Contributory Pension Fund Administrations in Nigeria: Stochastic Frontier Analysis of Its Efficiency and Implications for Policy Designs

The study assessed the technical efficiency of pension fund administrators in Nigeria using Stochastic Cost Frontier Model to generate efficiency scores for each of the eleven (11) selected pension fund administrators from a popula-tion of twenty-one (21). Panel data gathered from the annual reports of the selected pension fund administrators and the National Pension Commission were analysed using the maximum likelihood technique. The result showed that inefficiency, in varying degrees, existed in the selected fund administrators due to input costs on labour, equipment and premises and the mean and median efficiency scores were about 75% and 72% respectively. While the most efficient pension fund administrator recorded inefficiency score of 0.077, the least efficient pension fund administrator had inefficiency score of 0.388. The study concluded that increase in profitability, number of contributors, engaging in open fund investment activities and merger and acquisition reduce operating cost. It was therefore recommended that there should be a regulator-initiated merger and acquisition in the industry to eliminate waste, with positive impact on investment income. Besides, the regulatory agency should ease and expand transfer windows for existing contributors to transfer their pension contributions from an inefficient pension manager to efficient one to engender competition in the pension industry.

as the inefficiencies of the institutions saddled with the responsibilities of managing pension funds, retirees not receiving monthly pension as at when due and having to go through rigorous verification processes before the receipt of their gratuities, pensions and other retirement benefits, and corruption of pension institutions officials that misappropriated the pension fund provided by government to offset pension liabilities.
The current study is motivated by several reasons. First, private entities that are not quoted on the Nigerian Stock Exchange have licences from the National Pension Commission to manage pension contributions of employees in Nigeria, implying that there would be information asymmetry between the contributors and pension managers managing the pension fund on behalf of the contributors.
Second, large proportion of the firms operating in the pension industry have parent holdings in the banking industry or some related ones. The banking industry in Nigeria, however, has consistently experienced varying degrees of operational health, with many banks that have gone under. The assessment of performance of pension fund managers would therefore be required in order to avoid some recent ugly experiences in the Nigerian banking industry.
Besides, the switch recently by Nigeria to Contributory Pension Schemes implies that post-employment benefits of all Nigerian employees in both the private and public sector will now depend on the contributions made by these employees during their active service years and investment income earned on the contributions by the pension managers. The efficiency of these pension managers in managing the pension fund assets and generating good investment income is germane to the value of monthly pension receivable and the length of periods to receive the monthly pensions at retirement as a pension manager with better investment income will render increased value of monthly pension over an extended period of time than the one that is operating with lower investment in- Moreover, the assessment of the performance of these private firms, based on the market values of their stocks, could be difficult or impossible except through frontier models to benchmark them. Economic efficiency is the ability of a firm to produce a given output level given a combination of optimal inputs (Coelli, 1996). Economic efficiency could either be technical efficiency or allocative efficiency. Technical efficiency is the firm's ability to produce optimum output from a given input set, while allocative efficiency is the firm's ability to use inputs of factors of production at optimal quantities while taking into consideration the available technology. Therefore, Pension Fund Administrator that is technically efficient will contribute positively to the investment income which will add to the total contributions available to the retirees at the time of drawing post-employment benefits. Several approaches have been used in literature by researchers to assess the technical efficiency of pension fund administrators. While some authors (Garcia, 2004(Garcia, , 2010Barrientos & Boussofiane, 2005;Barros, Ferro, & Romero, 2008) used parametric approaches, others (Ahmat, Aykut, & Huseyin, 2013;Dalkılıç & Ada, 2014) have used non-parametric approach. Parametric approaches are based on econometric regression models. Stochastic production, cost or profit frontier is usually estimated to generate efficiencies parameters with reference to their frontiers. Parametric techniques require econometric model which incorporates random disturbances to capture other explanatory variables not expressed in the model. The usual tests of significance can be performed in these models. On the other hand, non-parametric approaches do not require estimation of econometric parameters and they do not allow for random factors. Also, all deviations from the frontier are taken as inefficiencies. Tests of significance are not necessary in non-parametric approach and deviation from the frontier is expected to be lower than those in parametric techniques. However, the inefficiency effects are expected to be moderate.
The non-parametric tool often employed in efficiency and productivity measurement studies is Data Envelopment Analysis (DEA) while that of parametric tool is Stochastic Frontier Analysis (SFA). This study used Cobb-Douglas Stochastic Cost Frontier Analysis to assess the technical efficiencies of PFAs in Nigeria. This is because the relationship between output and input factors of production can be expressed in a functional form, and their parameters can be estimated based on the available data from the National Pension Commission (PENCOM) and financial statements of the PFAs.

An Overview of Pension Fund Administration in Nigeria
Under the new contributory pension scheme, potential contributors are meant B. M. Ololade et al. Journal of Financial Risk Management to choose pension fund administrators that will manage their pension fund contributions. Employers are required to deduct and remit monthly pension contributions to the Pension Fund Custodians (PFCs) of the contributors' chosen Pension Fund Administrators (PFAs). While the custodians hold the pension fund for safe keeping purposes, the administrators administer and invest the pension fund into different asset classes based on the investment guidelines issued by National Pension Commission (PENCOM), the regulatory authority of the pension industry. As at December 2017, there are twenty-one (21) licenced pension fund administrators, seven (7) closed pension fund administrators and four (4) pension fund custodians.
The total pension fund assets as at 31 st December 2015 is N5.3 trillion and has grown to N7.5 trillion ($24.6b, at official rate of ₦305 to $1) as at 31 st December, 2017(PENCOM, 2018. This implies a growth rate of 29% more than the growth rate of the Nigerian Gross Domestic Products (GDP) which is 3.1%. The pension fund assets had become critical financial assets for economic development and the assessment of its efficient management is expected to be continuous with a view to meeting the objectives of setting up the fund. An analysis of the investment of the pension fund in the financial markets showed that greater percentage of the fund were invested in Federal Government of Nigeria Securities (70.43%), followed by local money market securities (9.07%) and domestic ordinary shares (8.94%). Table 1 shows the industry portfolio summary of pension

Theoretical Framework
The study is anchored on theory of production frontier. Production frontier shows the minimum input of factors of production required to produce maximum output given the available technology. Producers operating on their production frontier are said to be technically efficient while those that are operating below their production frontier are said to be technically inefficient. Technical Efficiency (TE) measures the firm's ability to attain optimum output given the set of input parameters. Pension fund administrators are usually assessed using their stock returns as means of assessment Barros & Garcia (2007). However, this cannot be used in Nigeria as all the pension fund administrators analysed are not quoted on the Nigeria Stock Exchange. Therefore, their stock returns are not available, and it is appropriate to adopt production frontier models to assess the performance of the unquoted pension fund administrators. Besides, pension fund administrators seem to follow the same investment strategies which make ranking based on out-performance difficult to achieve. This further gives credence to the use of stochastic frontier model in assessing the technical efficiency of pension fund administrators.
Two approaches have been widely used in literature in assessing efficiency: parametric and non-parametric approaches. While stochastic cost frontier, stochastic production frontier, and stochastic profit frontier are parametric approaches that could be used, the non-parametric approaches include the Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH). The DEA model was created by Farrell (1957) and advanced by Charnes, Cooper, & Rhodes (1978) to analyze the technical efficiency of public and non-profit making organizations. Table 2 shows the DEA models used in literature for analyzing the technical efficiency of pension fund administrators, the input and output variables used in analysis and the summary of results.
Using DEA as a data estimation technique in analyzing the technical efficiency of the pension managers in Nigeria will be confronted with challenges of data as all the pension fund administrators in Nigeria are not listed entities and as such information on the number of employees, marketing and sales costs and executive pay will be difficult to obtain. However, Stochastic Frontier Analysis is considered appropriate for this study because of the availability of data to carry out

Data and Methodology
The study focused on the existing twenty-one (21)   Cobb-Douglas stochastic cost frontier model.
The efficiency score of each pension manager was derived and this could be used to predict their future capacity to earn fair returns for the participants. Keshari & Paul (1994). Relative efficiency of Foreign and domestic banks.
Sum of total amount of deposits and advances of a bank.
Stochastic frontier production function.
Foreign bank group was 1% less efficient than the domestic. The banks were found to record the same level of efficiencies. Banks with assets greater than $1 billion in 1998 are less efficient than the other subgroups. Also, the largest four banks subgroups (with assets greater than $400 million) experienced significant productivity gains when compared to the smallest eight banks subgroups.
6 Greene & Segal (2004). Profitability and efficiency in the U.S life insurance policy.
Labour, capital and materials.
Amount of life insurance, total annuity, total premiums, and investment.
Stochastic cost function model.
The study found significant cost inefficiency in the life insurance industry when compared to earnings and that there is negative relationship between inefficiency and profitability.

Model Specification
The model used for assessing the technical efficiency of the pension fund was Cobb-Douglas Stochastic Frontier Cost Model. The model was developed by Farrell (1957) and later used Aigner, Lovell, & Schmidt (1977), Battese & Corra (1977), and Meeusen & Van de Broeck (1977). The model is specified as: where: PL = the price of labour, measured by dividing total staff cost by the book value of total assets. Merger & Acquisition = Dummy variable: it is one if pension fund has been involved in mergers and acquisitions in the period and zero otherwise.
The variables are defined in literature by Barros & Garcia (2007) and Barros, Ferro, & Romero (2008). The traditional log-log econometric specification was used to allow for the non-linearity of the frontier. The variables were expressed over PK2 (Expenditure on premises and equipment) to impose the linear homogeneity of the input variables. Input and output variables are very crucial in assessing the technical efficiency of firms. Coelli, Rao, & Battese (1998) model was adopted for the study because data of the input variables of price of labour and capital are available to assess the technical efficiency of the PFAs in Nigeria.

Basic Descriptive Statistics
All the variables are expressed in their raw data form. The results are presented in Table 4 which shows the mean, standard deviation, minimum and maximum values of each variable. Table 4 shows that the series display consistency in relation to their mean values. Table 4

Cobb-Douglas Cost Frontier Pension Fund Function
The estimation of Stochastic Cost frontier model is as specified in Coelli, Rao, & Battese (1998) using the assumption of half-normal distribution. The result is as shown in Table 5. were used to estimate the data, but the results obtained were not meaningful. In order to examine the sensitivity of results in this study an attempt was made using translog function of other models and their distributions to estimate the data, but no meaningful results were obtained.   It is also deduced that contributors with negative coefficient of 0.0196 with operating cost, implies that 1%increase in numbers of contributors will reduce operating cost by 19.6%. Consequently, closed fund with positive coefficient value of 0.2047 with operating cost, suggests that 1%increase in closed fund investment will lead to increase in operating cost by 20%. In the same vein, open fund with negative coefficient of 0.0544 with operating cost, reveals that 1%increasein open fund investment will reduce operating cost by 5%. Meanwhile, Merger and acquisition which indicates negative coefficient value of 0.1650 with operating cost, suggests that 1% increase in merger and acquisition of pension fund firms will lead to decrease in cost of operation by 16.5%.
The overall chi-square value of 2177.29 and probability of 0.000 implies that in general the results are statistically significant. The operating costs increase as all the factors of production increase, except for number of contributors, profits, open fund and mergers and acquisition. Operating costs could be reduced significantly through acquisition of more contributors by the pension fund administrators as the number of contributors increase the size of the pension fund. In the case of profit, cost must be strategically curtailed by the pension fund administrators to sustain the business of pension fund management in perpetuity. Open fund contributes toward cost curtailment and this could be because of the flexibility embedded in open fund investment in relation to close fund. In case of merger and acquisition, this reveals that the strategy of merger and acquisition in pension fund management contributes towards efficiency. There has been mergers and acquisition in the industry which were carried out with the view to having the advantages of synergy and economic of scales. The results from the analysis of data as stated above are consistent with the findings of Barros & Garcia (2007) ;Ferro, Romero, & Covelli (2011) and Barrientos & Boussofiance (2005).  The technical efficiency refers to a situation on the frontier. It is achieved by firm that allocates minimum resources to produce maximum output and without waste of resources. Firms with a score of one are on the frontier and are thus efficient while firm below one is below the cost frontier and are thus less efficient. The value of waste in the production process of a firm is measured by taking the difference between one and the estimated efficiency score of each of the pension fund administrators. The efficiency scores in Table 6 showed that there was inefficient allocation of resources in the management of pension fund asset portfolios in Nigeria. The most efficient PFA is AIICO Pension though there is

Pension Fund and Technical Efficiency Scores
(1 − 0.923 = 0.077) waste that needed to be eliminated from its production processes. The least efficient PFA, Pension Alliance Limited (PAL) has (1 − 0.612 = 0.388) waste or underutilised resources to be eliminated from its production processes to be technically efficient. All the PFAs have varying degrees of waste that needed to be removed for them to upgrade their financial performance.
The mean score is 0.745. This means that the pension fund administrators can reduce their operating costs by 25.5%, which were the price of labour, price of capital-premises and price of capital-management services without decreasing their output. The maximum efficiency is one and there is no PFA that achieves maximum efficiency. PAL recorded the minimum efficiency score of 0.612. The median is 71.8 while the standard deviation is 7.8. The pension industry is Nigeria seems to be less competitive to engender robust competitions among the players, which may eventually translate to higher efficiency.

Conclusions and Recommendations
The result of the analyses of the technical efficiency of the pension fund administrators showed that technical inefficiency exists in the management of pension fund in Nigeria and the level of inefficiencies differs from one pension fund administrator to another, and none of the sampled PFAs is perfectly technically efficient. Besides, increase in profitability, number of contributors, engaging in open fund investment activities and merger and acquisition reduce operating costs. An industry-wide merger and acquisition may be initiated by the regulator to bring about synergy and economic of scales that will reduce cost of operations and generate higher returns to members of the contributory pension scheme.
Besides, pension managers in Nigeria should regularly publish their annual and efficiency reports to woo potential contributors to gain operating costs curtailment with the attendant increase in profit. PENCOM should also engender competition in the pension industry by opening the transfer windows for existing contributors to move from one pension to another as these windows have not been opened since 2004 even though the Pension Reform Act of 2004 makes provision for it. Finally, for pension fund to be managed efficiently, regulatory infrastructure should be robust to mitigate unnecessary input costs on labour, equipment and premises with negative impact on pension contributions and investment returns. This becomes necessary because input costs of labour, equipment and premises are presently being incurred by the pension fund administrators in Nigeria at their discretion without recourse to regulatory authorityas there is no regulation on the curtailment of these costs which have negative consequences on post-employment benefits of the contributors.

Conflicts of Interest
There is no conflict of interest.