DATA ENVELOPMENT ANALYSIS: AN APPLICATION TO MEASURE STATE POLICE EFFICIENCY IN INDIA

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1 DATA ENVELOPMENT ANALYSIS: AN APPLICATION TO MEASURE STATE POLICE EFFICIENCY IN INDIA Abstract Anupreet Kaur Mavi, Assistant Professor UIAMS, Panjab University, Chandigarh. E mail: anumavi@pu.ac.in The paper addresses the issue of measuring efficiency of police using Data Envelopment Analysis, a relative efficiency measuring technique. The basic organizational structure and uniformity of policing work irrespective of size, population etc., befits DEA modelling to be applied to find out police efficiencies. The CCR output model is used herein to calculate efficiencies. The paper measures the efficiencies of individual states/ut s for the year 2013 and also suggests the possibilities of improvements in the Decision Making Units(DMUs) by creating referent units, identifying slacks and analysing lambda values. Total Expenditure on Policing(in Crores of rupees)tecr, Number of Police Officers(NPO), Number of Investigating Officers(NIO), and Total number of Investigated Cases(TNIC) are the variables used as inputs. And, Number of Persons arrested(npar), Number of Persons Charge sheeted(npcs) and Number of Trials Completed(NTC) have been taken as outputs to measure the efficiency. The results so obtained suggest ways in which many State/U.T. police departments can improve the overall efficiency in relation to other States/UTs. The lambda values so generated also suggest as to which of the efficient referent unit the inefficient State police units emulate for its best practices to be followed. The larger lambda value efficient referent unit should be followed by the inefficient state unit. Keywords: efficiency, state police units, Data Envelopment Analysis(DEA), referent units. 1.0 Introduction The current era has brought many challenges to the police institutions as well as individual police officers as regards to the productivity and performance related evaluation. The role of police as an institution and its officers has always been contentious as the various tasks like crime prevention, law and order maintenance as well as enforcement is difficult to assess quantitatively. Although the origins of efficiency or benchmarking traces back to Farrell s(1957) study, theoretical development of Data Envelopment Analysis(DEA) was started in 1978 by Charnes et al who produced a measure to calculate efficiency for Decision Making Units(DMU s). Due to the complexities of defining the tasks of policing, no systematic attempt was perhaps made in this direction by researchers. Verma and Gavirnenei(2006) however made the first serious attempt to develop and apply scientific methodology to measure the police performance n states. In the current study also the author has analysed the police performance of Indian states on the lines of the above mentioned research paper after thorough considerations and reviewing of the existent literature. 2.0 Literature Review Thanassoulis (1995) has applied DEA to measure relative police force efficiency of English and Welsh police force. It focuses solely on the clear up rates for violent crime, burglary and other crimes, while also including the total numbers of each crime as inputs in the DEA analysis alongside the number of officers. It does not consider the major input measure i.e. total expenditure cost since all the effort and crime prevention measures are directly depend upon the money invested for the purpose. The limitation of the paper is in constructing weight restriction for measuring efficiencies since it is subjective in nature. Drake & Simper (2000) measured the size efficiency of English and Welsh police forces using DEA and multiple discriminant analysis. In this paper, inferences about the optimal size and structure of the English and Welsh police 45 P a g e

2 forces are made using DEA efficiency results and the issue of the statistical significance of the differences in efficiency scores across staff size groups is rectified using analysis of variance (ANOVA) and discriminant analysis techniques. It deals only with the problem of size and structure in English and Welsh policing and not with the overall efficiency of police forces. Drake & Simper (2003) compare four different distance function models i.e. DEA, free disposal hull (FDH) (Tulkens, 1993), super-efficiency DEA (Anderson & Petersen, 1993) and stochastic frontier analysis (Banker, 1993; Banker et al., 1992) in order to assess police force efficiency of English and Welsh police force. It does not highlight limitations of parametric and non-parametric approaches in case of different crime zones which is present in the data. Shinn Sun(2000) in the article titled Measuring the relative efficiency of police precincts using data envelopment analysis used Data envelopment analysis (DEA) to measure the relative efficiency of the 14 police precincts in Taipei city, Taiwan. The results indicate how DEA may be used to evaluate these police precincts from commonly available police statistical data for the years To sharpen the efficiency estimates, window analysis, slack variable analysis, and output-oriented DEA models were used with both constant and variable returns to scale. The problem of the presence of non-discretionary input variables is explicitly treated in the models used. Potential improvements in technical efficiency of police precincts were examined by readjusting the particular output/input indicators. The analysis indicates that differences in operating environments, such as resident population and location factors, do not have a significant influence upon the efficiency of police precincts. Aristovnik et al(2013) in their research paper titled Performance Measurement of Police Forces at the Local Level: A Non-Parametric Mathematical Programming Approach, attempt to measure the relative efficiency of police activities in the Slovenian police at the local level. As the state allocates a relatively large amount of budget funding to police operations and more than one-quarter of public employees is employed in the police, the efficient use of limited public funds is even more important. In particular, a three-stage Data Envelopment Analysis (DEA) technique is presented and then applied to measure the relative efficiency of police-work-related data for selected police units at the local level (i.e., police stations (PSs)) in 2010 with additional controlling for external (environmental) factors. The results of the DEA empirical analysis reveal that approximately 80% of the observed PSs are inefficient relative to their peers. More detailed analysis also shows that, in general, PSs with more than 50 posts occupied are on average less efficient. To some extent, the differences in efficiency scores are a consequence of external factors which the management of police stations cannot influence, yet they are even more a result of better governance and organized and police work. Thus, the presented methodology and obtained efficiency results can be a valuable tool in the hands of police management when deciding how to optimally allocate the limited public resources. Kumar, Surender and Kumar, Sudesh(2013) in the paper titled Does modernization improve performance: evidence from Indian police, aimed to measure the role of police modernization scheme in its performance in crime repression. The authors have used output distance function as an analytical tool and estimate it using stochastic frontier analysis framework in a single stage.the major finding was that the police modernization scheme is helping the state police departments in enhancing their performance, i.e., the police departments which have more modern communication equipments and which are spending more money on the training of their police personnel are doing better. The police density is found to be one of the major determinants of its efficiency along with the factors that creates more social cohesion. The total factor productivity is governed by the catch-up effect which is worsening over time though the technological progress has been observed in most of the states. In the paper titled, Measuring the Efficiency of Local Police Force, Isabel-Marı a Garcı a-sa nchez(2008) proposed a methodology of analysis for estimating the efficiency with which the competences in matters of public and road safety are carried out. This proposal seeks to mitigate (i) the subjectivity in the selection of variables; (ii) the partiality inherent to the productivity indicators; and (iii) the generality of the analysis in previous studies. Applying the methodology proposed to the areas of public and road safety, individually and jointly, obtaining the main conclusions: the mean pure technical efficiency of the police force as a whole is 69.42, with eight towns (27.59%) showing efficient behaviour and, in the evaluation of the disparity between behaviour by activity and the overall result, the comparative shows a high degree of similarity between the ordering of the towns in the overall analysis and in public safety. This is not extendable to the road safety service, since they differ notably in the results obtained both with the area of public safety and with the overall action of the force. Verma and Gavirneni (2006) in 46 P a g e

3 their Research paper titled, Measuring police efficiency : an application of data envelopment analysis made an attempt to develop a method for measuring police efficiency. The paper was designed to apply the technique of Data Envelopment Analysis (DEA), a comparative or relative efficiency measuring mechanism to police-workrelated data from India. This application provided a rationale for identifying good performance practices. It helped in generating targets of performance, the optimum levels of operations, role models that inefficient departments can emulate and the extent to which improvements can be made over a period of time. The paper measures the performances of State police units and the results suggested ways in which some State police departments can improve their overall efficiency. The paper suggested ways in which the efficiency of any unit of criminal justice systems may be formulated and compared across different units of the system. The paper introduced a new technique to police practitioners and researchers and demonstrated its efficacy by case analysis from India. Gupta et al(2008) in their paper titled Ranking Police Administration Units on the Basis of Crime Prevention- Measures using Data Envelopment Analysis and Clustering In this paper, a novel approach had been proposed to rank police administration units on the basis of their effective enforcement of crime prevention measures using Data Envelopment Analysis (DEA) and Clustering. The proposed approach has offered an effective mechanism not only to rank police administration units but also provided an evaluation tool to monitor the implementation of crime prevention measures at various levels of police administration. The paper discussed two major phases of the proposed approach. In the first phase, clustering is used to identify the crime zones and to form homogeneous groups in crime data. In the second phase, police administration units in a particular crime zone are ranked using DEA. The effectiveness of the proposed approach has been illustrated on Indian crime data. The comparative results of DEA with clustering and DEA without clustering are also given to highlight importance of linking DEA with clustering. Drake, Leigh and Simper, Richard(2001) in their paper, An Economic Evaluation of Inputs and Outputs in Policing: Problems in Efficiency Measurement emphasised the fact that the new Labour government recently instigated an initiative to establish whether English and Welsh police forces should be ranked into groups based on an efficiency measure. The estimation techniques proposed in the Public Service Productivity Panel (2000) report in order to rank the efficiency of forces are Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA). These procedures allow for multiple input/output configurations in a cost or production model in order to obtain efficiency scores. In order to produce comparative efficiency measures, however, it was essential that the services provided by police forces (the outputs or outcomes) be related to the resources (inputs) utilised by the forces in delivering these outputs (outcomes). A particular problem, however, was that policing included many inputs and outputs (outcomes) that could potentially be utilised in an efficiency model using DEA and SFA. Hence, this paper considered the problems associated with measuring relative police force efficiency given that a vast number of potential indicators must be reduced to a handful to allow feasible estimation. In addition, it discussed the input and output variables utilised in the first 'official' analysis of English and Welsh police force efficiency. 3.0 Research Methodology 3.1 Analytical Framework for Assessing the Efficiency of State/U.T. Police : In order to estimate the efficiency, we assume that the police output can be characterised by a production function, which provides the maximum possible output (i.e., output target), given the proper inputs (see also, Cracolici, 2004, 2005; and Cracolici and Nijkamp, 2006). For our aim, the following police production function for states/u.ts is as following: Police output = f (TECR, NPO, NIO, TNIC)...(1) Where, TECR = Total Expenditure on Policing(in Crores of rupees) NPO = Number of Police Officers NIO = Number of Investigating Officers TNIC = Total number of Investigated Cases 47 P a g e

4 As the functional form of the production function is not known, while we have to manage multiple inputs and outputs, a non-parametric method (i.e., DEA) is used. The main advantage of the DEA over a parametric approach is that it does not require any assumption concerning the production technology, while DEA can also easily accommodate multiple outputs. DEA is a non-parametric linear programming method of measuring efficiency to assess a production frontier. The efficiency of each police State/U.T. is evaluated against this frontier. In other words, the efficiency of an establishment is evaluated in comparison with the performance of other establishments. 3.2 The Study Area and Summary Characteristics of Variables Each State police is taken as a separate Decision Making Unit (DMU).Primary data is collected from all the 28 States for the year The input variables considered are Total Expenditure on Policing(in Crores of rupees)-tecr, Number of Police Officers(NPO), Number of Investigating Officers(NIO), and Total number of Investigated Cases(TNIC). Here, we apply DEA to each establishment considering them as a generic DMU, which use proper inputs to reach multiple outputs. For this purpose, we adopt an output-oriented DEA model, because we want to explore how well these States/U.T.s deploy their input resources with efficiency. In other words, given a set of input resources, the aim of the DMU(State/U.T.) police units is to prevent crime and maintain law and order in their respective areas. DEA can be a powerful tool when used wisely. 4.0 CCR and BCC models: In DEA models, we evaluate n productive units, DMUs, where each DMU takes m different inputs to produce s different outputs. The essence of DEA models in measuring the efficiency of productive unit DMUs lies in maximising its efficiency rate. However, subject to the condition that the efficiency rate of any other units in the population must not be greater than one. DEA methodology, originally proposed in (Charnes et al., 1978), is used to assess the relative efficiency of a number of entities using a common set of incommensurate inputs to generate a common set of incommensurate outputs. The original motivation for DEA was to compare the productive efficiency of similar organizations, referred to as DMUs. The problem of assessing efficiency is formulated as a task of fractional programming, but the application procedure for DEA consists of solving linear programming (LP) tasks for each of the units under evaluation. Let x ij - denote the observed magnitude of i - type input for entity j ( x ij > 0, i = 1, 2,..., m, j = 1, 2,..., n) and y rj - the observed magnitude of r-type output for entity j (y rj > 0, r = 1, 2,..., s, j = 1, 2,..., n). Then, the Charnes-Cooper-Rhodes (CCR) model is formulated in the following form for the selected entity k: Where: n v i is the weights to be determined for input i; n is the number of inputs; u r is the weights to be determined for output r; n is the number of outputs; n h k is the relative efficiency of DMU k ; n is the number of entities; n ε is a small positive value. The relative efficiency hk, of one decision-making unit k, is defined as a ratio of the weighted sums of their outputs (virtual output) and the weighted sums of their inputs (virtual input). As for the decision-making unit k, for which a maximum in objective function (1) is 48 P a g e

5 sought, the condition (2) is true, meaning that it is obviously 0 < h k 1, for each DMU k. The weights v i and u r show the importance of each input and output and are determined in the model so that each DMU is efficient as much as possible. Given that the condition (2) is true for every DMU, it means that each of them lies on the efficiency frontier or beyond it. If Max h k = h k * = 1, it means that efficiency is being achieved, so we can tell that DMU k is efficient. Efficiency is not achieved for h k * < 1 and DMU k is not efficient in that case. DMU k is to be considered relatively inefficient, if it is possible to expand any of its outputs without reducing any of its in-puts, and without reducing any other output (output orientation), or if it is possible to reduce any of its inputs without reducing any output and without expanding some other inputs (input orientation). Problem (1) - (4) is nonlinear, non convex, with a linear and fractional objective function and linear and fractional constraints. Using a simple transformation developed by and Cooper (1962), the above CCR ratio model can be reduced to the LP form (the Primal CCR model) so that the LP methods can be applied. In this model, the denominator has been set equal to 1 and the numerator is being maximized. The input oriented CCR primal model is: The mathematical model given above is linear and can be solved using any of the familiar programs packages for LP. However, in practice, it is often solved dual task for problem (5) - (9), which is: The basic idea behind DEA is best conveyed in the dual CCR model (M3), which is easy to solve because of its calculating size. The dual model for a given unit using input and output values of other units tries to construct a hypothetical composite unit out of the existing units. If it is possible, the given unit is inefficient, otherwise it is efficient and lies at the efficiency frontier. The efficiency frontier is a set of segments interconnecting all the efficient DMUs and it acts as an envelope for inefficient units. An inefficient unit can be enveloped below (input-oriented model) or above (output-oriented model). Because the problems described by models (M 2 ) and (M 3 ) are associated and because of the duality theorem in linear programming, DMU k is efficient if and only if conditions for optimal solution (λ*, s+*, s-*, Zk*) are accomplished for the problem (10)-(13): 49 P a g e

6 Using the optimal solution(λ*, s+*, s-*, Z k *) of the problem (10)-(13), it can be determined: It can be shown that after CCR projection (16), (17), DMUk with altered inputs X k and out-puts Y k becomes efficient. The difference ΔXk = X k - X''k and ΔY k = Y''k - Yk respectively shows the estimated amount of input and output inefficiency. Thus it can be seen for inefficient DMUk, how to change its inputs and outputs, so it would become efficient. We should emphasize that, for each DMUj (j = 1, 2,..., n) taken as DMU k, an appropriate linear programming problem is solved (10) - (13). Hence, we should solve n linear programming tasks with the form (10) - (13), with (s+m+1) variables and (s+m) constraints per task. The CCR models (dual and primal) with input orientation are still the most widely known and used DEA models despite the numerous modified models that have appeared. The CCR models assume constant returns to scale. DMU operates under constant returns to scale if an increase in the inputs results in a proportionate increase in the output levels. These models calculate an overall efficiency in which both its pure technical efficiency and its scale efficiency are aggregated into a single value. The envelopment surface obtained from the CCR model has the shape of a convex cone. The efficient DMUs would lie on top of the structure, while the inefficient ones would be covered under the cone. In a single input and output case, the efficiency frontier is reduced to a straight line. The CCR model yields the same efficiencies regardless of whether it is input or output-oriented. The most important extension of the original CCR models is given in Banker et al. (1984) where an additional constraint was introduced in model (M3): This constraint enables variable returns to scale and provides that the reference set is formed as a convex combination of DMUs, which are in the set (those that have positive value for λ in the optimal solution). The DMU operates under variable returns to scale if it is suspected that an increase in inputs does not result in a proportional change in the outputs. The convexity constraint ensures that the composite unit is of similar scale size as the unit being measured. The BCC model yields a measure of pure technical efficiency that ignores the impact of the scale size by only comparing a DMU to a unit of similar scale. Often, small units are qualitatively different from large units and a comparison between the two may distort measurements of comparative efficiency. The measured efficiency is always at least equal to the one given by the CCR model. The envelopment surface obtained from the BCC model results in a convex hull. Data Envelopment Analysis is a method for assessing comparative efficiencies in terms of resource conservation without detriment to its outputs or alternatively the scope for output augmentation without additional resources (Cooper et al., 2000). The efficiencies assessed are comparative or relative because they reflect scope for resource conservation or output augmentation at one unit relative to other comparable benchmark units rather than in some absolute sense. It is better to seek relative rather than absolute efficiencies because in most practical contexts sufficient information to derive superior measures of absolute efficiency are not available. DEA was originally developed for assessing the comparative efficiencies of organizations such as banks, schools and restaurants (Thanassoulis, 2001). The basis for comparison is that they perform the same function in terms of resources they use and the types of outputs they produce. DEA therefore becomes a useful technique for assessing 50 P a g e

7 comparative police productivity since every police department uses similar resources- personnel and technology and provides similar outputs of service, crime control and order maintenance. As described above, some outputs like crime control and order maintenance are difficult to quantify. However, police efforts in these directions can be measured and compared in terms of offenders arrest and crime figures. DEA can assist in assessing comparative efficiencies since these reflect scope for resource conservation or output augmentation at one department relative to other comparable departments. This provides a way out to measure police productivity since we lack sufficient information to derive superior measures of absolute efficiencies. DEA also provides a rationale for identifying good performance practices, in generating targets of performance, the optimum levels of operations, role models that inefficient departments can emulate and the extent to which improvements can be made over a period of time. DEA builds an understanding of how the transformation of resources to outcome works. It suggests what operating practices, mix of resources, scale sizes, scope of activities and so on the operating departments may adopt to improve their performance. Measuring police efficiency in Benchmark departments could be used as role models for other units to emulate. More specialized uses of DEA could suggest identification of types of unit they are rather than through operating practices they adopt. DEA can also be used to measure productivity changes over time both at operating unit level and at organizational level. Furthermore, resources need not be material or labour or capital but could be environmental and situational. For example, the community within which a police department operates may be treated as a resource that the department taps for seeking information about the suspects of crime. DEA can be used to assess the relative efficiencies of police departments in converting local communities cooperation to arrests of suspects. Alternatively, DEA can be used to assess the impact of police presence or response time for dealing with specific problems. DEA can be used to judge how the resource of one police unit in a given place impacts on the situation and then assess the relative worth of placing more such units or in measuring the impact between different situations. While there are reports (Thanassoulis, 1995; Carrington et al., 1997) of some applications DEA to police work, Indian police have never used this technique for evaluating their performance. The Indian police system, through its organizational structure and uniformity in operating policies, is ideal for DEA as per recommendations of experts through a literature review.not surprisingly, these approaches fail to generate a satisfactory picture of the performance of these complex operations. The single measure based gap analysis is inadequate in the presence of multiple measures of performance. In the presence of many inputs and outputs, as is the case with police units, it is very difficult to identify a single measure that enables one to generate a head-to-head comparison of the units. When one unit out performs another in one dimension, (say in terms of property crimes) but is worse off in another (in terms of violent crimes), how does one say which is more efficient? In addition, this approach does not adequately capture the interaction between the various inputs and the outputs. The averages based analysis is so focused the centre, that it distracts one from identifying the best practices. Obviously, the units that are doing the best are going to be away from the center, and through the process of averaging, significant amount of information on the performance of these best practice units is lost. Data Envelopment Analysis (DEA) recognizes the need for an approach that overcomes the issues in performance evaluation. DEA is a linear programming based method for evaluating the relative performances of Decision Making Units (DMUs) in the presence of many inputs and outputs. Using DEA, one can: (1) for each DMU, compute a single measure of relative efficiency; (2) identify referent efficient DMUs from which best practices can be transferred; and (3) overcome the deficiencies of traditional approaches based on one-dimensional measures or averages. 5.0 Data Analysis: DEA measures the relative efficiency of each DMU by transforming the multiple inputs and outputs to a single virtual input and a single virtual output. These virtual input and output are computed as weighted sums where 51 P a g e

8 Table1.1:Relative levels of Performance of State Police Units based on Ratio Analysis STATE TECR NPART NPC NPARTCR NPCCR Andhra Pradesh Arunachal Pradesh Assam Bihar Chhattisgarh Goa Gujarat Haryana Himachal Pradesh Jammu & Kashmir Jharkhand Karnataka Kerala Madhya Pradesh Maharashtra Manipur Meghalaya Mizoram Nagaland Odisha Punjab Rajasthan Sikkim Tamil Nadu Tripura Uttar Pradesh Uttarakhand West Bengal Source: Author s Calculations the weights are selected in a manner that each DMU has the highest possible (but no greater than unity) efficiency rating. This is achieved through the formulation and solution of a sequence of linear programs, one associated with each DMU. The DMUs that have an efficiency rating of 1.0 are deemed efficient and the convex envelope connecting them is called the efficient frontier. The DMUs inside the efficient frontier are identified as inefficient and their relative efficiency rating is based on the distance from the efficient frontier. For each inefficient DMU, the point on the efficient frontier which is closest (it could be an efficient DMU or a convex combination of a few efficient ones) is identified as its reference point. It is from this reference point that best practices can be identified and can be identified and transferred to an inefficient DMU in order to make it efficient. Table 1.1 contains, for each of the states, total expenditure in crores of rupees(tecr), number of persons arrested(npart) and, number of person convicted(npc). In addition, there are two columns that list the number of persons arrested per crore rupees(npartcr) and number of trials comleted per crore of rupees(npccr)(table 1.1). Ratio based analysis is a useful method for comparing performance of police units. However, it can lead to significant confusion about how competitive they really are. For example, consider the case of Jammu & Kashmir and Sikkim. The former has better performance on the basis o number of arrests per crore of rupees, while the latter has better performance on account of number of persons convicted per crore of rupees. Both the state police units can, therefore, claim good performance. The case discussed here is regarding just two of the outputs and the data can, thus, be displayed easily on a graph as well (Figure 1.1). 52 P a g e

9 Kerala Uttar Pradesh Uttarakhand Jammu & Sikkim Kashmir Rajasthan Madhya Pradesh Figure 1.1: Efficiency Frontier( with Number of persons arrested per Crore of Rupees on X-Axis and Number of Persons Charge Sheeted per Crore of Rupeeso the Y-Axis) The graph displays six efficient units, namely, Jammu & Kashmir, Sikkim, Uttar Pradesh, Uttrakhand, Kerala, Madhya Pradesh and Rajasthan since there will be no unit above them. The line that connects them is called efficient frontier which is the convex hull of the data(beasley,2003). This efficient frontier is derived from the examples of best practices contained in the given data and represents a performance level that other units below this frontier would perhaps try to achieve. The relative efficiencies have a very limited interpretation as this analysis does not mean that a state is most efficient and another is least efficient. The only implication from ratio analysis is that the least efficient state so determined can perhaps utilize the best practices of the relatively more efficient states by adopting similar administrative practices. But if we have to analyse greater number of inputs and outputs simultaneously, the power and significance of DEA becomes quite obvious. Table 1.2 and Table 1.3 contain the four inputs and outputs for the states respectively. Under these circumstances, it is no longer possible to use the ratio analysis and/or the graphic analysis from the ratios to determine the optimal solution for a particular state police unit. Instead, a linear programming approach to derive the optimal solution for each state police unit was used by the author. Table 1.2:Inputs used in the model DMUs STATE/UT TECR NPO NIO TNIC DMU 1 Andhra Pradesh DMU 2 Arunachal Pradesh DMU 3 Assam DMU 4 Bihar DMU 5 Chhattisgarh DMU 6 Goa DMU 7 Gujarat DMU 8 Haryana DMU 9 Himachal Pradesh DMU 10 Jammu & Kashmir P a g e

10 DMU 11 Jharkhand DMU 12 Karnataka DMU 13 Kerala DMU 14 Madhya Pradesh DMU 15 Maharashtra DMU 16 Manipur DMU 17 Meghalaya DMU 18 Mizoram DMU 19 Nagaland DMU 20 Odisha DMU 21 Punjab DMU 22 Rajasthan DMU 23 Sikkim DMU 24 Tamil Nadu DMU 25 Tripura DMU 26 Uttar Pradesh DMU 27 Uttarakhand DMU 28 West Bengal Source: Crime Statistics, NRCB (various issues) Notes: TECR- Total expenditure in crores of rupees; NPO-number of police officers; NIO-Number of investigation officers; TNIC Total number of investigated cases. Table 1.3:Outputs used in the model DMUs STATE/UT NPART PCST NPC NTC DMU 1 Andhra Pradesh DMU 2 Arunachal Pradesh DMU 3 Assam DMU 4 Bihar DMU 5 Chhattisgarh DMU 6 Goa DMU 7 Gujarat DMU 8 Haryana DMU 9 Himachal Pradesh DMU 10 Jammu & Kashmir DMU 11 Jharkhand DMU 12 Karnataka DMU 13 Kerala DMU 14 Madhya Pradesh DMU 15 Maharashtra DMU 16 Manipur DMU 17 Meghalaya DMU 18 Mizoram DMU 19 Nagaland DMU 20 Odisha DMU 21 Punjab P a g e

11 DMU 22 Rajasthan DMU 23 Sikkim DMU 24 Tamil Nadu DMU 25 Tripura DMU 26 Uttar Pradesh DMU 27 Uttarakhand DMU 28 West Bengal Source: Crime Statistics, NRCB (various issues) Notes: NPART: Number of persons arrested; PCST: Number of persons chargesheeted; NPC: number of persons convicted; NTC: number of trials completed. The Table1.4 gives the results for the same for the 28 state police units. The table contains the results from an analysis that determines the relative efficiencies and the target input and output level for all the states. There are six efficient states and all the inefficient state police units identify the referent efficient units from among the efficient units. This helps in identifying the referent efficient state police units, which is done in order to study the practices of those units and try to implement some of their best practices in the relatively inefficient units. The DEA analysis presents some unexpected results. The states of Jammu & Kashmir, Sikkim, Uttar Pradesh, Sikkim, Rajasthan and Uttarakhand have a low social standing so far as the police image is concerned, yet they stand out as efficient state police units(efficiency =100) in the analysis based on the dimensions chosen by the author for performing DEA analysis. The only plausible cause behind this is that these states are indeed making best use of their resources and following good administrative practices even though public perception is quite unlike the results obtained. It was also observed that size of the state does not play a significant role in determining its efficiency as large states like Madhya Pradesh and Uttar Pradesh which are spending Rs crores and Rs crores respectively are getting efficiency rate of 100 alongwith the small state Sikkim (TECR is Rs.167 crores only). From the Table 1.4 the following state police units of Jammu & Kashmir, Kerala, Madhya Pradesh, Rajasthan, Sikkim, Uttar Pradesh and Uttrakhand are identified to be the relatively most efficient state police units having an efficiency rating of 100.The states having Table 1.4 :Efficiency Report for Output-Oriented CCR Model: DMUs DMU Name Efficiency Referent Efficient Units Objective Value 1/Objective value DMU 1 Andhra Pradesh Jammu & Kashmir, Madhya Pradesh DMU 2 Arunachal Pradesh Madhya Pradesh DMU 3 Assam Madhya Pradesh, Uttar Pradesh DMU 4 Bihar Madhya Pradesh DMU 5 Chhattisgarh Madhya Pradesh, Uttarakhand DMU 6 Goa Madhya Pradesh, Uttarakhand DMU 7 Gujarat Kerala, Madhya Pradesh, Uttar Pradesh DMU 8 Haryana Madhya Pradesh, Uttarakhand DMU 9 Himachal Pradesh Madhya Pradesh, Uttarakhand DMU 10 Jammu & Kashmir Jammu & Kashmir DMU 11 Jharkhand Jammu & Kashmir, Madhya Pradesh DMU 12 Karnataka Jammu & Kashmir, Madhya Pradesh DMU 13 Kerala Kerala DMU 14 Madhya Pradesh Madhya Pradesh DMU 15 Maharashtra Madhya Pradesh DMU 16 Manipur 6.87 Madhya Pradesh DMU 17 Meghalaya Madhya Pradesh DMU 18 Mizoram Madhya Pradesh, Sikkim DMU 19 Nagaland Madhya Pradesh, Sikkim DMU 20 Odisha Madhya Pradesh, Uttarakhand P a g e

12 DMU 21 Punjab Madhya Pradesh DMU 22 Rajasthan Rajasthan DMU 23 Sikkim Sikkim DMU 24 Tamil Nadu Kerala, Madhya Pradesh, Uttarakhand DMU 25 Tripura Madhya Pradesh DMU 26 Uttar Pradesh Uttar Pradesh DMU 27 Uttarakhand Uttarakhand DMU 28 West Bengal Madhya Pradesh, Uttarakhand Source: Author s Calculations efficiency value less than 100 are termed as inefficient relative to those which have been found to be efficient. The state of Chhattisgarh with an efficiency of is 99% efficient and needs only > 1 % change in output to improve upon its efficiency levels so as to reach the 100% efficient state of Jammu &Kashmir or Sikkim or Rajasthan. Whereas the State police unit of Manipur is hardly 7% efficient and needs nearly 93% change in output to improve upon its efficiency to reach the 100% efficient state police units. Table 1.4 also indicates the reference efficient units of each of the state police units which simply indicates the group of state police units which the particular state ought to emulate to be reaching the most efficient state(s) level. The reference unit for the efficient unit is the state itself. For example, Jammu & Kashmir will have its referent efficient unit as its own self. But the other states will have some other state units in the group of referent units which are generated on the basis of weights assigned to various input/output dimensions taken into consideration in the calculations. For example, Chhattisgarh(99.87% efficiency) has Madhya Pradesh(100% efficient) and Uttarakhand(100% efficient) in its peer group or referent group; and, Manipur(6.87% efficiency) has Madhya Pradesh(100% efficient) as its referent unit. The dimensions on which these state police units have to make improvements are made evident through Table1.5 in the ensuing paragraphs. 5.1 Efficiency and Inefficiency Observing the 1/Objective Value column, DMUs having scores greater than 1 are identified as inefficient in the output-oriented model. These DMUs can improve their efficiency, or reduce their inefficiencies proportionately, by augmenting their outputs (since we run an output-oriented model). For example, in Table 1.4, DMU 1 can improve its efficiency by augmenting certain outputs up to 28 % ( ). Similarly, DMU 16 can do so with approximately 1455 % increases. However, DMU 5 is closer to the efficiency frontier and needs only a 1 % increase in outputs. The following table is indicating the efficiency improvement options which are displayed as the difference column in Table 1.5. For clarity, if we take Andhra Pradesh state police unit and observe the value of differences as calculated in the above mentioned table, it is observed that it can improve by reducing Total Police Expenditure in Crores of Rupees (TECR) by Rs crores (12.96% reduction); reduce the number of police officers (NPO) by (14.59%); and the projections show that the outputs of this state police unit need to be increased tremendously( NPART by 44%, PCST by 46%, NPC by 98%, and NTC by 27.70%). The target values / projections for the efficient states are equivalent to their original input and output values ( for example check the values of percentage change for Jammu & Kashmir, DMU 10). Table 1.5: Projections of Inputs and Outputs of State Police Units. DMUs STATE 1 / OBJECTIVE PROJECTIONS DIFFERENCE PERCENTAGE VALUE ANDHRA DMU PRADESH TECR NPO NIO TNIC NPART PCST NPC NTC ARUNACHAL DMU P a g e

13 PRADESH TECR NPO NIO TNIC NPART PCST NPC NTC ASSAM DMU TECR NPO NIO TNIC NPART PCST NPC NTC BIHAR DMU TECR NPO NIO TNIC NPART PCST NPC NTC CHHATTISGARH DMU TECR NPO NIO TNIC NPART PCST NPC NTC GOA DMU TECR NPO NIO TNIC NPART PCST NPC NTC GUJARAT DMU TECR NPO NIO TNIC NPART PCST NPC PCST HARYANA DMU TECR NPO NIO TNIC NPART PCST NPC PCST HIMACHAL PRADESH DMU TECR P a g e

14 JAMMU & KASHMIR NPO NIO TNIC NPART PCST NPC NTC DMU TECR NPO NIO TNIC NPART PCST NPC NTC JHARKHAND DMU TECR NPO NIO TNIC NPART PCST NPC NTC DMU KARNATAKA TECR NPO NIO TNIC NPART PCST NPC NTC KERALA DMU TECR NPO NIO TNIC NPART PCST NPC MADHYA PRADESH NTC DMU TECR NPO NIO TNIC NPART PCST NPC NTC MAHARASHTRA DMU TECR NPO NIO TNIC NPART PCST NPC NTC MANIPUR DMU TECR NPO P a g e

15 NIO TNIC NPART PCST NPC NTC DMU MEGHALAYA TECR NPO NIO TNIC NPART PCST NPC NTC MIZORAM DMU TECR NPO NIO TNIC NPART PCST NPC NTC NAGALAND DMU TECR NPO NIO TNIC NPART PCST NPC NTC ODISHA DMU TECR NPO NIO TNIC NPART PCST NPC NTC PUNJAB DMU TECR NPO NIO TNIC NPART PCST NPC NTC RAJASTHAN DMU TECR NPO NIO TNIC NPART PCST NPC NTC SIKKIM DMU TECR NPO NIO P a g e

16 TNIC NPART PCST NPC NTC TAMILNADU DMU TECR NPO NIO TNIC NPART PCST NPC NTC TRIPURA DMU TECR NPO NIO TNIC NPART PCST NPC NTC UTTAR PRADESH DMU TECR NPO NIO TNIC NPART PCST NPC NTC UTTARAKHAND DMU TECR NPO NIO TNIC NPART PCST NPC NTC WEST BENGAL DMU TECR NPO NIO TNIC NPART PCST NPC NTC Source: Author s Calculations Table 1.6 displays the results of various DMUs with regard to their benchmarks from the Refferent Efficient Units created in our analysis(from Table 1.4). In the output oriented model chosen by the author, the efficient hospitals will consider themselves as their own benchmark. Thus, the benchmark for Jammu & Kashmir is Jammu & Kashmir itself, and so on. The benchmark states for Tamil Nadu are Kerala Madhya Pradesh and Uttarakhand. But it will try to emulate best practices of Kerala which has the highest lambda value amongst the referent efficient units. 60 P a g e