a comparative analysis of parametric and...

A Comparative Analysis of Parametric and Non-Parametric Models for Predicting... 105

* Department of Economics, University of Nigeria, Nsukka 4100002, Enugu State, Nigeria, E-mail:[email protected]

Asian-African Journal of Economics and Econometrics, Vol. 12, No. 1, 2012: 105-133

A COMPARATIVE ANALYSIS OF PARAMETRIC ANDNON- PARAMETRIC MODELS FOR PREDICTINGCOMMERCIAL BANK EFFICIENCY IN NIGERIA

Alilu Noah* & Hyacinth E. Ichoku

ABSTRACT

There is concern that, the state dominated inefficient and fragile banking system in a developingeconomy like Nigeria is a hindrance to economic growth and development. This workcomprehensively evaluated efficiency performance in Nigeria commercial banks using StochasticFrontier Analysis (SFA) and Data Envelopment Analysis (DEA) models along with its technicaland allocative efficiency components to ascertain the causes of systemic bank crisis in Nigeria..DEA results shows 52% mean technical efficiency, implying that improvement in technicalefficiency is still possible by 48% while the SFA mean technical efficiency shows 49%, meaningthat 51% possible improvement is required. Equally, SFA indicates 28% mean allocative efficiencywhich similarly suggests a further improvement by 72%, while the DEA mean allocative efficiencywas 32% implying that 68% possible improvement is needed. The direction of causality betweenefficiency estimates and the basic factors that determines efficiency was assessed using Tobitmodel.

Keywords: Efficiency; Date Envelopment Analysis; Stochastic Frontier Analysis; Tobit Modeland Nigeria Commercial Banks.

1. INTRODUCTION

The role of the banking sector in the development process has been noted in the literature. Theyhelp to intermediate funds from the surplus units to the deficit unit of the economy. Apart fromthe intermediation role, bank stimulates investment, economic growth, employment as well asinternational trade and payment. This underscores why every economy takes interest in creatingand nurturing a virile and efficient banking system. A higher degree of commercial bankefficiency is sin qua-non-to greater financial stability, product innovations, access by householdand firms to financial service, which in turn can improve the prospect for economic growth.

The ongoing reforms in the Nigeria banking system may have not come as a surprise tosome people. This is because the health of the banks portrays some incidence of distress. Theearlier closure of five (5) banks in 1994/95 and unprecedented liquidation of twenty-six (26)banks in 1998 did not put an end to the distress syndrome. In 1998, more institutions ought tohave been closed. However, that was not done because the Nigeria Deposit InsuranceCorporation (NDIC) did not have adequate funds in it Deposit Insurance fund (DIF) to pay

106 Alilu Noah & Hyacinth E. Ichoku

depositors (Umoh P. N. 2005). Also, government was ab kinitio unwilling to provide the neededfunds for the exercise as had been done in other countries where government financial supportamounted to a significant proportion of the Gross Domestic producer (GDP). For exampleArgentina (early 1980-82) 55% of GDP; Indonesia (1997 to 2001) about 50% GDP; cote d-Ivoire (1988 -1991) about 25% of the GDP and melaysia (1987 to 2001) about 16.4 of theGDP (see Honahan and Klingebiel, 2001; Diamond D.W, 2001; Nasution A. 2001). The mergersand acquisition strategy of 2005 consolidation exercise reduced the 89 weak bank to 25 bankbased on N25billion capital base requirement.

In a well functioning economy of the world, banks serves as quality controllers for capitalseeking successful project, ensuring higher returns and accelerating output growth. However,a competitive banking system is required to ensure that banks are effective force for financialintermediation, channeling savings into investment thereby fostering higher economic growth.(Thierry B and John M. 2005; Bikker,J.A and Haaf, K 2002; Vesala J. 1995).

Recent development in Nigeria banking industry underscores the need for bank managersto explore the potentials of synergy as a corporate level strategy (Adeyami K.S. 2004). Thesuccess of any monetary policy initiative by the central bank of any economy partly dependson the efficiency of the commercial banks to implement such policies to it logical conclusion.

Prior to 2005 consolidation exercise, there was widespread speculation surrounding thecontinuity or collapse of the then new generation banks in Nigeria in spite of the fact that thesebanks employ a large proportion of Nigeria labour force. The central bank accused most of thecommercial banks of engaging in financial indiscipline –illicit foreign exchange deals, in otherto pile up profit. These banks engage in “round stripping and financing of fraudulent business”(see Ezirim 2004, Oduyemi 1992; Ojo 1992; Umoh 1999, and Adebiyi 2000). It was believedtherefore, that the banks that indulge in such illicit activities have a high probability ofexperiencing crisis in the event of structural change in the economy via stabilization policy ora contractionary monetary policy. The scenario was succinctly summarized by Soludo (2004)that, “it is in this context that we view with serious concern the spate of frauds, ethicalmisconduct, falsification of returns by the banks to the central bank, unprofessional use offemales staff in some banks in the name of ‘marketing’. The implications are that, the resourcebase of such bank is weak and volatile rendering their operation highly vulnerable to swing ingovernment revenue, arising from uncertainties of the international market. In this respect,there is a concern that state dominated, monopolistic, inefficient and fragile banking system inlow income economy like Nigeria is a hindrance to economic growth and development”.

This situation requires an extensive research, given the importance of the role of banks inthe financial sectors of Nigeria economy. Against the forgoing, the broad objectives of thestudy is to carry out an in-depth efficiency performance evaluation of commercial banks usingalternative model (SFA and DEA) and indexes and further compare the predictive power ofthese models and indexes.

1.1. Policy Relevance of the Study

The corpus of evidence from an international survey of financial institutions highlights theusefulness of performance studies to policy makers (see Berger and Humphery, 1997).Essentially


poverty and unemployment are of great concern to policy makers in developing counties,particularly against the backdrop of forecast by World Development Report (1990) ondevelopment indicators that sub-Saharan Africa‘s economic growth rate would hardly exceedits population growth rate during the 1990s. The WDR estimated the annual growth rate to be3% for the modern sector, 4% for the rural sector (farm and non-farm), and 4.5% for the informalsector. The efficient allocation of resources at individual bank levels has implications forinvestment and employment at the national level. It has implications for technical andtechnological progress resulting in supply shifts. Needless to add that gross national product(GNP) and per capita income will also be expected to rise, which will help to serve importsubstitution purpose by supporting domestic demand.

For analytical simplicity, the measurement of efficiency is important for the followingreasons. First, it is a success indicator and performance measure by which production in bankinginnovations are evaluated. Second, it is only by measuring efficiency and separating its effectsfrom the effects of the production environment that one can explore hypotheses concerningthe sources of efficiency differentials. Identification of sources of inefficiency is essential tothe institution of public and private policies designed to improve performance. Third, the abilityto quantify efficiency provides decision makers with a control mechanism with which to monitorthe performance of the production system or units under control.

Among others, it is important to look at this study in the context of the fact that, since early90s, the banking system in Nigeria has been characterized by periodic crisis. An attempt isnecessary therefore to carry out a research work on the performance of Nigeria commercialbanks so as to forestall any impending crisis and to avoid subsequent colossal loose. Capiro,(1992) note that banking crisis entails high fiscal cost, often about 10–20% of the GDP and iscapable of derailing stabilization and any structure adjustment in the economy. Equally it islikely to affect savings and savings habit which translate into negative multiplier effect oneconomic growth through its effect on investment. The reason is that the ability of commercialbanks to mobilize deposit depends, to a large extent, depend on the measure of confidence thatthe non-bank public has in the bank with respect to safety of deposit and size of the capitalbase. The size of the bank’s capital base should not matter to the operation of the bank. Thoughit is necessary that bank should be big to be efficient. But, it’s not a sufficient condition forefficiency. Efficiency connotes “best practice” and risk optimality as well as the ability ofbank management to explore the potential of synergy as a corporate level strategy. (See BorjaAmer et’al 2006). This implies Nigeria and Nigerians should look at banking sector beyondthe 2005 CBN N25 billion-recapitalization bench mark.

Records have shown that government and taxpayers have largely shouldered the directimpact of banking system collapse. “Government of 40 developing countries spent 14.3% oftheir GDP to clean up their financial system after banking crisis. Developing economies asgroups have suffered cumulative fiscal costs in excess of $1 trillion” see Honahan and Klingebiel(2002). Developing economies can benefit much from inefficiency studies that shows thepossibility of increasing productivity by improving efficiency without increasing the resourcesbase or developing new technologies. Measurement of the extent and determinants of efficiencyindicates which aspect of banks characteristics can be addressed by investment to improve


efficiency. Thus the results of this study are expected to give appropriate policyrecommendations designed to increase bank productivity by identifying key characteristics.

2. REVIEW OF LITERATURES

2.1. Theoretical

The fundamental aim of a commercial bank is profit maximization like any other businessenterprise. Its capacity to maximize profit depends upon its investment policy. Its investmentpolicy, in turn depend on the manner it manages its investment portfolio. Portfolio managementrefers to “The prudent management of a bank’s assets and liabilities in order to seek someoptimum combination of income or profit, liquidity and safety”. (Jhnigan M. L, 2002). Thuscommercial bank investment policy emerges from a straightforward application of the theoryof portfolio management, given a particular circumstance of commercial banks. Commercialbanking operation is premised on acquisition and disposing of income-earning assets. Theaddition of assets and cash make up what is known as portfolio. Commercial banks earningassets consist of securities and financial obligations, and its style of management have significanteffect on the financial market, borrowing capacity and the spending practice of household,firms and on the entire economy.

Economic literature admits that, there exist three main objectives of portfolio management– liquidity, safety and income. These objectives are trade-off oriented (Jhingan M.L, 2002).Deductively, the conflicting objectives of portfolio management lead to a conclusion that for abank to earn more profit, it must strikes a judicious balance between liquidity and safety. Thisconclusion is worthy of note in Nigeria as most banks even after consolidation complain ofinadequate cash at customers demand.

In consistency with economic theory, Agu (1988) defines commercial banks performanceas profitability and output while Farrel and Lovell (1990) and Athanassopoulous and Giolcas(2000) defines it in terms of production. Vitas and Neal (1992) and Boray and Sieria (1993)defines banking performance in terms of profitability and efficiency. In the same vein, Denizer,Dinc and Tarimcilar (2002) adopted the theory, which defines commercial bank performancein terms of efficiency. Whichever perspective one look at commercial bank performance eitheras production units or intermediary institution or both, the ability of a commercial bank toresolve the conflicting objectives of liquidity, safety and profitability with the best practicedetermines the performance of the commercial bank.

2.2. Empirical Literatures

In Thailand, Chansarn (2007) investigated the efficiency of Thailand’s financial sector includingbanking sector after the financial crisis in 1997 by looking at the total factor productivity (TFP)growth. He also investigated the efficiency of domestic and foreign commercial banks. Basedon the sample of 12 commercial banks listed on the Stock Exchange of Thailand over theperiod of 1998 – 2004, the study reveals that the efficiency of commercial bank sector wasdiminishing over the period 1998 – 2004. However, the sharp decrease in efficiency in bankingsector occurred only over the period 1998 – 1999, while the efficiency was decreasing very


slightly over the period of 1999 – 2004. The study also suggests that domestic and foreigncommercial banks were not different in efficiency.

Rangkakulnuwat (2007) utilized Data Envelopment Analysis (DEA) to estimate thetechnical efficiency of nine Thai commercial banks from 2000 to 2005. The results indicatethat commercial banks in first tier had always produced at the production frontiers and hadhigher technical efficiency than the second and third tiers. Commercial banks in second andthird tiers could sometimes produce at the production frontiers. Nevertheless, there was noevidence that technical efficiencies of banks in second tier were higher than those in third tier.

Casu and Molyneux (2000) employed the DEA approach to investigate the efficiency inEuropean banking systems. They attempted to examine whether the productive efficiency ofEuropean banking systems has improved and converged towards a common European frontierbetween 1993 and 1997, following the process of EU legislative harmonization. Halkos andSalamouris (2001) utilized the DEA approach to measure the efficiency of the Greek bankingsector with the use of a number of suggested financial ratios for the time period 1997 – 1999.

Jemric and Vujcic (2002) used DEA to analyze bank efficiency in Croatia. They attemptedto measure the relative efficiency of banks in Croatian market according to size, ownershipstructure, date of establishment and quality of assets in the period from 1995 until 2000. Wu(2002) conducted productivity and efficiency analysis of banks operation in Australia sincethe deregulation of the Australian financial system in early 1980s. DEA was employed inorder to investigate the levels of and the changes in the efficiency of Australian banks over theperiod from 1983 to 2001.

Ozkan-Gunnay and Tektas (2006) assessed the technical efficiency of non-publiccommercial banks in Turkey between 1990 and 2001, following the DEA model. Debasish(2006) attempted to measure the relative performance of Indian banks, using the output-orientedCRR DEA model. The analysis used nine variables and seven output variables in order toexamine the relative efficiency of commercial banks over the period 1997 – 2004. Finally,Luciano (2007) illustrated the efficiency features of Italian banking system through the reviewof the most important empirical studies over the last fifteen years. Particular emphasis is givento DEA studies.

Allen and Rai (1996) use Data Frontier Analysis (DFA) and stochastic frontier approach(SFA) for a systematic comparison of inefficiency measures across 15 developed countriesunder different regulatory environments. They found that large banks separated bankingcountries (that prohibit the functional integration of commercial and investment banking) hadthe largest measure of input inefficiency amounting to 27.5% of total cost as well as significantlevels of diseconomies of scale. More specifically, they found that large banks are significantlymore (less) inefficient than small banks in Australia, Canada, Italy, Japan and the U.S. However,when environmental variables are included in the model the differences between both bankingindustries are reduced substantially. In particular, the specific environmental conditions ofeach country play an important role in the definition and specification of the common frontierof different countries. They take into account three categories of environmental variables: (i)Those that describe the main macroeconomic conditions, which determines the banking product


demand characteristics; (ii) Those that describe the structure and regulations of banking industryand (iii) Those that characterize the accessibility of banking service [Altunbas et’al. 1988;Lozano, Pastor and pastor 2002 and Dietsch and Lozano 2002] shared the same opinion.

2.2. Overview of the Nigeria Banking System

A review of development in the Nigeria banking and financial system indicates that the bankingsector has undergone remarkable changes over the years, in terms of the numbers of institutions,ownership, structure, as well as the scale of operations driven largely by the deregulation of thefinancial sector in line with the global trend. (Ogunleye, 2005).

Nigeria’s first bank, the Africa Banking Corporation, was established in 1932. While theearliest banks were essentially foreign owned, several wholly or partially indigenous bankswere essentially in the 1930s. No banking legislation existed until 1952. The 1952 ordinanceset standards, required reserve fund, established bank examination and provided for assistanceto indigenous banks. At that point Nigeria had three foreign banks (The Banks of British WestAfrica, Barclays Bank and the British and French Bank) and two indigenous banks (The NationalBank of Nigeria Continental Bank). The central bank of Nigeria empowered to regulate theindustry-commenced operations on July 1959. In the context of the structural Adjustmentprogramme (SAP) in 1986, Nigeria undertook a broad program of financial liberalization.Interest rate and entry into the banking system were deregulated.

In 1993, the Federal Government acquired a 40% equity ownership in the three largestbanks. Also in 1996, under the second Nigeria enterprise decree requiring 60% indigenousholding, the government acquired an additional 20% holding in the three banks (first, unionand UBA) and 60% in the other foreign owned banks (see NDIC and CBN annual reports1996). At the same time, while ending direct rationing of foreign exchange for the real sector,the government maintained a multiple exchange rate regime, thus opening a new era of arbitrageand rent seeking for financial institutions that had privileged access to foreign auctions. Theconsequence was the quick entry of many new players into the banking system, especiallymerchant banks that specialized in foreign exchange operations. Entry requirements was verylow accompanied with high market premiums that could earn with arbitrage activities in theforeign exchange markets allowed a returns on equity of 300%. Consequent upon this, thenumber of banks tripled from 40 to Nearly 120. Employment in the sector doubled and its,contribution to GDP almost tripled (see Lavis and Stain 2002; CBN report, 1997). Despite theboom recorded, there was high financial dis-intermediation. This is because the increasingnumber of banks and human capital in the sector was channeled into arbitrage and rent-seekingactivity rather than financial intermediation.

By 1990, the bubble started to burst; Net-Performing loan (NPL) increased sharply.Especially the merchant bank sector where most of the foreign exchange speculators wereconcentrated and the government own banks showed increasing signs of distress. In 1991, thecentral bank imposed moratorium on new licenses. New prudential Guidelines, introduced in1990-91 made the extent of distress in the banking system even clearer. During 1992, severalbanks were scrutinized and delicensed. By mid 1993, political uncertainty following a failedtransition to civilian rule triggered a bank run, which resulted in paralyses of the financial


system, temporary closures and failures. Finally, in 1994, three merchant banks and onecommercial bank were liquidated by the new military government that reintroduced exchangerate and interest rate controls. (See table 1). Then following inflationary burst, rising blackmarker premium on the Naira and economic decline resulted in windfall gains for someconnected market participant, negatively enhance deepening the overall distress in the financialsystem.

Table 1Analysis of Bank Liquidation in Nigeria (1994 – 2004) before the Consolidation Excises of 2005

Year Commecial Bank Merchant Bank Number Liuidated

1994 1 3 41995 1 - 11998 12 14 262002 1 - 12003 - 1 12005 89 banks decomposed into 25

through mergers and acquisition 64

Source: Authors Computation

Political economy’s explanation of the liberalization and boom – and burst period focuseson rent-seeking activities of the governing elites (Lavis and Stein 2002). While moving forwardwith structural reforms in many areas, liberalization measures were selective to maintainpatronage opportunities and insulate the governing elites and their supporters from the economiccosts of these reforms. The expanding financial sector and the new arbitrage possibilities throughthe mult-fiered exchange rate system offered numerous patronage opportunities for politicaland military leaders. Bank licensing was a politically influenced process and managing boardsof banks were dominated by politicians and senior military officers. It was in this volatileenvironment, that in 1992 the privatization agency (technical committee on privatization andcommercialization, TCPC) scheduled the sale of government shears in some commercial andmerchant banks in which the federal government had an ownership stake. Few privatized bankchanged their senior management or governing boards following privatization, and recurrentstruggle between shareholders and management were reported (Levis and Stein, 2002).

A Failed Bank Decree was used to persecute cases of misconduct and fraud in the bankingindustry, but the federal government had equity investment of at least 45% in thirteen out ofthe fourteen banks and 4.45% in merchant bank of Africa. There was politically motivateddetention of some top management. Few failing banks were resolved and the authorities focusedmore on containing the resolving the crises. It is only under the new government in 1993,which eventually handed over power to a civilian regime in May 1999, that a more seriouscleanup started in the financial system; with 26 bank licenses revoked in 1998. Additional 4liquidated in 2000 and one in 2003 (See table 1). That was the caricature scenario that envelopedthe Nigeria banking system, which invited the current wave of reforms of banking institutionsthrough mergers and acquisition in 2005. The vision is to build a sound and reliable bankingstructure for the 21st century among others.


3. METHODOLOGY

In economic theory there are algebraic and geometric characterizations of production plans thatcan unambiguously be regarded as non-wasteful (efficient). A production vector y € Y is efficientif there is no yi € Y such that yi � y and yi � y. (Halvarian, 2003: koopman, 1951: and Hoffmanand Binger, 2004), this concept means a production vector y is efficient if there is no otherfeasible production vector yi that generates as much output as y using no additional inputs. Thisphilosophy is the basis of illustrative production possibility frontier (PPF), from which themethods of analysis used in this study originate.

Measurement of efficiency started with Farrel (1982) who following Debreu (1951) andKoopmas (1951), proposed a division of efficiency into two components: technical efficiency,which represents a firm’s ability to produce a maximum level of output from a given inputs,and allocative efficiency, which is the ability of a firm to use inputs in optimal proportions,given their respective prices and available technology. The combination of these two measuresyields the level of economic efficiency.

Using the Farrel illustration, considering the output oriented measure with two outputs Y1

and Y2 by using a single input X.

Figure 1: Technical and Allocative Efficiencies from Output Orientation

The level of output of fully efficient banks can be estimated using parametric and nonparametric method (SFA and DEA) of frontier estimation on given data. As presented in figure1, ZZ1 is the production possibility curve of two outputs with single input or given resourceset and DD1 is iso-revenue curve which is drawn on the basis of the prices of outputs. Theproduction possibility curve ZZ1 represents all those points of two outputs that are technicallyefficient. While DD1 represents all those points which are allocativelly efficient. If the banksunder consideration operates at point A, the technical efficiency (TE), allocation efficiency(AE) and economic efficiency (EE) of banks under consideration is defined as


TE = OA/OB (1)

AE = OB/OC (2)

The value of all these efficiency measures lies between zero and one. If the revenue oftechnical efficiency is closer to one, it indicates that the input of the bank yield outputs that iscloser to technically efficient point while a value closer to zero indicates that the level of inputproduces combination of outputs closer to the most technically inefficient point. Similarly, avalue closer to one of allocative efficiency indicates the output combinations that are closer toallocatively efficient point for a given level of input while a value closer to zero indicates theoutput combination for a given level of input is closer to the most allocately inefficient point(Coelli et al., 1998). If the efficient banks operate under constant return to scale, both inputand output oriented measure give the same results for technical efficiency of banks understudy (Fare and lovell, 1978).

Based on the above enunciation, the measurement of commercial banks performance theparametric (SFA) and non parametric (DEA) methods can be used

3.1. Stochastic Frontier Analysis (SFA)

This work employs the stochastic frontier analysis approach to evaluate the efficiency ofcommercial bank in Nigeria. The study looks into different contexts of parametric indexes inanalyzing the performance of commercial banks in terms of efficiency.

The stochastic frontier analysis (SFA) model is the prominent form of parametric methodfor efficiency measurement that specifies the relationship between output and inputs levelsand decomposed the error term into two components: (a) a random error, and (b) an inefficiencycomponent. The random is assumed to follow a symmetric distribution is the traditional normalerror term with zero mean and a constant variance while the inefficiency term is assumed tofollow an asymmetric distribution which may be expressed as a half-normal, truncation, andexponential or two-parameter gamma distribution. The fundamental assumption underlyingstochastic frontier analysis model is that, the inefficiency component and the random componentof the residual will be distributed differently. In particular, the random component is assumedto be distributed normally, as is consistent with the OLS model. If �t is normally distributed asall residual variance is interpreted as arising from random noise and measurement error(Wagstaff, 1989). If �t is skewed, then it is taken as evidence that there is inefficiency in thesample. Subject to t being skewed, stochastic frontier analysis decomposes the error terminto two parts with zero covariance. t = V

t + U

t cov (V

t, U

t) = 0.

Ut is the controllable (non-negative) component that captures the cost of inefficiency in an

organization. Hence, Ut defines how far an organization operates above the cost frontier. If V

t

= O, production lies on the stochastic frontier and the Dmu is technically efficient, of Vt, >o,

production lies below the frontier and is inefficient. The extraction of this requires distributionalassumptions on the two error components thus:

Vi ~

iid N (O, 2); U

t ~ iid N+(0, 2), that is nonnegative half, normal, exponential truncated

or gamma distributed. Allows by standard and (frontier 4.1 and LIMDEP 2000 computersoftware) measuring that Vt and Ut and are distributed independently of each other, and of the


regressor. Because of the erratic continues management styles in Nigerian banks, the probabilityof a bank to be efficient at one period of time is almost the same as the probability for it to beinefficient at any other subsequent period. Therefore the half normal distribution assumptionfit best the analysis at hand.

3.1.1. The SFA Models

3.1.1a Output Function

[i] Cobb-Douglas

Y = F(L, K) (4)

Where F(.) describes the functional form relationship between output and different mixes oflabour and capital. Cobb-Douglas production function is thus:

Y = �L�1 K�2 (5)

and estimated in logarithmic form as

1 2 2i iIn InL InK� � �� (6)

Where �1

and �2

are parameters describing the contributions to output made by labour andcapital respectively. The logarithmic form allows these parameters to be interpreted as elasticities-a one percent increase in the amount of labour employed is predicted to lead to a one percentincrease in output to the value of �

1. �

t= error term decomposed into two (V

t-U

t)

[ii] Translog Model: The attraction of the Translog is it flexibility as it can approximate virtuallyany functional form (Intriligator, 1978, Christensen, Jorgenson and Lau, 1973). The translogis estimated by including the squares and cross-product of the explanatory variables. Thusthe translog production function is expressed below:

1 1 2 2 3 3 4 1 1 5 2 2 6 3 3

7 1 2 8 1 3 9 2 3 t

In i In In In In In In

In In In

� � ��

�� (7)

If 4,

5,

6,

7,

8, &

9 are not significantly different from zero, the function reduces to a

Cobb-Douglas. One of the drawbacks of this model is that there is likely to be a largenumber of variables of parameter to be estimated: for every additional variable added to themodel, it is necessary to include a square term and cross-product with the existing variables.

To estimate parameters for the predication of efficiency using the standard Cobb Douglasfunction, and trans-log frontier models the variables are expressed in the models as;

1 32INV LON OVHD LLP DEP

i iTA TA TA TA TAIn In In In� � �� (8)

IVN LONTA TAand are outputs while :OVHD LLP DEP

TA TA TAand are inputs

In Y = vector of outputs [loans asset ratio and investment asset ratio] while; x1 = OVH/TA

[overhead asset ratio]; x2

= LLP/TA [loans loose provisioning asset ratio]; x3

= DEP/TA[total deposit asset ratio] : the rest are trans-log interactions .but t = error decomposed intotwo(v

1 – u

1).


3.1.1b. Cost Function

The cost function equivalent to the Cobb-Douglas production function of (5) can be written as:

C = f(Y, w, r) (9)

Where w and r, represents input prices for labour (wages) and capital (rent) respectively. Thecost function equivalent to the Cobb-Douglas production function is

1 2 1 /( 1 2)1( , , ) ( , )C w r w r� � � �� (10) or

TC = ƒ (Q, P) exp v – µ (11)

In the translog form the cost function is expressed in it logarithmic form thus:1 1

1 1 1 12 2

112 i i

InTC InQ InP InQInQ InPInP

InQInP

� ��

�� (12)

Where In Tc = Total cost ie [x1; x2; x3] as explained in equation—— (8) above.

InQ = outputs; InP = input price; InpInp =prices interaction; InQInp =output-priceinteraction; InQInQ =outputs interaction while v

1-u

1 = the inefficiency and the traditional error

term

3.2. Data Envelopment Analysis [DEA]

Data envelopment analysis (DEA) is a linear programming based technique for measuring therelative performance of organizational units where the presence of multiple inputs and outputsmakes comparisons difficult. It involves constructing a non-parametric piecewise frontier overthe data so as to calculate efficiency relative to this frontier. DEA calculates the relative efficiencyscores of various decision making units (DMU) in a particular sample. The DMUs can be banksor branches of banks.

The DEA measure compares each of the banks/branches in that sample with the best practicein the sample. It tells the user which of the DMUs in the sample are efficient and which are not.The ability of the DEA to identify possible peers or role models as well as comparative simpleefficiency scores gives it an edge over other methods. Since the mid-eighties, DEA has becomeincreasingly popular in measuring efficiency in different national banking industries, for examplein Sherman and Gold (1985), Rangan et al. (1988), Ferrier and Lovell (1990), Berg et al.(1993), Brockett et al. (1997), and in many other papers. Leibenstein and Maital (1992) arguethat DEA is the superior method for measuring overall technical inefficiency.

DEA is an alternative analytic technique to regression analysis such as stochastic frontieranalysis. Regression analysis approach is characterized as a central tendency approach and itevaluates DMUs relative to an average. In contrast, DEA is an extreme point method andcompares each DMU with the only best DMU. The main advantage of DEA is that, unlikeregression analysis, it does not require an assumption of a functional form relating inputs tooutputs. Instead, it constructs the best production function solely on the basis of observed data;hence statistical tests for significance of the parameters are not necessary. Despite the existenceof several DEA models, this study utilizes CCR-Model which is an output-oriented model


where DMUs deemed to produce the highest possible amount of output with the given amountof input.

3.2.1. The DEA Model

CCR-Model is introduced by Charnes, Cooper and Rhodes (1978). This model measures theefficiency of each DMU which obtained as a maximum of a ratio of total sum of weightedoutputs to total sum of weighted inputs. Consequently, the efficiency can be defined as follow.

weighted sum of outputsEfficiency

weighted sum of inputs� (13)

The weights for the ratio are determined by the restriction that the similar ratios for everyDMU have to be less than or equal to unity, thus reducing multiple inputs and outputs to asingle “virtual” input and single “virtual” output without requiring pre assigned weights.Therefore, the efficiency score is a function of the weights of the “virtual” input-outputcombination. Suppose that there are n DMUs, each with m inputs and s outputs, relativeefficiency score of a given DMU0 is obtained by solving the following linear programmingmodel.

01

01

max

J

j jj

M

m mm

u y

v x

�

�

� ��

�� (14)

Subject to:1

1

1 1,...

J

j jij

M

m mim

u yi I

v x

�

�

� ��

Where: yj0

= quantity of output j for DMU0

uj = weight attached to output j, 0, 1,....,ju j J��

Equation (14) makes it clear that a different set of weight is associated with each DMU.Obviously, equation (14) is a fractional linear program equation but can be made more tractableby converting it to a system of linear equations in which the objective function can be maximizedsubject to a set of linear constraints. In that case, the variable weights u and v, are maximizedsubject to the specified constraints. The maximized values of u and x, measure the efficiencyof the ith DMU subject to the constraint that no unit has efficiency greater than 1. Anotherproblem with equation (14) is that in its present form it has an infinite number of solutions.This implies that if u* and v* is solutions to (14), so also are �u* and �u* (Jacob et al. op cit).Additional constraint is therefore imposed such that either the numerator or the denominatorof equation (14) is made equal to 1. By constraining the denominator to equal 1, leads to themaximization problem: maximize weighted output subject to weighted input being equal to 1.This implies writing equation (2) in the form:

xm0

= quantity of input m, for DMU0


vm = weight attached to input m, 0, 1,....mv m M��

, 0max ( ' )u v u y (15)

Subject to

' 1

' ' 0 1,...

, 0

i

i i

v x

u y v x i I

u v

�

� � �

�

The maximization problem in (3) can also be expressed as a minimization problem (Jacobset al., op cit):

min�,��

Subject to:

0

0

0

i

i

y Y

x X

� � � �

� � � �

� �(16)

where xi represents the column vector of inputs and y

i represents column vector of outputs for

each DMU. X and Y represent respectively, the matrix of inputs and outputs for all the DMUs. � isa scalar quantity that lies in [0,1] range and represents the technical efficiency score of each.When a DMU has its ��= 1, then the DMU is at a point on production frontier. It is technicallyefficient relative to other DMUs in the comparative group. But for ��< 1 implies that the DMU isrelatively inefficient. It is below the production frontier. The amount by which the score of theinefficient DMU differs from 1 indicates the extent the DMU could reduce inputs without reducingits output. � is a column vector of constants. The solution to the linear programming problem is toseek the minimum value of � that reduces the input variables x

i to �x

i but at the same time ensures

the output level given by yi (Jacobs et al. op.cit). The linear programming problem must be solved

for each DMU in order to obtain the technical level of efficiency of that DMU.

In this study, DEA approach reflects the way of evaluating the efficiency of commercialbank from the perspective of output maximization as earlier noted with one output and threeinputs chosen for each commercial bank.

y = vector of outputs [loans asset ratio and investment asset ratio]

input; x1 = OVH/TA [overhead asset ratio];

input x2 = LLP/TA [loans loose provisioning asset ratio;

input x3 = DEP/TA [total deposit asset ratio]

There are several assumptions for this study. Each commercial bank is assumed to operatingat an optimal level. Implying that they are producing the highest possible amounts of outputwith a given amounts of inputs. Hence, production function of each commercial bank performsconstant return to scale (CRS). Therefore, we can expect that doubling the amount of inputwill double the amount of output.


3.3. Factors which Derives Inefficiency

As defined in equation 16 the SFA and DEA scores falls between the interval of 0 and 1 (0 < h �1), making the dependent variable a limited dependent variable which is the necessary and sufficientconditions for the application of a Tobit model. It has been noted in literature that Tobit model canhandle the features of the distribution of efficiency measures and thus on the long run provideestimates that can assist or guide policies that could improve performance. See Luoma et al.,(1996), Chilingerian,(1995), Kirjavainen and Loikkanen, (1998). SFA and DEA efficiency estimatesobtained in the first stage are the dependent variables in the second stage Tobit model. Tobitmodel was first suggested in econometrics literature by Tobit (1958). These models are known astruncated or censored regression models where expected errors are equal to zero. It is truncated ifthe observations outside a specified range are totally lost and censored if one can at least observethe exogenous variables (Amemiya, 1984). Consequently estimation with ordinary least squares(OLS) regression of h would lead to a biased parameter estimates since OLS assumes a normaland homoscedastic distribution of the disturbance and the dependent variable (Maddala, 1983).

The standard Tobit model can be defined as follows for DMUs (10 banks) 0:* ,0 0 0y x� � �� (17)

* *0 0 0, ,y y if y o and� � (18)

y0 = 0, otherwise (19)

Where [0~N(0, �2)3, x

0 and � are vector of explanatory variables and unknown parameters,

respectively. The y*0 is a latent variable and y

0 is the SFA and DEA scores.

The likelihood function (L) is maximized to solve � and � based on observations ofexplanatory variables and the SFA and DEA scores.

210 02( 2 )

2*

0 0

( )1

0 (20 0

(1 )xy

y y

L F Xe ��

��

� ��

�(20)

L = where20

1/2

/ / 210 (2

x t

xF e dt

� � �

��

�� (21)

The first product is over the observations for which the banks are 100 percent efficient(y = 0) and the second product is over the observations for which banks are inefficient (y > 0).F0 is the distribution function of the standard normal evaluated �x

0/�.

Technical and allocative efficiency of firm (bank) is assumed to be determined by a numberof factors, including firm specific variables as well as variables concerning the manager ordecision-maker of the firm. For this study, technical and allocative efficiency of banks is modeledto depend on inputs of production as well as on bank management – specific characteristics inNigeria. These factors are capital adequacy, asset quality, management quality, earnings stability,and liquidity (CAMEL). Although financial ratios have short term measures of performance(Sherman and Gold, 1985; Oral and Yolalan, 1990) the limited competitiveness status of bankingactivities in Nigeria has increased the need for the usage of these environmental ratio factorsas a take base of determining their level of performance


Ineff = f (C, A, M, E, L) (22)Where ineff denotes inefficiency index estimated from the standard SFA and DEA models.

C is capital adequacy. A is a proxy for asset quality. M is the management quality (NIM/TA),E is the bank earning stability indicator variable which measured the management capacity tosustain growth over time and L is excess liquidity variable. Inefficiency function iseconometrically expressed in the model below.

(Ineff)t=

0+

1C

t+

2A

t+

3M

t+

4E

t+

5L +

t. (23)

This means efficiency index is estimated for all inefficient observation; otherwiseobservations that are efficient have indices of zero inefficiency.

4. DATA PRESENTATION AND ANALYSIS

The bank of interest for this study are Access Bank, Afri-Bank, Equatorial Trust Bank, DiamondBank, First Bank, Guaranty Trust Bank, Union Bank, United Bank for Africa, Wema Bank, andZenith Bank. The selection was randomly done taken cognizance of their years of establishmentand scales of operations in order to ensure heterogeneity among the sampled banks as well as toallow for cross-sectional scale comparison. Cross-sectional secondary data are collected fromNDIC to allow estimation of the technical and allocative efficiencies for the banks. The dataincluded information on physical quantities of production inputs as well as outputs. To identifyfactors that influence efficiency, data were collected on factors such as – capital adequacy,asset quality, management quality, earnings stability, and excess liquidity of the sampled banks.The technical and allocative efficiency for the entire sampled banks were computed and comparedover time. Data collection covered a period of sixteen (16) years annually.

4.1. Empirical Results

Following the methodology described, we evaluated the efficiency of all sampled banks in theestimated set and calculated the SFA and DEA efficiency scores obtained by running separateprograms. We pooled the cross bank data and used them to define a common best practiceefficiency frontier. This allowed us to focus on determining the relative difference inperformances across banking industries in Nigeria. The same approach was previously followedby Casu and Molyneux (2000), Dietsch and Weill (2000) as well as Grigorian and Manole(2002). The analysis is divided according to the two model used- the stochastic frontier analysisand the data envelopment analysis. These models shall equally be analyzed in two indexes fromthe technical and allocative efficiency perspective of the commercial Bank

(A) Stochastic Frontier Model Analysis: the analysis of the estimation involved twoparametric models-(the C-D frontier model, and the translog frontier model) with two indexes(output function for technical efficiency and cost function for allocative effidiency). Robustnessof the estimated models and indexes indicated by the values of the maximum log- likelihoodfunction estimates. The values were compared and the model with higher magnitude of thelog-likelihood functions provides the better model for the data. Table 2-3 shows the result ofthe of the maximum likelihood estimates of the models and indexes as computed with the useof Frontier 4.1 econometric software.


Table 2Results of Estimated Models (Technical Efficiency Index)

Variables Parameter Cobb-douglas Model Trnslog Model

Coeff T-ratio Coeff T-ratio

CONSTANT A0 2.1203(0.228)* 3.528 0.2644(0.573)* 0.462OVH/TA[X1] A1 -0.0113(0.234)* -2.410 -0.797(0.429)* -0.185LLP/TA[X2] A2 -0.6379(0.102)* -2.627 0.415(0.479)* 0.868DEP/TA[X3] A3 0.1842(0.365)* 2.504 -0.106(0.492)* -0.216X4 [X1*X1] A4 0.418(0.148)* -0.283X5[X2*X2] A5 0.908(0.849)* 0.107X6[X3*X3] A6 0.239(0.972)* 0.246X7[X1*X2] A7 0.229(0.319)* 0.936X8[X1*X3] A8 0.610(0.209)* 0.292X9[X2*X3] A9 -0.341(0.334)* -0.102C [Z1] A1 0.1378(0.649)* 2.212 -0.176(0.810)* -0.217A [Z2] A2 -0.5419(0.855)* -1.632 -0.772(0.177)* -0.436M [Z3] A3 0.0364(0.822)* 2.102 -0.511(0.747)* -0.684E [Z4] A4 0.2944(0.620)* 1.467 -0.968(0.742)* -0.131L [Z5] A5 -0.8959(0.171)* -2.524 0.410(0.102)* 0.39Sigma2 �2 =��u

2 + �v2 0.110 0.6708(0.11)* 0.57

Gamma � =��u2/�2

u + �v2 0.5715 0.4919(0.12)* 0.42

Loglikelihood LLf 0.7841 0.16020

Source: Authors Computation. *Figures in parentheses are standard errors, significant at 5% level

Table 3Results of Estimated Models (Allocative Efficiency Index)

Varibles Parameter Cobb-douglas Model Translog Model

Coeff T-ratio Coeff T-ratio

Constant A0 0.189(0.773)* 2.245 0.329(0.685)* 3.482OUTPUT[Q1] A1 -0.356(0.614)* -1.579 -0.302(0.651)* -1.464PRICE [P1] A2 0.184(0.762)* 2.241 -.0925(0.652)* -2.142Q2 [Q1*Q1] A3 -0.587(0.169)* -2.346P2 [P1*P1] A4 -0.121(0.102)* -2.119PQ [P1*Q1] A5 0.57(0.441)* 2.129C [Z1] A1 0.196(0.258)* 1.761A [Z2] A2 -0.178(0.349)* -1.508M [Z3] A3 -0.107(0.272)* -2.394E [Z4] A4 0.467(0.551)* 1.848L [Z5] A5 0.307(0.435)* 1.705Sigma2 �2 = �u

2+�v2 0.259(0.755)* 2.344 0.294(0.388)* 1.759

Gamma � =��u2/�2

u+�v2 0.2626(0.209)* 2.125 0.987(0.164)* 1.602

Loglikelihood LLF -0.1014 -0.7663

Source: Authors Computation*Figures in parentheses are standard errors, significant at 5% level.

From the table, the Cobb-Douglas model for technical efficiency index proves higher thanthe translog model. Hence the Cobb-Douglas model becomes the preferred model for the analysisof the technical efficiency index. The emerging of Cobb-Douglas (C-D) as the preferred model


has solved the problem of degree of freedom normally encountered in the translog modelestimation. Thus the discussion shall be based on the result of the estimated C-D function. Theestimates show that some of the variable have positive coefficient while others are negative.The implication of the variable having positive coefficient is that, an increase in the level ofany of the variable would lead to an increase in the output of the banking firm. The coefficientof the overhead cost to asset ratio and Deposit Asset ratio is positive with respect to productionindex, while that of loans-loose provisioning is negative. In spite of the fact that the overallmean efficiency was 52% see table, efficiency was at least less than 10% in most periods understudy. Instead, inefficiency was on increase from 70% in 1991 to the highest rate of 83%recorded in 2001. The record of 2004 designates an upward reverse of the trend of inefficiencycompared to the previous year’s situation. See appendix 3 for the yearly efficiency results.

On the other hand, the maximum likelihood estimates for the allocative (cost) efficiencyindex of the two models (Cobb-Douglas and Translog) are presented in table 3. The resultshow that, Cobb-Douglas model with log likelihood of -0.10142038 is equally better, comparedto the translog model which has (-0.76631082).

A critical sensitivity analysis of the results shows that some of the variables portraydisappointing signs of the coefficient. Loans-Asset ratio has negative sign while InterestExpenses to Deposit ratio show the expected a prori negative sign. This means that, over timeunder study most commercial bank in Nigeria engaged in financial round-tripping in conformitywith Soludo, (2004).It is an indication that huge profits declared over time by most Nigeriancommercial banks are virtually product of illegal business.

Analytically, the computed technical efficiency varies between 0.17 and 0.84 with a meanvalue of 0.49. This result shows that the highest mean technical efficiency comes from theFirst Bank of Nigeria (FBN) 0.84 and United Bank for Africa (UBA) 0.73. For the allocativeefficiency the highest values comes from First Bank of Nigeria (FBN), and UBA of 0.36,followed by the United Bank for Africa (UBA) and Zenith Bank of 0.36. While EquatorialTrust Bank has the lowest mean allocative efficiency of 0.12 as tabulated in table 4 andgraphically shown in figure 2.

Table 4

Banks Sfa Model

Mean tech EFF Mean Alloctive EFF

ACESS 0.307 0.193AFRIK 0.173 0.170DIAMOND 0.612 0.274ETB 0.126 0.124GTB 0.687 0.356UBA 0.729 0.417FIRST 0.842 0.500UNION 0.424 0.214WEMA 0.333 0.182ZENITH 0.656 0.356Mean 0.49% 0.28%



(B) Data Envelopment Analysis Model: The estimation of efficiency under dataenvelopment analysis DEA is based on constant return to scale as specified in the model(equation 14). The estimated technical and allocative efficiency scores of commercial banksfor the year 1991 to 2006 are reported in table 5 with the use of Banxia Frontier Analyst 4(DEA software). Unfortunately none of the commercial bank is fully efficient. Some of thebanks that performed fairly better though not fully efficient are First Bank, United Bank forAfrica, Guaranteed Trust Bank and Zenith Bank with average technical efficiency scores of0.86%, 0.79%, 0.69% and 0.65% respectively. While the average allocative efficiency scoresof 0.50%, 0.49%, 0.46%, and 0.36% are for First Bank, Zenith Bank, Union Bank and WemaBanks respectively. The most inefficient banks for the year under review are Equatorial TrustBank (ETB), Afrik Bank and Access Bank with average technical efficiency scores of 0.16%,0.27% and 0.33% respectively. Allocatively, the following scores of 0.14%, 0.16%, 0.18%,and 0.27% were for Access Bank, ETB, Afrik Bank and Diamond Bank respectively.

Table 5

Banks Dea Model

Mean Tech EFF Mean Alloctive EFF

ACESS 0.33 0.1403AFRIK 0.27 0.1893DIAMOND 0.618 0.2746ETB 0.164 0.1646GTB 0.691 0.2349UBA 0.788 0.3381FIRST 0.858 0.5001UNION 0.456 0.4559WEMA 0.363 0.3616ZENITH 0.658 0.4989Mean 0.52% 0.32%


Figure 2: SFA Model of Technical & Allocative Efficiency Scores of Banks


Consequently, the fairly efficient banks could be converted to technical efficient banks ifthey were able to produce obtained level of output by utilizing 0.14%, 0.21%, 0.31% and0.35% less of currently utilized inputs respectively. Equally the most inefficient banks (AccessBank, ETB, Afrik Bank and Diamond Bank) for the year under review with estimated score of0.14%, 0.16%, 0.18%, and 0.27% could be converted to allocative efficient banks under CRSif the banks was able to choose optimal inputs proportions of 0.86%, 0.84%, 0.82% and 0.73%respectively at a given input prices.

4.2. Efficiency Range Distributions of both Models

(A) SFA Model: Figure 3 indicates that technical efficiency ranges under stochastic frontiermodel varies between 13 to 84%. It shows that 20% of the bank has technical efficiency rangebetween 10-20%, while 20% has efficiency range of 31-40. Other ranges indicted that 10% ofthe entire banks has efficiency range of 41-50 while three banks (constituting 30%) has efficiencyof between 61-7. Only one bank each (UBA and First Bank) fall into efficiency range of 71-80and 81-90 respectively scores constituting 10% each.

Table 6

SFA Model

EFF Rang Mean Tech EFF Mean Alloctive EFF

10-20 20% 40%21-30 0% 20%31-40 20% 20%41-50 10% 20%51-60 0% 0%61-70 30% 0%71-80 10% 0%81-90 10% 0%


Figure 3: DEA Model of Technical & Allocative Efficiency Scores of Banks


On the other hand the computed allocative efficiency varies between 0.12 and 0.50 with amean value of 0.28%. The forgoing analysis has indicated a wide variation in the technical andallocative efficiency of the sampled banks within and across their scales of operations. Giventhe existence of significant technical and allocaative inefficiencies, it is important to analyzethe determinants of the technical and allocative inefficiency of Nigerian commercial bank.

(B) DEA Model: essentially the computed technical efficiency varies between 0.16% and0.86% with the mean efficiency value of 0.52% while the allocative efficiency scores variesbetween 0.14% and 0.50% with the mean efficiency value of 0.32%.

Table 7

DEA Model

EFF Rang Mean Tech EFF Mean Alloctive EFF

10-20 10% 30%21-30 10% 20%31-40 20% 20%41-50 10% 30%51-60 0% 0%61-70 40% 0%71-80 10% 0%81-90 0% 0%


Only 10% of the bank falls within the efficiency range of 71-80 while the efficiency rangeof 61-70 has 40% of the entire banks. Equally just 20% of the banks falls within the efficiencyrange of 31-40 and 21-30, 10-20 efficiency range has 10% of the bank each respectively. Fromthe allocative perspective, the efficiency range of 10-20 and 41-50 has 30% of the bank each,while 20% of the bank each falls within the efficiency range of 21-30 and 31-40 respectively.

Figure 4: SFA Model Efficiency Range of Technical & Allocative Scores


This implies that there exists wide variation in the technical and allocative efficiency of sampledbanks within and across their scales of operations, thus necessitating the determinations offactors that cause the variations.

Comparatively the result reveals that technical efficiency is generally higher than theallocative efficiency. The findings are not surprising given the fact that the former incorporatesboth cost and revenue. What is striking however is that the estimates for cost inefficiency aregenerally high, which suggest that there is a greater potential for efficiency improvement bybetter management and control of the cost side, compared to the revenue side.

Determinants of Efficiency Using Tobit Regression

An exploration of inter-banks and cross- bank differences in efficiency necessitates a two-stageanalysis whereby efficiency scores from the first stage SFA and DEA scores are regressedagainst environmental variables. We used SFA scores obtained from the standard Cobb-Douglasestimation and the DEA (CCR) output orientation scores obtained from the constant return toscale (CRS). The estimation is based as specified equation 23.

In the analysis of the determinants of efficiency, the computed technical and allocativeefficiencies were modeled to depend on some identified factors-(capital adequacy, asset quality,management quality, earnings stability, and liquidity). Inefficiency indexes were regressedagainst these five explanatory variables. Their estimated coefficient, the respective standarderrors and T-ratios of the Tobit models are obtained using LIMDEP is presented in table 8 & 9.The coefficient estimates of the explanatory variable are of great interest because they haveimportant policy implications. The result in table 8 & 9 shows that most of the determinants ofefficiency are significant implying that the variables identified as determinants of efficiencyare very relevant in explaining the level of individual technical and allocative efficiency of thesampled Banks which is used as reference to all commercial bank in Nigeria.

Figure 5: DEA Model Efficiency Range of Technical & Allocative Efficiency Scores


Determinants of Technical Efficiency

Using the consolidated data for all sampled inefficient commercial banks, the estimated resultsare presented in table 7. The result indicated that with the exception of one variable (assetquality) which is insignificant in both SFA and the DEA models, the test suggests plausiblerobustness of all the estimates. Starting with capital adequacy variable(C), from the two modelsit is discovered that it is significant and bears a negative sign. The intuition is that as long as thebank spends more on improvement of its capital base, it increasingly adds to its efficiency gain.Spending on capital goods in commercial bank caters among other thing – for equipment likeATMs, Computers, and network development to enhance efficient service provision. Under-investment in fixed capital goods is thus among the factors that drives inefficiency in banks.Capital adequacy improves market perception and market values of financial institutions. Itleaves banks in a good financial risk level (leverage) and thus reduces the cost of fund as wellas improves availability of funds.

Table 8Explaining Technical Efficiency of both Models using Tobit Regression

Technical Efficiency

Variables Parameter SFA Model DEA Model

Coeff Std Error T-ratio Coeff Std Error T-ratio

CAP. ADQ ð 1 -0.081142 0.0061791 -2.313 -0.0610747 0.002238 -2.760ASST .QULT ð 2 0.366133 0.0065204 0.615 0.018099 0.002543 0.440MANGT.QULT ð 3 -0.047194 0.0026035 -1.633 -0.0247085 0.001344 -2.395EAN.STBT ð 4 0.073752 0.0020338 1.361 0.1674252 0.001266 1.572LQDTY ð 5 -0.166210 0.0070392 -2.361 0.2121278 0.003643 -2.382


Consequently, it helps to guard against liquidity problems and also encourage deposit as itprovides a cushion of safety to all categories of creditors. The inverse relationship of capitaladequacy to commercial bank efficiency in Nigeria indicates that, as capital rises relative tothe total assets, the rise is not translated into loans assets and other advances; rather this capitalis transformed to fixed assets and other near earning asset (NEA) like Cars, Building, furniture,increased branch network etc.

From both SFA and DEA asset quality variable indicates that commercial banks efficiencyis significantly driven by the quality of loans asset. However, the growth in technical efficiencyaccounted for by the growth in performing loans is infinitesimal. In fact, the model shows thata 100% improvement in the quality of loans asset of commercial banks will bring aboutapproximately (4%) rise in efficiency. This means that the major part of public perception ofcommercial bank efficiency in Nigeria is driven by other factors than the quality of their loansassets.

The incentive to work variable represented by management quality is significant and has anegative sign in both models indicating that when incentive to work increase inefficiency inbanks decreases. Earning stability in both models is statistically significant and has the most


positive effect on efficiency. Its low coefficient however is with the implication that there areother determinants of efficiency not included in the model. Statistically, a 100% rise in earning(from activities that are embodied in sound banking practice), will bring about 15% rise inefficiency.

Determinants of Allocative Efficiency

Using the allocative inefficiency measures in both SFA and DEA models as the dependantvariable, the impact of regulatory capital adequacy level as proxy by bank capital ratio,inefficiency is positive and statically significant. It is shown that an increase in the ratio ofequity to net loan leads to an increase in the technical efficiency, while an increase in the ratioof equity to total assets leads to cost (allocative) inefficiency. These results indicate that duringthe period under review bank in Nigeria are maintaining high capital ratio relative to an optimallevel, thereby eroding the banks cost efficiency. This however does not mean that the bank’sasset base has being high (except after the 2005 consolidation exercise) but considering theportfolio management decision over time, high capital ratio was prevalent. The finding isconsistent with the argument by Berger and Mester (1997) that banks keep high capital andreserve at an opportunity cost of earning returns from investment.

Table 9Explaining Allocative Efficiency of both Models using Tobit Regression

Allocative EfficiencyVariables Parameter SFA Model DEA Model

Coeff Std Error T-ratio Coeff Std Error T-ratio

CAP. ADQ � 1 0.2010747 0.003198 2.033 0.1650027 0.003198 2.647ASST .QULT � 2 0.3018099 0.003740 2.051 0.2022209 0.003742 2.387MANGT.QULT �3 -0.0247085 0.001347 -2.261 -0.0247085 0.001440 -2.303EAN.STBT �4 0.1674252 0.005286 1.590 0.1600526 0.001052 1.533LQDTY �5 0.0001278 0.003643 1.617 0.0021278 0.003133 1.845


The result equally shows that asset quality explanatory variable which represents the badloans hypothesis, bears a statistically significant positive impact on allocative inefficiency.The implication is that deterioration of asset quality specifically the bad loans syndromecontributes to allocative inefficiency. Hence, in Nigeria loans are very costly to recover(especially 1991 – 2004) and the whole effort amount to “throwing good money after bad”.Specifically, problems loans have preceded inefficiency when some weak bank management[and possibly some exogenous factor beyond the control of bank management] have led to thedeterioration of asset quality and high loan recovery cost and associated cost inefficiency.From the management quality perspective, although this study do not control for the size ofthe bank by partitioning the sample bank according to size [this was evidence to the flat 25billionasset base bench mark] it is discovered that only the larger banks (like First Bank, Zenith etc)tend to be closer to the efficient frontier than other banks, but also they are more likely toachieve an optimal mix of inputs, The evidence is consistent with argument of Deyong (1998)


that larger bank have the resources to attract high caliber personnel and thus attain lowerinefficiencies.

The allocative efficiency index result equally shows that bank liquidity bears a positivebut weak statistically significant impact on cost inefficiency from both SFA and DEA models.The results suggest that as banks in Nigeria increase their liquidity position, they do so at theopportunity cost of expanding their loans portfolios and thus suffer cost inefficiency. Onepossible interpretation of this evidence is that if the banking sector in Nigeria is not competitive(as observe in 1991-2005) the bank may manipulate prices in their favor (insider abuse) andincrease their profitability without necessarily reducing cost or improving efficiency.

5. CONCLUSION

The remarkable comment from the finding of this study is that efficiency status of commercialbank in Nigeria is disappointing (especially 1991 – 2004) to the financial sector reforms becausethe scores turned out to be low. Evidence from the findings indicate that inefficiency in bankswas the outcome of inadequate fixed capital, poor labour compensation, low managementcapacity as banks expand and the overwhelming accumulation of excess liquid assets. Theimpact of the 2005 consolidation excises is yet to be felt by the result of this finding as thepositive result of the 2005 – 2006 was eroded in regression by the prolong woofing performance.

In this study, one main finding of interest is that irrespective of the measure of inefficiency,technical (production) inefficiency is higher than the allocative (cost) inefficiency across theboard, from which we infer that the revenue inefficiency is rather small. Given that bank managershave substantial control on the cost side, the finding reflect the managers cost preference behaviorseven where it subjugates the shareholder’s best interest thus increasing agency costs.

From the Cobb – Douglas preferred model, the main evidence suggest three (3) importantfindings. First, in consistent with what researchers have reported, we find that determinationof asset quality especially between (1991 - 2004) specifically the bad loans syndrome contributesto allocative inefficiency as well as production inefficiency. This poor loan portfolio beingcarried by many commercial banks in Nigeria has led to banking system collapse in the past.This finding supports the bad loan hypothesis. Second, it was discovered that high capital ratioincrease costs relative to an optimal level and deteriorate the banks allocative and technicalefficiency. However, these finding needs to be further investigated and qualified by determiningthe optimum level of bank capital ratios. Third, it’s obvious that bank size matters: large banks(asset base quality) are likely to have the resource to attract high caliber of personnel thatcould enhance efficiency. Capital adequacy is among the critical impediments to inefficiency.Banks may want to optimize productivity through rearrangement of their capital labour balance.From the estimates of the sources of inefficiency, poor labour compensation is among thesource of uninspired work effort in banks. It implies that bank should offer competitivecompensations to their employees to reactivate workers exuberance in order to raise productivity.The weak coefficient of management quality which represents a poor variable returns on assets(ROA) is an indicator of how capable the bank management team can transform the availableresources into earnings and their responsiveness to adjust to the macroeconomic environmentof the bank (strategic management) (Rose, 1999).


Furthermore, the weak coefficient and negative sign of the overhead - total asset ratio(OVH/TA) reflects the expensive cost incurred in carrying out both the traditional function ofmobilizing deposit and the modern function of financial intermediation among others. Thisconforms to researcher’s conclusion that over 60% of the Nigeria Gross domestic product(GDP) is in the informal financial sector of the economy (Soyibo 1995). Equally, the weakcoefficient of the bank’s loans asset ratio (L/TA) is suggestive of the fact that, banks maketheir profits from other sources. Though profitability does not connotes efficiency, this is becausea bank may record high profit but not efficient, apparently the sources of profit could be illegal(devoid of best banking practice) or off balance sheet transaction. In reality efficiency issynonymous to best banking practice.

5.1. Policy Recommendations

Following the major condition drawn from empirical analysis, next are crucial policy implicationsthat practitioners, policy makers and other stakeholders may take into consideration. Becausethe average cost curve of commercial banks were eventually turning up, enhanced competitionin the existing banks should be the prime emphasis. It is important to encourage internationalbanking. The critical challenge is on the aspect of capital flight from Nigeria economy throughforeign banks, which may not have compensating effect if banks in the country do not equallyrise up for outreach to other economies. Equally, substantial foreign ownership of the bank canpromote corporate governance structure of banks in Nigeria, it can engender greater scrutiny ofthe management of the bank in order to mitigate agency-related problem (devoid of insiderabuse) and the pertinent agency costs, thus enhancing performance and reducing cost inefficiency.This recommendation reinforces the conclusion drawn by Murinde Ard Ryan (2003) that banksin Africa have nothing to fear from opening the sector to foreign bank entry.

Another policy advocacy to address the higher estimates for cost inefficiency resultingfrom theory problem (where bank managers may not be acting in the best interest of theirprincipals, and shareholders) is that banks operations deserves greater monitoring not onlythrough the internal corporate governance mechanism, but also through external regulation.For example by regularly accessory and evaluating the banks internal budgetary performancereports generated for internal management. This is particularly important because the ‘true aidfair’ philosophy which guides the external auditors does not sufficiently cover inefficienciesin the internal use of resources, provided such inadequacies are neither fraudulent normisrepresented in the bank of accounts. It is pertinent to note that the current wave ofconsolidation has the potential of evolving a strong and resilient banking system for the nationand as well poses a number of challenges both to the operators and regulatory/supervisors. Inorder to harness the opportunities of bank consolidation the regulators/ supervisory monetaryauthority should note the following recommendations.

First the need for adequate executive capacity with competency, properly skilled andprudency should be emphasized. The ability of executive management to build and articulatesa management team that is able to lead the merged banking entity through the painful processof emerging information technology (IT) system, business times and products, culture andpeople is of critical importance. The forgoing implies that, if the current wave of consolidation


exercise to engendered the needed efficiency in banking systems is to be sustained, there isurgent need for a change of orientation, attitudes, value system and above all capacity buildingby the operators at all levels, particularly at the top management level to address the challengingissues.

Secondly, responsive corporate governance devoid of insider abuse should be an aspectthat should be closely monitored by the regulatory authority in order to ensure transparencyand accountability by the management of banking institutions and the curtailment of their riskappetites. Weak or poor corporate governance becomes an issue as it can course a rapid collapseof an institution. In view of the fact that the systemic repercussion on the failure of a bigbanking institution is grievous the regulatory authority should therefore continue to encouragethe enthronement of responsive corporate governance structures (devoid of insider abuse) foreffective risk management.

More so, the current information disclosure requirements in the banking industry are grosslyinadequate to effectively bridge the information asymmetry between banks and investing publicthat consolidation may create. With consolidation, it is important that the accounting as well asdisclosure requirement of emerging banks be reviewed. Adequate information disclosurerequirement will force bank to pay greeter attention to reputation risk result in loss of confidenceas well as patronage. As a necessary step to promote market discipline, it is important that thefull weight of the provision of relevant Laws are brought to bear on erring operation in other tohelp promote safe and sound Banking practices under consolidated banking environment. Thepolicy of zero-tolerance against unethical behavior should be strictly applied.

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