EVALUATING EXCESSES AND SHORTFALLS IN PRISON SERVICES

Using data envelopment analysis, an unbiased index was establish by evaluating the ability of states to maximize their objectives subject to minimizing some conditions (inputs). This approach, which rank state from the most robustly efficient to the most robustly inefficient in its ability to maximize goals (output), while minimizing conditions (input) avoid using equal or subjective weight employed in conventional ranking scheme. The ranking of 36 states yield unexpected result and suggest a very different way of measuring and evaluating development policy.


INTRODUCTION
Data Envelopment Analysis (DEA) is a mathematical programming methodology based on the Frontier approach.It has been successfully used to study the comparative performance of units that consume similar inputs and produce similar outputs.The units are generally referred to as Decision Making Units (DMUs).Certain benefits are derived when measuring productivity.These include identifying dimension on which to improve productivity.Others providing useful information to management of DMU and indicating target in order to guide future operation (Farrell, 1957;Cooper et al., 2007).DEA provides an approach for achieving efficient targets for inefficient operation (Charnes et al., 1978).The input oriented models consider the possible ratio input reduction while maintaining the current level of output.Whereas the output oriented model consider possible ratio output augmentation while keeping the current level of inputs.The objective of this study is to track down the relative efficiency of states in terms of provision of prison services in comparison with one another using four attributes.In doing so, states that have e xcess inmate in captivity and those that have shortfall of prison capacity will be identified hence target for achieving efficiency will be provided.
To the best of our knowledge, DEA has not been employed to study the socio economic performance of states in terms of prison services.In Nigeria, this paper therefore helps to provide a comparative picture of performance of states.The paper is organized as follows: In section 2, methodology is presented.In section 3, data is presented and summarized.In section 4, the results are presented and the determinant of efficiency is analyzed.In section 5, policy implication is drawn.Finally, in section 6, the conclusions are derived.

Slack Based Models (SBM)
The productivity measurement approach used in this paper adopts the slack base model (Charnes et al., 1985), which focus on the two stage process that can identify inefficient in the form of input and output slack.SBM shows that these input and output slack optimized directly to identify the efficient frontier.SBM is a unique appropriate index, since it is neither input-oriented nor output oriented.Rather, it simultaneously minimizes conditions (input) while maximizing goals (output) (Charnes et al., 1994).In order to consider both input decrease as well as an output increase simultaneously, the inputs are reduced proportionately, and the outputs are increased in different proportion.Model (1) identify a CRS frontier, and therefore, is called CRS additive model.1. J = 1,. . ., 36 2. n = 36 There is a need to run DEA model (1) 36 ti mes, one for each DMU ( state) in order to determine whether we can find a set of weights so that the convex combination of these 36 states perform better than one of the 36 states.If the answer is yes then the targeted state ( ) DMU is inefficient, otherwise if the answer is no then the targeted state ( )

Data
Data is obtained from the National Bureau of Statistics publications (NBS, 2009).
Thirty six (36) states in Nigeria including the Federal Capital Territory (FCT) were employed as DMU.Due to lack of data on Bayelsa state, it was not considered in the analysis.Male and female inmates were employed as inputs variables and the maximum capacity of the prison houses represents the output variable.With these conditions (inputs) to be minimized and goal (output) to be maximized, the form of the proposed model is given as SBM (1) above.The analysis assumes Constant Return to Scale (CRS).CRS is said to prevail when an increase in all input by 100\% leads to corresponding increase in all output by 100% (Golany and Thore, 1997).
The reason is obvious, that CRS measures technical efficiency and efficiency loss when the DMU does not operate in its most productive scale size.Table 1 shows data summary.The study also reveals that there is more capacity than the number of inmates in Nigeria prisons.
Table 3 also gives information about peer (s) for state considered inefficient in the analysis.Peer(s) are efficient states with a performance score of 100% and all slacks at zero level.Abia s peer is Benue, meaning that Abia can try to emulate Benue by achieving better values of attributes that would result in an efficiency score of 100%.Note that Borno is considered as peer for many of the inefficient countries.Interestingly, Lagos and Zamfara are not considered as peers for any inefficient states.This might have resulted from the existence of alternate optima (Cook and Zhu, 2008).

Policy implication
The result of this study has interesting policy implications for the development of Nigerian prisons.The researcher wish to stress here that the findings of this study are critically based on the choice of attributes (data) and hence, the policy implications discussed below should be considered within this perspective.This study revealed that 16.67% of the 36 states studied are efficient.The smallest CRS efficiency score is 30.31%, which is Oyo state.This is a significant result highlighting the wide disparity in socio-economic status amongst states in Nigeria.

CONCLUSION
The paper attempted to look into issues related to the appraisal of prison services in Nigeria for the year 2009.A CRS additive DEA model was applied to simultaneously identify the excesses and deficits in Nigerian prison services.Various attributes were selected for the purpose of assessment.First, the evaluation of overall performance shows that 16.67% of 36 states are efficient while 83.33% are inefficient.This does not exhibit good performance.The study demonstrates that 98.22% of the total inmates are male, while female inmates constitute 1.78%.Furthermore, the study revealed that there is no shortage of prison capacity.In assessing services, the inefficiency in performance is actually caused by an excess input rather than a deficit in output.DEA provides efficient input and output targets for reducing the excess and improving the deficits.As for future developmental plans, forecasts of inputs and output values can be included in a DEA analysis so that decision makers can determine which factors negatively or positively affect estimation and therefore adjust the economic , Department. of Statistics and Operations Research, School of Pure and A pplied Sciences, Modibbo Adama University of Technology, P.M.B 2076, Yola.Adamawa State.In linear programming terminology, the objective function is to maximize the sum of all specific national development goals subject to minimizing specific resource availability indicators.These goals are observations measured and represented as outputs and denoted by input slack; + r k be an output surplus and j l be a set of unknown weights (decision variables), where n j ,..., 1 = corresponding to each DMU, in this paper, 36 = n .Four measures were used.They are as f ollows: Male Female Number of prisons n Outputs (r = 1; s = 1) Prison capacity n 36 State (DMU)

Table 1 :
Descriptive statistics on input and output s data Measures of central tendency such as mean and measure of dispersion such as standard deviation, maximum and minimum values are shown against their respective input variables.Table

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The table depicts in detailed excess inputs at each states.For instance, Adamawa state had 651 excess in male inmates, 8 excess in female, 6 excess in prison houses, and no shortage of facility.The total number of male inmates in Nigeria prisons is 38,983 and 708 of female inmates spread across 227 prisons.This brings to the grand 39,691 to inmates in Nigerian prison.The maximum capacity of the 227 prisons studied is 46,706.

Table 3 :
Distribution of scores, sources of inefficiency and peers in overall performance