68 CHAPTER FOUR TECHNICAL EFFICIENCY OF ETHIOPIAN MICROFINANCE INSTITUTIONS 4.1 Introduction This chapter aims to measure the technical efficiency and its determinants of the MFIs. Methodologically, efficiency of the MFIs is estimated using the preferred DEA and then complimented the SFA for the robustness of the results. The remaining part of this chapter is structured as follows. Content wise, the chapter begins with discussion of prior empirical finding on efficiency of MFIs in the globe. The next section provides the methodology i.e., the DEA model specification, and input and output selection. Then section three presents results and discussions. Finally, section four presents the conclusion. 4.2 Prior empirical works on efficiency of MFIs Though the efficiency of the banking sector is adequately examined, researches related to the efficiency of MFIs in general are limited. This fact is substantiated by Berger and Humphrey (1997). Their survey shows that more than 130 studies have used the frontier techniques in analyzing efficiency of banks in different countries. On the other hand, a survey by Cummins and Weiss (2000), which focuses on efficiency in the insurance industry, has found 21 studies which applied frontier techniques. A more recent survey
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68
CHAPTER FOUR
TECHNICAL EFFICIENCY OF ETHIOPIAN
MICROFINANCE INSTITUTIONS
4.1 Introduction
This chapter aims to measure the technical efficiency and its determinants of the MFIs.
Methodologically, efficiency of the MFIs is estimated using the preferred DEA and then
complimented the SFA for the robustness of the results. The remaining part of this
chapter is structured as follows. Content wise, the chapter begins with discussion of prior
empirical finding on efficiency of MFIs in the globe. The next section provides the
methodology i.e., the DEA model specification, and input and output selection. Then
section three presents results and discussions. Finally, section four presents the
conclusion.
4.2 Prior empirical works on efficiency of MFIs
Though the efficiency of the banking sector is adequately examined, researches related to
the efficiency of MFIs in general are limited. This fact is substantiated by Berger and
Humphrey (1997). Their survey shows that more than 130 studies have used the frontier
techniques in analyzing efficiency of banks in different countries. On the other hand, a
survey by Cummins and Weiss (2000), which focuses on efficiency in the insurance
industry, has found 21 studies which applied frontier techniques. A more recent survey
69
by Luhen (2009) found more than 93 studies using frontier efficiency measurement with
application to the insurance industry. However, only studies of (Nghiem,2004; Gutierrez-
Nieto et al., 2005; Gutierrez-Nieto et al., 2009; Hassan and Tuffe, 2001; Qayyum and
Ahmed, 2006; Haq et al., 2007; Sufian, 2006; Bassem, 2008; Hermes et al., 2009; Hassan
and Benito, 2009; Nawaz, 2009; Masood and Ahmed, 2010,Oteng-Abayie et al., 2011)
are found in microfinance institutions. The findings of these empirical studies are
thoroughly discussed below.
Guitierrez-Nieto et al. (2005) applied a DEA non-parametric approach to analyze the
efficiency of 30 Latin American MFIs. In their study, they tried to explore the
multivariate analysis of the DEA results by developing 21 specifications using two inputs
and three outputs. Their study found that an NGO and a non-bank financial institution are
the most efficient among the various group of MFIs.
Bassem (2008) estimated efficiency of 35 microfinance institutions in the Mediterranean
zone during the period 2004–2005 using DEA and found that eight institutions were
efficient. Further, the study revealed that size of the MFI has a negative effect on
efficiency.
Hassan and Sanchez (2009) applied DEA to investigate the technical and scale
efficiencies of microfinance institutions (MFIs) in three regions: Latin America countries,
Middle East and North Africa (MENA) countries, and South Asia countries, and
compares efficiencies across regions and across type of MFIs. They found that technical
efficiency is higher for formal MFIs (banks and credit unions) than non-formal MFIs
(nonprofit organizations and non-financial institutions). Furthermore, South Asian MFIs
70
have higher technical efficiency than Latin American and MENA MFIs. Finally they
concluded that the source of inefficiency was pure technical rather than scale, suggesting
that MFIs were either wasting resources or were not producing enough outputs (making
enough loans, raising funds, and getting more borrowers).
Masood and Ahmed (2010) applied a stochastic frontier model to estimate the efficiency
of 40 Indian microfinance institutions for the period 2005-2008. They found that mean
efficiency level of microfinance institutions is low (34%) but it increases over the period
of study. The study also estimated determinants of efficiency and the result showed that
age of microfinance institution is positive determinant of efficiency. Further, the study
found regulated microfinance institutions are less efficient.
Haq et al. (2009) investigates the efficiency of 39 MFIs in developing world (Africa,
Asia, and Latin America) using the data envelopment analysis (DEA) based
intermediation and production approaches. These diffident approaches tend to give them
conflicting results. Their findings show that non-governmental microfinance institutions
under production approach are the most efficient. On the other hand, the study shows
bank-microfinance institutions outperform and are more efficient under intermediation
approach.
Servin et al. (2012) using stochastic frontier analysis examines technical efficiency of
different types of microfinance institutions in Latin America. Their sample includes 315
MFIs operating in 18 Latin American countries for the period 2003-2009. Their
methodology permits them both the production frontier and error structures to differ
between four types of ownership types of MFIs (NGO, Cooperative/Credit Union, Non-
71
Bank Financial Intermediary and Bank). They differentiate between intra-firm and inter-
firm efficiency. Their results show that Non-Governmental Organizations and
Cooperatives/Credit Unions have much lower inter-firm and intra-firm technical
efficiencies than Non-Bank Financial Intermediaries and Banks, which indicates the
importance of ownership type for technical efficiency. According to the authors, the
finding that NGOs and Cooperative/Credit Unions now are, on average, less efficient
than mutual NBFIs and Banks seem to suggest that further increases in regulation and
competition will be needed to curtailing inefficiencies of non-share holder MFIs.
Abdul Qayyum and Ahmad (2006) tried to investigate the efficiency of 85 MFIs in South
Asia (consisting of 15 Pakistani, 25 Indian, and 45 Bangladeshi). The analysis revealed
that the inefficiency of the MFIs in Pakistan, India, and Bangladesh is mainly of technical
nature and to improve their efficiencies, they suggest that the MFIs need to enhance their
managerial expertise and improve technology.
Nghiem et al. (2004) investigates the efficiency of microfinance industry in Vietnam
through a survey of 46 schemes in the north and central regions by employing the Data
Envelopment Analysis (DEA). The result of the study reveals that the average technical
efficiency score of schemes is 80%. Further, the study found that age and location have
positive effect on efficiency of the schemes.
Hassan and Tufte (2001) examine cost inefficiency and determinants of the Grameen
Bank (GB) using branch level cost data over the 1988-1991 period. Using a stochastic
frontier analysis they found that Grameen Bank’s branches staffed by the female
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employees operated more efficiently than their counterparts staffed by the male
employees.
Gregorio and Ramirez (2004) analyzed the efficiency of Microfinance Institutions (MFIs)
in Peru between 1999 and 2003 by estimating a stochastic cost frontier. They found
that MFIs with the largest assets tend to post the highest efficiency levels and
that MFIs operating in less concentrated market tend to be more efficient. Further their
study shows that cost efficiency of MFIs is affected by average loan size, proportion of
net assets, financial sufficiency, financial leverage, business experience and proportion of
farm loans.
Sufian (2006) also analyzed the efficiency of 80 Non Bank Financial Institutions (NBFI)
in Malaysia for the period 2000–2004 using DEA. His study revealed that only 28.75% of
80 observations are efficient. Moreover, his study revealed that the size and the part of
the market have a negative effect on efficiency.
Martinez-Gonzalez (2008) examined the relative technical efficiency of a sample of
microfinance institutions (MFIs) in Mexico using the data envelopment analysis (DEA).
The study found that most of the MFIs have been more successful in achieving the type
of efficiency related to sustainability rather than outreach. Further the study found that
average size of loan, proportion of assets used as performing portfolio, percentage of
FINAFIM funds, scale of operations, ratio of payroll to expenses, age, structure of
the board, and for-profit status of the MFI have significant impact on efficiency of
MFIs.
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Hermes et al. (2008) used stochastic frontier analysis to examine a trade-off between
outreach to the poor and efficiency of microfinance institutions based on 435 MFIs and
found that outreach and efficiency of MFIs are negatively correlated. Their finding
further indicates that efficiency of MFIs is higher if they focus less on the poor and/or
reduce the percentage of female borrowers.
Nawaz (2010) attempts to measure the financial efficiency and productivity of
Microfinance Institutions (MFIs) worldwide taking into account the subsidies received by
MFIs by using the non-parametric Data Envelopment Analysis (DEA). The study carried
out a three-stage analysis. Firstly, technical and pure efficiency scores are calculated by
splitting subsidies into input and output and entered into the DEA framework
specifications depending on whether they are generating benefits (negative subsidies) or
cost (positive subsidies) to the society. Secondly DEA-based Malmquist indices are
calculated to analyze the intertemporal productivity change. Thirdly, Tobit Regression
analysis are carried out to test a series of hypotheses concerning the relationship between
financial efficiency and other indicators related to MFIs productivity, organization,
outreach, sustainability and social impact. The study concludes that overall subsidies
contribute to financial efficiency of MFIs albeit marginally. The study also provides
evidence on the tradeoff between outreach to the poor and financial efficiency. That is
MFIs which cater to the poor tend to be more inefficient than those with clients relatively
well off. Also evident is the fact that lending to women is efficient only in the presence of
subsidies MFIs in South Asia and Middle East & North Africa tend to be less efficient
than the others.
74
Ahmad (2011) has attempted to estimate the efficiency of microfinance institutions in
Pakistan. The non parametric Data Envelopment Analysis has been used to analyze the
efficiency of these institutions by using data for the year 2003 and 2009 respectively.
Both input oriented and output oriented methods have been considered under the
assumption of constant return to scale and variable returns to scale. He found that three
MFIs are on efficiency frontier in the year 2003 under both constant return to scale and
variable return to scale assumptions. Further, in year 2009, four microfinance institutions
are efficient under constant return to scale and nine are efficient under variable return to
scale assumption.
Oteng-Abayie et al. (2011) estimates economic efficiency of 137 microfinance units in
Ghana for 2007-2010 sample periods using a Cobb-Douglas stochastic frontier model.
They found that the MFIs are producing at constant cost to size with an overall average
economic efficiency for the group of MFIs to be 56.29%. Further their study reveals that
the main sources of inefficiencies in the microfinance sector in Ghana are due to the
variation in management practices and differences in technical capacities (both in training
and portfolio quality). Finally, the study reveals that age and savings indicators of
outreach and productivity, and cost per borrower are found to be significant determinants
of economic efficiency.
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Source: Author’s survey
Table 4.1: Efficiency studies on MFIs
Author Data description Approach
Hassan and Sanchez(2009) 215 MFIs in the world DEA
Gutierrez-Nieto et al. (2007) 21 MFIs in Latin America DEA
Hamiza Haq et al. (2007) 39 MFIs from the world DEA
Abdul Qayyum and Munir Ahmed (2006) 85 MFIs from India, Pakistan and Bangladesh DEA
Nghiem (2004) 46 MFIs in Vietnam DEA and SFA
Ahmed Nawaz (2009) 204 MFIs around the world DEA
Bassem(2008) 35 MFIs in Mediterranean DEA
Hassan and Tufte (2001) Grameen Bank branch level over the 1988-1991 period SFA
Hermes et al. (2009) 435 MFIs in the world for the period 1997-2007 SFA
Oteng-Abayie et al. (2011) Ghana MFIs for the period from 2007-2010 SFA
Masood and Ahmed (2010) 40 Indian microfinance institutions for the period 2005-2008 SFA
Gregorio and Ramirez (2004) Peru MFIs for the period of 1999-2003 SFA
Martinez-Gonzalez (2008) Sample MFIs in Mexico DEA
Ahmed (2011) MFIs in Pakistan DEA
Servin et al. (2012) 315 MFIs from Latin America SFA
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4.3 Methodology
In empirical works on the efficiency of financial institutions the parametric - SFA and the
non parametric – DEA are overwhelmingly dominating (Berger and Humphrey, 1997).
The DEA involves the use of linear programming whereas SFA involves the use of
econometric methods (Coelli et al., 1998). As the SFA impose functional and
distributional forms on the error term, the DEA does not require any functional form to
be specified. Further, while the former distinguishes the component of inefficiency in to
random and inefficiency effect, the later deems any deviation from the efficiency frontier
to the result of inefficiency. Studies acknowledged that both approaches have advantages
as well as limitations (Berger and Humphrey, 1997).The superiority of one approach over
the other has been a discussion and is still debatable in literature of financial institutions.
However, still others suggest that, for instance, Resti (1997); Ondrich and
Ruggiero(2000); and Leon(2001) both produce similar rankings, and conclude that both
approaches are complimentary to measure efficiency. Indeed, the nonparametric DEA is
more frequently used than parametric methods (Berger and Humphrey, 1997).
Parametric measurement includes specifying and estimating a stochastic production
frontier or stochastic cost frontier. In this method, the output (or cost) is assumed to be
function of inputs, inefficiency and random error. The main strength of the stochastic
frontier function approach (SFA) is its incorporation of stochastic error, and therefore
permitting hypothetical testing. An often quoted disadvantage of this approach, however,
is that it imposes an explicit functional form and distribution assumption on the data.
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In contrast, the linear programming technique of data envelopment analysis (DEA) does
not impose any assumptions about functional form; hence it is less prone to mis-
specification. Further, DEA is a non-parametric approach so does not take into account
random error. Hence, it is subject to the problems of assuming an underlying distribution
about the error term. However, since DEA cannot take account of such statistical noise,
the efficiency estimates may be biased if the production process is largely characterized
by stochastic elements.
For the purpose of this study the non parametric DEA is preferred at least for three
reasons. First it considers multiple inputs and multiple outputs to assess the efficiency of
MFIs (i.e the dual objectives of social and financial).Second it does not require a prior
assumption about the analytical form of the production function. Third, DEA works well
with small number of observations as the case of Ethiopian MFIs.
4.3.1 Data envelopment analysis (DEA)
Originally, DEA was first introduced in the work of Farrell (1957) and then developed in
the work of Charnes et al. (1978) and is applied to non-profit organizations where the
objective of profit maximization and cost minimization may not be considered as the vital
factor. It has been extensively applied in performance evaluation and benchmarking of
schools, hospitals, bank branches, production plants, financial institutions (Charnes et al.,
1994; and Berger and Humphrey, 1997).
The DEA technique is essentially a linear programming technique that converts multiple
inputs and outputs into a measurement of efficiency. This conversion is conducted by
78
analyzing the resources (inputs) used and the results (outputs) achieved for each decision
making unit (DMU) or microfinance institution. The inputs and outputs of each DMU
(microfinance institution) are compared to the same quantities for all the remaining units.
The DEA identifies the most efficient units in a population and provides a measurement
of inefficiency for all the others. The method constructs a frontier based on actual data.
Firms on the frontier are efficient, while firms off the efficiency frontier are
inefficient.DEA is based on the concept of relative efficiency and is widely used in
efficiency and productivity analysis of financial institutions (see, Berger and Murphy,
1997). Moreover, DEA provides information about peers, which are the efficient schemes
that have similar input-output structure as some inefficient schemes.
In DEA, efficiency can be measured by an input-oriented process, which focuses on
reducing inputs to produce the same level of outputs, and an output-oriented process,
which aims to maximize outputs from a given set of inputs. The two measures provide
the same results under constant returns to scale but give different values under variable
returns to scale (Fare and Lovell 1978; Coeli et al., 1998). Furthermore, the choice of an
orientation will have only minor influences upon efficiency scores (Coelli et al., 1998).
However, this study is based on output oriented DEA which assumes the optimal output
that can be produced given a set of inputs. The output orientation seems more appropriate
to MFIs because such institutions are expected to reach many discriminated poor people
using a given level of inputs.
The DEA technical efficiency is calculated by assuming both Constant Returns to Scale
(CRS) and Variable Returns to Scale (VRS). The CRS assumption is only appropriate
79
when all DMUs are operating at an optimal scale. However, factors like imperfect
competition and constraints on finance may cause a DMU not to operate at optimal scale
(Coelli et al., 1996). Banker, Charnes and Cooper (1984) suggested an extension of the
CRS DEA model to account for variable returns to scale. The use of the CRS
specification when not all DMU’s are operating at the optimal scale will result in measure
of technical efficiencies which are confounded by scale efficiencies. The use of the VRS
specification will permit the calculation of pure technical efficiency devoid of these scale
efficiency effects. This study assumes the variable return to scale as it seems appropriate
for MFIs particularly operating in developing countries such as Ethiopia. However, for
comparison both assumptions are pursued to estimate the efficiency of the MFIs. By
running both CRS and VRS it is possible to decompose technical efficiency into pure
technical efficiency and scale efficiency and therefore to determine whether a DMU has
been operating at optimal returns to scale, increasing returns to scale, or decreasing
returns to scale ( Celli, 1996).
The study is based on Charnes, Cooper and Rhodes (1978) - CCR model and Banker,
Charnes and Cooper (1984)- BCC model. The basic difference between these two models
is the treatment of returns to scale. While the latter takes into account the effect of
variable returns to scale (VRS), the former restricts DMUs to operate with constant
returns to scale (CRS).
Assume that there are n Decision Making Units (DMUs), and each DMU has m inputs to
produce s outputs. This model measures the relative efficiency ratio of a given DMU (ho)
80
by the sum of its weighted outputs to the sum of its weighted inputs. It can be formulated
where ℎ𝑜is the efficiency ratio of the DMU𝑜;𝑢𝑖 ,𝑢𝑟are virtual multipliers (weights) for the
i th input and the r th output, respectively; m is the number of inputs, s is the number of
outputs and n is the number of DMUs; 𝑥𝑖𝑜is the value of the input i for DMUo, 𝑦𝑟𝑜is the
value of the output r for DMUo.
The equation (1) is fractional programming and has an infinite number of solutions. It can
be solved by adding an additional constraint, ∑ 𝑣𝑖 𝑚𝑖=1 𝑥𝑖𝑜 = 1 . The form then converts to
the multiplier form of the DEA LP problem:
Maxℎ𝑜 = � 𝜇𝑟 𝑦𝑟𝑜𝑠
𝑟=1 (4.2)
Subject to
� 𝜇𝑟 𝑦𝑟𝑜 −� 𝑣𝑖 𝑥𝑖𝑗𝑚
𝑖=1
𝑠
𝑟=1≤ 0, 𝑗 = 1, … ,𝑛,
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To reflect the transformation, the variables from (u, v) have been replaced by (μ, ν). ε is a
non‐Archimedean quantity defined to be smaller than any positive real number. The dual
form of equation (2) can be written as an equivalent envelopment form as follows:
minℎ𝑜 = 𝜃𝑜 − 𝜀(� 𝑠𝑖− + � 𝑠𝑖+𝑠
𝑟=1
𝑚
𝑖=1)
Subject to
� 𝑥𝑖𝑗
𝑛
𝑗=1𝜆𝑗 + 𝑠𝑖− = 𝜃𝑥𝑖𝑜, 𝑖
= 1, … ,𝑚, (4.3)
� 𝑦𝑟𝑗𝑛
𝑗=1𝜆𝑗 − 𝑠𝑟+ = 𝑦𝑟𝑜, 𝑟 = 1, …,
𝜆𝑗 ,𝑠𝑖−, 𝑠𝑟+ ≥ 0, 𝜀 > 0, 𝑗 = 1, … ,𝑛,
Where 𝜃𝑜 the proportion of DMUo′s inputs needed to produce a quantity of outputs
equivalent to its benchmarked DMUs identified and weighted by the𝜆𝑗 . 𝑠𝑖−. and 𝑠𝑟+are the
slack variables of input and output respectively. 𝜆𝑗is a (𝑛 × 1)column vector of constants
and can indicate benchmarked DMUs of DMUo. If ℎ0∗ = 1 is meant efficient and ℎ𝑜∗ < 1
is meant inefficient where the symbol “*” represents the optimal value.
However, the CCR model is calculated with the constant returns to scale (CRS)
assumption. This assumption is not supportable in imperfectly competitive markets. The
BCC model proposed by Banker, Charnes and Cooper (1984) modifies the CCR model
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by allowing variable returns to scale (VRS). The CRS LP problem can be easily modified
to account for VRS by adding the convexity constraint
∑ 𝜆𝑗𝑛𝑗=1 = 1 to equation 4.3 to provide
minℎ𝑜 = 𝜃𝑜 − 𝜀(� 𝑠𝑖−𝑚
𝑖=1+ � 𝑠𝑟+
𝑠
𝑟=1)
Subject to
� 𝑥𝑖𝑗𝑛
𝑗=1𝜆𝑗 + 𝑠𝑖− = 𝜃𝑥𝑖𝑜, 𝑖 = 1, … ,𝑚, (4.4)
�𝑦𝑟𝑗
𝑛
𝑗=1
𝜆𝑗 − 𝑠𝑟+ = 𝑦𝑟𝑜, 𝑟 = 1, … , 𝑠,
� 𝜆𝑗𝑛
𝑗=1= 1,
𝜆𝑗,𝑠𝑖−, 𝑠𝑟+ ≥ 0, 𝜀 > 0, 𝑗 = 1, . . ,𝑛,
The Overall Technical Efficiency (OTE) from CCR model can be decomposed into Pure
Technical Efficiency (PTE) and Scale Efficiency (SE). The PTE can be obtained from
BCC model. We can measure the SE for a DMUo by using CCR and BCC model as
follow:
𝑆𝐸 = 𝑂𝑃𝐸𝑃𝑇𝐸� ( 4.5)
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If the ratio is equal to 1 then a DMU𝑂is scale efficient, otherwise if the ratio is less than
one then a DMU𝑂is scale inefficient.
4.3.2 Tobit Model
The efficiency scores obtained from the DEA in the first stage may be regarded sufficient
to identify whether a particular microfinance is technically efficient or not. However,
there are institutional and environmental factors that are beyond the control of managerial
actions. More recently, in literatures of banking, education, hospitals and ports, among
others, apart from estimating the efficiency of various decisions making units (DMUS),
substantial number of studies have been tried to examine the determinants of efficiency
and productivity by employing a second stage DEA models(Aly et al., 1990; Miller and
Noulas, 1996; Rangan et al ,1988; Fethi, et al. 2000; Jackson and Fethi 2000; Stavarek,
2003; Casu and Molyneux, 2003; Chang and Chiu, 2006; Gupta et al, 2008; Delis and
Papanikolaou, 2009).
In the second stage, the efficiency scores from the first stage are (as dependent variable)
regressed upon institution’s specific and environmental variables to determine what
causes differences in efficiency levels across the DMUs under a given study. Generally,
in literatures the commonly used approaches are ordinary least square, Tobit regression
model, Tobit censored regression, Truncated regression and more recently double
bootstrap approach. An important issue, however, is that efficiency scores are censored at
the maximum value of the efficiency scores.
84
As Wooldridge (2000) noted, traditional methods of regression are not suitable for
censored data, since the variable to be explained is partly continuous and partly discrete
and thus, ordinary least squares analysis generates biased and inconsistent estimates of
model parameters. The empirical results using the Tobit regression model analysis is
more efficient and consistent than using the ordinary least squares model. According to
Hoff (2007), in most case the Tobit approach is sufficient in representing the second
stage DEA models. But McDonald (2009) argues that this approach might be
inappropriate because the efficiency scores are fractional data, not generated by a
censoring process. Based on the results of post-estimation regression analyses it has to be
decided as to which approach is more appropriate. Simar and Wilson (2007) however
recently criticized the Tobit model approach, and suggested instead a double bootstrap
approach in which it is possible to improve the accuracy of the regression estimates.
According to Afonso and Aubyn(2005),even if Tobit results are possibly biased, it is not
clear that bootstrap estimates are necessarily more reliable. In cross country efficiency
studies, Afonso and Aubyn(2005) apply both the usual Tobit procedure and two very
recently proposed bootstrap algorithms and the results are strikingly similar with these
three different estimation processes. Similarly, Borge and Haraldsvik (2009) performed
Tobit regressions and single and double bootstrap procedures in order to explain the
variation in efficiency scores across municipalities. It turns out that the bootstrapping
procedures yields similar results as Tobit in terms of sign and significance of the
coefficients except one variable that loses its significance with the single bootstrap
procedure. In terms of quantitative effects, however, the double bootstrap estimates are
substantially larger than the single bootstrap and Tobit estimates.
85
Based on the justification and given to limited nature of the dependent variable (the range
of efficiency estimated is limited to 0 and 1) a censored Tobit regression model is used
for the study, however, for robust analysis an alternative bootstrap approach suggested
by Simar and Wilson (2007) is also applied to estimate the determinants of Ethiopian
MFIs efficiency.
The Tobit model may be specified for observation (MFIs) i as follows
𝑦𝑖 ∗ = 𝛽′𝑥𝑖 + 𝜀𝑖
𝑦𝑖 = 𝑦𝑖∗𝑖𝑓𝑦𝑖∗ > 0, and (4.6)
𝑦𝑖 = 0, otherwise
Where 𝜀𝑖 ~ N(0, σ2), 𝑥𝑖and 𝛽 are vectors of explanatory variables and unknown
parameters respectively.The 𝑦𝑖∗is a latent variable and 𝑦𝑖 is the DEA score. The
likelihood function (L) is maximized to solve b and based on 19 observations (MFIs) of
xi and yi as
𝐿 = �(1 − 𝐹𝑖)�1
√2𝜋𝜎2𝑦>0𝑦𝑖
× 𝑒1(𝑦𝑖−𝛽𝑥𝑖)
2 𝜎2 (4.7)
Where
𝑭𝑖 = �1
√2𝜋
𝛽𝑥𝑖𝜎
−∞
𝑒𝑡2
2𝑑𝑡
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The first product is over the observations for which the MFIs are 100% efficient (y = 0)
and the second product is over the observations for which MFIs are inefficient (y >0). Fi
is the distribution function of the standard normal evaluated at𝛽′ 𝑥𝑖 𝜎⁄
4.4 Inputs and output variables
In empirical studies on efficiency of financial institution an important and controversial
issue is choice of inputs and outputs. For banking there are two main approaches - the
production approach and the intermediation approach (Berger and Humphrey, 1997).
Both approaches differ in their view of the role of banks and neither fully captures the
dual roles of banks. Consequently, the outputs and inputs used have not been consistent
in empirical studies and the issue remains debatable in literature. Under the production
approach, banks or financial institutions in general are viewed as institutions making use
of various labor and capital resources to provide different products and services to
customers. Thus, the resources being consumed such as labor and operating cost are
deemed as inputs while the products and the services such as loans and deposits are
considered as outputs. Under the intermediation approach, financial institutions are
viewed as financial intermediaries which collect deposits and other loan able funds from
depositors and lend them as loans or other assets to others for profit. Microfinance
institutions are also financial institutions but their approach and motive differs from other
financial institutions. They are special banks that target mainly poor persons often
without any collateral requirements (Gutierrez-Neito et al., 2005; Tariq et al., 2008).
The selection of inputs and outputs for this study is based on the dual objectives of micro
finance institutions viz., outreach and sustainability framework which is in line with the
87
prior study of (Gutierrez-Neito et al., 2005). Specifically, outputs in this study are defined
to include gross loan portfolio, number of loans and interest and fee income. These items
represent the dual objectives of MFIs. To produce these outputs, the study assumes MFIs
use two main inputs: labor and operating expenses. The selected variables along with
definitions are given below (Table 4.2).The definition for inputs and outputs are based on
the MIXMARKET2.
Table 4.2: Selected inputs and outputs along with definitions
Variables Definition
Inpu
t
Total number of employees Total number of staff members or employees at end of period who were actively employed by the MFI. This number includes contract employees or advisors who dedicate the majority of their time to the MFI, even if they are not on the MFI’s roster of employees.
Operating expenses
Expenses related to operations, such as all personnel expenses, rent and utilities, transportation, office supplies, ,depreciation and amortization, and administrative expense
Out
put
interests and fee income All income on loans made to clients
Gross loan portfolio
All outstanding principal for all outstanding client loans including current, delinquent and restructure loans but not loans that have been written off. It excludes interest receivable and employee loans
Number of loans outstanding(number)
Number of loan accounts associated for any outstanding loan balance with the MFI and any portion of the loan portfolio.
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Finally, the three outputs and the two inputs are specified as follows:
Out put Input
y1: Gross loan portfolio x1: Labor
y2: Interest and fee income x2: Operating expenses
y3: Number of loans
4.5 The Data
The study is based on annual data covering the period from 2004-2009 for the 19 micro
finance institutions operating in Ethiopia. In fact, there are 29 MFIs currently operating in
the country; however, data cannot be generated from all the MFIs as some lack sufficient
data while others are new to be included in the analysis. The study period is limited to
this period due the availability of the data. The data is extracted from the financial
statements provided by the Association of Ethiopian Microfinance Institutions (AEMFI),
National Bank of Ethiopia (NBE) and the Mix Market3.
4.6 Empirical Findings
In this section the study provides the efficiency results of for the industry as well as for
specific microfinance institutions under both the assumptions - Constant Returns to Scale
and Variable Returns to Scale. As discussed earlier, the DEA technical efficiency is
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calculated by assuming both Constant Returns to Scale (CRS) and Variable Returns to
Scale (VRS). The Constant Returns to Scale assumption is only appropriate when all
MFIs are operating at an optimal scale. However, factors like imperfect competition and
constraints on finance may cause a microfinance not to operate at optimal scale. In order
to exploit the scale efficiency or inefficiency the study makes use of both assumptions.
Table 4.3 presents descriptive statistics of all input and output variables used in this
study.
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Table 4.3: Descriptive statistics of variables (inputs and outputs) in US dollars