori assumptions with respect to the analytical form of the frontier; data envelopment analysis avoids specification error by imposing somewhat less structure on the optimization problem. The decomposition of efficiency into its component is also considered in mathematical programming method.

The method can be used to estimate production, cost, and revenue frontiers and provides a particularly convenient way for decomposing efficiency into its components. E.g., technical efficiency can be conveniently decomposed into pure technical, and scale efficiency. Intuitively, the method involves searching for a convex combination of firms in the industry that dominate a given firm. These firms constitute the given firm’s reference set. If the reference set consists only of the firm itself, it is considered self-efficient and has an efficiency score of 1. However, if a dominating set can be found consisting of other firms, the firm’s efficiency is less than 1. The implication is that the firm’s outputs could be produced more cheaply (in the case of cost efficiency) by the “best practice” firms in the industry. The researcher chooses this non parametric approach to evaluate Ethiopian insurance companies’ technical efficiency regarding the above explained benefit of using DEA.

DEA efficiency is estimated by solving linear programming problems. For example, technical efficiency is estimated by solving the following problem, for each firm, illustration not visible in this excerpt = 1, 2... S, in each year of the sample period:

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where illustration not visible in this excerpt is anillustration not visible in this excerpt output matrix and illustration not visible in this excerpt is a illustration not visible in this excerpt input matrix for all firms in the sample, illustration not visible in this excerpt is aillustration not visible in this excerpt output illustration not visible in this excerpt vector and illustration not visible in this excerpt a illustration not visible in this excerpt input vector for firmillustration not visible in this excerpt, and illustration not visible in this excerpt is a illustration not visible in this excerpt intensity vector (the inequalities are interpreted as applying to each row of the relevant matrix). The constraint illustration not visible in this excerpt imposes constant returns to scale. The firms for which the elements of illustration not visible in this excerpt are non-zero constitute the firm’s reference set.

Technical efficiency is separated into pure technical and scale efficiency by re-estimating problem with the additional constraint for a variable returns to scale (VRS) frontier (this step estimates pure technical efficiency), and again with the Constraint for a non-increasing returns to scale (NIRS) frontier.

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2.1.4. Basics of DEA

DEA represents a mathematical programming methodology that can be applied to assess the efficiency of a variety of institutions using a variety of data. This section provides an intuitive explanation of the DEA approach. DEA is a linear programming technique that enables management to benchmark the best-practice decision-making unit (DMU), i.e., by calculating the scores denoting their efficiency with a linear programming procedure. Furthermore, DEA provides estimates of the potential improvement that can be made by the inefficient Decision Making Unit (DMU). Technical efficiency represents the ability of a decision unit (DMU) to minimize inputs for the given set of output. In other words a single decision maker is a converter that takes inputs in to output (Eling & Luhnen, 2010).

It is a relatively new “data oriented” approach for evaluating the performance of a set of peer entities called Decision Making Units (DMUs) which convert multiple inputs into multiple outputs. Recent years have seen a great variety of applications of DEA for use in evaluating the performances of many different kinds of entities engaged in many different activities in many different contexts in many different countries (cook &Zhu, 2008). These DEA applications have used DMUs of various forms to evaluate the performance of entities, such as insurance industry, hospitals, business firms, and others, including the performance of countries, regions, etc, because it requires very few assumptions.

2.1.5. DEA and Technical Efficiency

The discussion of the DEA approach is undertaken in the context of technical efficiency in the microeconomic theory of production. In microeconomics, the production possibility set consists of the feasible input and output combinations that arise from available production technology. The efficiency of a production unit is a comparison between observed and optimal values of its output and input (Lovell, 1993). Farrell (1957) stated that, efficiency consists of two components, technical efficiency and allocative efficiency. Technical efficiency is the ability to use inputs/resources to obtain the given level of output, while allocative efficiency is the ability to regulate input at a rate which results in maximum profit. Farrell employed an input-oriented approach in the efficiency measurement, this approach measures technical inefficiency as a proportional increase in input use by keeping output constant. A single firm is considered “technically efficient” if it cannot increase any output or reduce any input without reducing other outputs or increasing other inputs.

The decomposition of technical efficiency in to its component of, overall technical efficiency, pure technical efficiency and scale efficiency were bases its decomposition on the development of DEA. The original work of the DEA model introduced by Charnes, Cooper and Rhodes (1978), denoted CCR hereafter, assume Constant Returns to Scale (CRS)(overall technical efficiency) and the redeveloped DEA model by Banker, Charnes and Cooper (1984) proposed the variable-returns-to-scale (VRS) denoted as BCC hereafter(Pure technical efficiency). The detail is presented in the following section.

2.1.6. The Constant Return to Scale (CRS) DEA

DEA is usually used to evaluate the efficiency of a number of firms or decision-making units (DMUs) with the frontier provide relative measurement of each unit. The frontier that comprises efficient units is the expected target for inefficient units. The first DEA was suggested by Charnes et al. (1978) based upon the assumption of constant return to scale. In this study, an input-oriented CCR model, a form of envelopment, was used to measure efficiency of insurance companies. The mathematical form is expressed as follows:

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Where illustration not visible in this excerpt scalar and λ is vector of constants in illustration not visible in this excerptnd illustration not visible in this excerpt is the illustration not visible in this excerpt unit’s efficiency score illustration not visible in this excerpt in equation 1. The estimated illustration not visible in this excerpt will satisfy the restriction illustration not visible in this excerpt with a value θ=1 indicating a technically total efficient firm. When the linear programming problem foretasted is solved, illustration not visible in this excerpt efficiency scores are obtained. In the equation illustration not visible in this excerptis theillustration not visible in this excerptfirm, illustration not visible in this excerpt is the matrix (1xS) and illustration not visible in this excerptis the illustration not visible in this excerpt firm’s level of input use.

2.1.7. The Variable Return to Scale (VRS) DEA

Banker et al. (1984) modified the DEA model, which depends upon the assumption of constant return to scale (CRS), taking into consideration the variable return to scale (VRS). The use of CRS when not all firms are working at the optimal scale, results in measures of technical efficiency (TE) that are confounded by scale inefficiency (SE). The use of VRS permits the calculation of these SE effects (Battese et al., 1998). This study also used input oriented BCC model form of DEA analysis. The CRS linear programming problem can be easily modified to account for VRS, by adding the convexity restriction N1’ λ =1 (Equation 2).

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2.1.8. Scale Efficiency

The total technical efficiency measure, obtained from constant return to scale DEA, is decomposed into pure technical efficiency and scale efficiency. If there is a difference in CRS and VRS of technical efficiency scores for a particular firm, this indicates that the firm has scale inefficiency, and that the scale inefficiency can be calculated from the difference between the VRS and CRS of technical efficiency (TE) scores: Total Efficiency (TECRS) = Pure Technical Efficiency (TEVRS) * Scale Efficiency (SE). Total technical efficiency covers both pure technical efficiency and scale efficiency. Scale efficiency points out the losses due to non-optimal production size (Fare, Groskopf & Lovell, 1985). The decomposition of scale efficiency gives pure technical efficiency. The purpose of the decomposition is to determine the source of inefficiency (Lorcu & Unakitan, 2011).

The rationale for interpreting the pure technical efficiencies as management skills is based on the contrast between the constant returns to scale and variable returns to scale versions. The constant returns to scale model identifies the overall inefficiency, whereas variable returns to scale models differentiates between pure technical efficiency and scale efficiency. Scale efficiency of a firm can be computed by taking ratio of the firm's overall efficiency to its pure technical efficiency.

In relation to estimation of technical efficiency in insurance firm, the DEA uses to explore the contributions of technical and efficiency change to the growth of productivity in the insurance industries by applying the generalized output-oriented Malmquist index in the study period. To have clear awareness about growth of productivity in insurance industry it is important; to careful identify the components of total frontier productivity changes by the help of Malmquist productivity index of DEA.

2.1.9. Malmquist Productivity Index

Malmquist productivity index is defined using distance functions from frontier. This study adopts the efficient frontier approach, using the Malmquist productivity index based on DEA. The Malmquist productivity index allows for changes in productivity to be broken down into changes in technical efficiency and changes in technological efficiency as explained in Barros, barroso and Borgos (2005). Although the terms productivity and efficiency are often used interchangeably, they are in fact different economic concepts. Simply, efficiency refers to how well firms are performing relative to the existing technology in an industry; whereas productivity refers to the evolution of technology over time.

Frontier efficiency methods are to be had for measuring both efficiency and productivity. To set the scene for productivity measurement, this study followed the framework presented in Figure 1, which shows two observations of the input (x) and output (y) bundles used by a firm in an industry at time t and t + 1. The aim is to measure the productivity growth between t and t + 1 in terms of the change from input–output bundle z(t) to input–output bundle z(t + 1). Productivity is measured through the possible production frontier that is imposed on the production bundle in Figure 1. The production frontier represents the efficient levels of maximum output (y) that can be produced from a given level of input (x); this is also used by Barros, barroso and Borgos (2005). If the firm is technically efficient in period t, it produces along the frontier the maximum output achievable y (t). Point z (t) =[x (t), y (t)] corresponds to a inefficient firm, which uses more than the minimal amount of input to produce a given level of output.

Figure – 1: Input-output observations over the time

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Source: Barros et al. (2005)

The input x (t) should be multiplied by the horizontal distance ratio, ON/OS, in order to making of y (t) technically efficient. By correspondence, and assuming frontier t as reference, the input x(t + 1) should be multiplied by the horizontal distance ratio, OQ/OR, in order to achieve technical efficiency in the production of output y(t + 1), that is bundle z(t + 1). Since the frontier has shifted in the meantime, z (t+ 1) is technically inefficient in x (t +1) must be reduced by the horizontal distance ratio, OP/OQ, resulting in bundle z` (t + 1). Globally, the input ratio inefficiency in t + 1 is OP/OR.

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The relative efficiency distances of each observation from the original frontier measure the catching -up effect. The shift effect of frontier is measured by the relative distance between the frontiers at output level y (t + 1), for example, (OP/OQ).

The relative movement of a production observation over time may result from firms technical efficiency change or may result from the frontier shifting upwards over time (technological efficiency change). The Malmquist index of productivity growth (M) is the ratio of the input inefficiencies at t + 1 and t. In this an output-oriented Malmquist productivity index is estimated based on DEA. Output-oriented efficiency measurements are appropriate assuming that insurance companies operate in a competitive market (khumbhakar 1987; Zellner et al. 1966 as cited in Barros et al., 2005).

Figure-2: Malmlquis index and productive change over time

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Source: Barros et al. (2005).

Formally, the Malquist index is based on the output distance function defined as:

illustration not visible in this excerpt

Where X = (x1, x2, …, xM) is the input vector and

Y = (y1,y2,…,yS) is the output vector

Caves, Christensen and Diewert (1982b) provided an alternative interpretation of production technology using the concept of “distance function”. They defined the output distance function as:

Do(x, y) =min 𝜇 (𝜇: F(x, y/𝜇) =0

Where μy the minimum equi-proportional change in the output vector. Output distance function measures the maximum proportional change in output required to place illustration not visible in this excerpton the efficiency frontier. If the evaluated production unit is efficient,illustration not visible in this excerpt, otherwise,illustration not visible in this excerpt. Distance function may also be computed with input orientation, reference technology in a certain time period and CRS or VRS specification. Let Dt0 (CRS) and Dt0 (VRS) denote the output distance function computed with period t technology and with CRS and VRS specification respectively.

Caves et al. (1982) defined the output based Malmquist productivity index to compare performance of a production unit in time period t and t+1 with reference to period t technology as:

illustration not visible in this excerpt

M0 >1 indicates higher productivity in period t than in period t+1.

Fare, Grosskopf, Norris and Zhang (1994) (as cited in Idris & Md Saad, 2011) also defined an index that incorporates Malmquist indices in both periods. This, they suggest, helps to avoid choice of the time period arbitrarily. Fare, Grosskopf, Norris and Zhang specified the output based Malmquist productivity change index as

illustration not visible in this excerpt

Where illustration not visible in this excerptis the change in relative technical efficiency between t and t+1 and

illustration not visible in this excerpt capture the shift in technology between the two time periods evaluated at (xt, yt) and (xt+1, yt+1). A value of less than 1 in the index indicates a decline in efficiency, equal to 1 indicates stagnation and greater than 1 indicates a growth between period t and t+1 from the perspective of period t technology (Don and Piyadasa, n.d.).

2.1.10. Inputs and Output Determination

The choice of inputs and outputs is fundamental to the success of any efficiency analysis. In general, inputs such as land, labour and capital represent the resources that are utilized to produce the firm’s output, and the acquisition of these inputs represents a cost to the firm. Outputs, on the other hand, represent those goods or service which the customers of the firm are prepared to purchase, and the sale of these outputs generates revenue.

In insurance company inputs can be classified into three principal groups: labor, business services and materials, and capital. For some applications it also may make sense to split labor into agent labor and all other (mostly home office) labor because the two types of labor have different prices and are used in different proportions by firms in the industry (e.g., some firms use direct marketing in whole or in part, while others rely heavily on agents) (Cummins & Weiss, 1998).

And also, there are at least three types of capital that can be considered – physical capital, debt capital, and equity capital. However, it is rare for insurance efficiency studies to utilize more than four inputs (Commins & Weiss). Accordingly, many insurance industry studies include equity capital as an input. The rationale for the use of equity capital is that insurers must maintain equity capital to back the promise to pay claims even if losses are higher than expected and to satisfy regulatory requirements. The rationale for the use of debt capital is similar to that for the use of deposits as an input in banking, i.e., that insurers raise debt capital by issuing insurance and annuity policies and invest the capital as part of the intermediation function.

The debt capital of insurers consists mainly of funds borrowed from policyholders. For life insurers, debt capital includes the aggregate reserve for life policies and contracts, the aggregate reserve for accident and health policies, the liability for premium and other deposit funds, and other reserve items. Due to their availability, Operating/Management expenses, Debt Capital, and Equity Capital are used for determination of Ethiopian insurance companies’ technical efficiency.

On the other hand, the output determinant of insurance companies are identified on the bases of three principal approaches which have been used to measure outputs in the financial services sector: the asset or intermediation approach, the user-cost approach, and the value-added approach (Berger and Humphrey, 1992b as cited in Cummins & Weiss, 1998).

The asset approach treats financial service firms as pure financial intermediaries, borrowing funds from one set of decision makers, transforming the resulting liabilities into assets, and receiving and paying out interest to cover the time value of funds used in this capacity.

The user-cost method determines whether a financial product is an input or output on the basis of its net contribution to the revenues of the financial institution (Hancock, 1985). The third approach to measuring output, the value-added approach which is the most appropriate method for studying insurance efficiency. The value-added approach considers all asset and liability categories to have some output characteristics rather than distinguishing inputs from outputs in a mutually exclusive way. There has been considerable disagreement over the appropriate proxies to use for the output of insurance services. When it comes to considering insurance company output, the majority of efficiency studies have used premium income as a proxy for the output (of non-investment related) insurance services even though premiums are really a form of revenue, that is price times quantity rather than a count of output units.

The problems with using premium income to proxy output have led some authors –particularly Professor David Cummins to use the value of claims payments instead. However it is difficult to understand why the management of insurance companies would seek to maximize the value of insurance claims (particularly for general insurance), and this therefore violates the principle of output characteristic that more output should be preferred to less. Indeed some researchers have included insurance claims as an input rather than an output. So as to difficulty to use claims as output, the researcher in this study taken net earned premium as an output measure of Ethiopian insurance companies’ efficiency. Net earned premium and investment income are the two outputs used in this study. Investment income is included as an output variable because insurance companies can be considered as financial institutions seeking to maximize income from investments (Diacon, 2001).

Even if any appropriate inputs and outputs are used, this does not mean that, there is no factors affect the efficiency of insurance company. There are environmental, individual company’s factors which influences the efficiency of firms (external and internal factors). To identify whether the efficiency of Ethiopian insurance companies are exposed to these factors, the researcher is used Mann Whitney U-test, which is recommended by researchers for non parametric approach; the detail discussion is presented in chapter three of this paper.

2.2. Empirical Literature Review

Several studies have been carried out on measuring the insurance company performance using the DEA approach, since the work of Charnes, Cooper and Rhodes and later by Banker, Charnes, and Cooper, and others in operations research in DEA technique. In this section empirical findings are presented on the study area.

Cummins and Zi (1998) applied a variety of econometric and non-parametric techniques to estimate cost efficiency for a sample of U.S. life insurers. They found that econometric efficiency estimates are robust to the choice of distributional assumptions from the error term but not non parametric. Thus, the choice of estimation method can have a significant consequence on the conclusions of an efficiency study. Most of the insurers in the sample were displayed with either increasing or decreasing returns to scale, and stock and mutual insurers are found to be equally efficient after controlling for firm size.

Diacon (2001) made his studies on the value-based approach to measure the technical efficiency of UK general insurers, which was undertaken by comparing the relative performance of 431 general insurers licensed in six European countries using data from Standard & Poor’s Eurothesys database. The data was made available on a (roughly) comparable basis as a result of the EU insurance Accounts Directive which only came fully into operation in 1996. The study used the variable returns to scale formulation of the well-known data envelopment analysis to identify the locally-efficient and inefficient insurers within each country. The results for 1999 (the latest year of available data) indicate that UK general and composite insurance companies have the potential to be among the most efficient in Europe. However there is also evidence that many UK companies are not currently realizing their potential for efficiency improvements in comparison with their European counterparts.

The study conducted by Bawa and Ruchita (2011), on Indian health insurance business of general insurance companies during 2002-2009 evaluated the efficiency of 10 general insurance companies including 4 public sector companies. They used the equity capital and labour (including commission, agents’ fees, referral and other expenditure) as input and net premium as output. They were observed that overall general insurers carrying health insurance business at an average technical efficiency of 73%, pure technical efficiency of 92% and scale efficiency of 78%. On the other hand sector wise performance analysis has indicated that technical efficiency of all the private sector companies is 77%, which is 10% more than that of public sector Companies. This can be attributable to the fact that private sector companies are operating on increasing return to scale and taking the advantages of pure technical efficiency and scale efficiency.

Brien et al. (2002) studied the relative efficiency of 450 European life insurance companies with regarding the factors affecting efficiency of insurers during 1996 and 1999 with a two-stage approach. In the first stage, they estimated efficiency scores (pure technical efficiency, scale efficiency and mixed efficiency) with a VRS DEA model. The inputs used were total operating expenses net of reinsurance commissions, total capital (including shareholder capital, reserves, participating rights, and long-term funds for future appropriations), total technical reserves and total borrowings from creditors. The outputs used were insurance net earned premiums and total investment income. In the second stage, they estimated a Tobit regression with the three efficiency scores regressed in terms of financial ratios, characteristics of the insurance companies, national dummies and year dummies. The general conclusion is that efficiency scores are U-shaped, with both small and large insurers appearing to have higher efficiency scores.

Barros, Caporale and Ibiwoye (2008) explored the efficiency determinants of Nigerian insurance companies. In the first stage, their relative technical efficiency is estimated with DEA (data envelopment analysis) to establish which ones perform most efficiently, and they are ranked according to their technical efficiency over the period 1994-2005. They tested for the roles played by dimension; bank network and market share in the efficiency of the Nigerian insurance companies. They found that competition for market share is the main driver of efficiency in the Nigerian insurance market in the period analyzed. The implications of the research for managerial purposes were drawn.

Abudulai et al . ( 2010) used DEA to evaluate the relative performance of Ghanaian general insurance companies from the year 2002 to 2007. They used Debt capital, Equity capital and Management expenses as inputs that are used by insurers to produce premium, claims and investment income. They tested hypotheses relating to the roles played by dimension and market share in the efficiency of the Ghanaian general insurance companies. It was observed that Ghanaian general insurers with higher dimension and market shares tend to have higher efficiencies; implying that general insurers could increase their efficiencies by trying to increase among other things their dimension and market shares.

Hatzigayios et al. (2001) analyzed a variable number of Greek non-life insurance companies for the years 1991–1996 with DEA analysis. The outputs used are revenue from insurance related activities (premium income) and revenue from investment activities. The inputs used are salaries and expenses and payment to insurers. The general conclusion is that the industry is highly inefficient, with notable differences existing between the different companies analyzed.

Idris and Md Saad (2011) focused on the efficiency of the life insurance industry in Brunei and Malaysia and explored that the contributions of technical and efficiency change to the growth of productivity in the Malaysian and Brunei life insurance industries by applying the generalized output-oriented Malmquist index for the year 2000-2005. The output-input data were panel of 9 life insurance firms in Malaysia and 2 life insurance companies in Brunei that were chosen as the sample of the study. They used two inputs and two outputs, namely, commission and management as well as premium and net investment income, respectively . They found that, on average, the TFP of the life insurance industry is mainly due to both efficiency and technical changes where the main source of the efficiency change is scale efficiency rather than pure efficiency.

Assaf, Barros and Nektarious (2010) analyzed 71 insurers operated in the Greek insurance industry over the period 1994 to 2003. They employed two stages Data Envelopment Analysis (DEA).They found that overall technical inefficiency is 12% whereby the gap inefficiency recorded at 5% in 1994 and increased to 24% in 2003. The main findings indicate the majority of insurance companies are operated on declining efficiency after 1997. This is due the inadequacies in management, scale and technology.

Barrosa and Obijiaku (2007) expanded upon previous research in insurance company efficiency by analyzing the efficiency of Nigerian insurance companies in two stages with a DEA model in the first stage. They used Data Envelopment Analysis (DEA) to calculate both technical and scale efficiency. In the second stage, the Mann-Whitney U-test is used to test some hypotheses; the result signifying that dimension acts as a restriction on the efficient performance of small insurers. In similar way taking in to account the situation for developing country, the present paper followed the two stage analysis of insurance companies’ efficiency in Ethiopian insurance companies.



ISBN (eBook)
ISBN (Book)
Catalog Number
Institution / College
Mekelle University – Business and economic college
MSc in Finance and Investment
Ethiopian insurance DEA Measurment




Title: Measurment of Technical efficiency of Ethiopian insurance companies.Technical efficiency