Ranking Veterinary Dispensaries in Odisha Using DEA and PCA

Abstract

The idea of measuring efficiencies of service delivery of veterinary dispensaries (VDs) and ranking them is an unexplored territory. However, since governments spend considerable amounts of money on promoting service delivery of VDs to enable animal production and productivity, and thereby promote rural livelihoods, efficiency measurement and ranking of VDs based on efficiency are necessary in a futuristic ‘transparency in governance’ environment apart from guiding in better performance. Given the non-quantifiable nature of the production function of veterinary service delivery, a non-parametric method like data envelopment analysis (DEA) can be an answer. Hence, this study measures the efficiencies of 101 VDs belonging to 2 ecosystems in Odisha, India, using DEA and ranks them using principal component analysis (PCA) along with average efficiency based on multiple data models. Analysis of various variables in models revealed that the presence or absence of variables—institutions; vaccination; a weighted variable combining castration, insurance and training (CIT); large animals’ population; and breedable animals’ population—lead to differences in average efficiencies. PCA of efficiency scores reveals that vaccination, CIT and large animal population are significant in factor loadings on first principal component (PC). The study finds high correlation between ranking based on average efficiency and ranking based on PCA, suggesting that the two methods are comparable. Both the efficiency measures and ranking reveal that VDs of the coastal ecosystem performed better than those of the western ecosystem.

Keywords

DEA efficiency PCA factor loading factor scores VD rank sum test

Background and Introduction

Animal husbandry is the most important non-agriculture activity in rural areas and contributes a major chunk of the rural GDP of most developing countries. It is next to agriculture in terms of contribution to GDP and employment in rural India. It is more equitable in nature compared to agriculture as more farm animals are owned by landless, marginal and small farmers in India. Livestock production is an important part of rural livelihood system in Odisha, India, and is a mixed-crop–livestock system. The majority of the animals are local cattle, which are known for their low productivity. Animal husbandry is backward in Odisha and has been a neglected sector in the state historically (GoO 2010).

The Fisheries & Animal Resources Development (FARD) Department of the Government of Odisha, which formulates and implements plan, policies and programmes for animal husbandry and fisheries sectors in the state, visualised a lot of scope for promoting animal husbandry as a viable livelihood option for the rural people. Therefore, a 10-year perspective plan for the sector was developed named ‘Perspective Plan Animal Resources Development Sector 2010–20’. The plan has the vision:

to excel as a holistic support system by providing, securing and facilitating effective and efficient services to become self sufficient/surplus in milk, egg and meat by enhancing Livestock productivity along with helping the poor to secure sustainable livelihood through livestock development and management while working in close coordination and partnership with allied institutions. (GoO 2010, 2)

Achievement of self-sufficiency in milk, egg and meat production and offering employment opportunities for the rural poor through ‘efficient’ and effective service delivery are the missions of the plan (GoO 2016, 1). The service delivery of the livestock sector to the farmers is provided through a network of various veterinary institutions spread across the state. Veterinary dispensaries (VDs) are such veterinary institutions which are the main service providers to the animal husbandry sector in both India and Odisha. The state of Odisha has 540 VDs functioning for service delivery (GoO 2010, 4).

Services Delivery at the Grassroots by Veterinary Department

Figure 1 gives the organogram of the Animal Resources Development (ARD) Department of the Government of Odisha, depicting the organisation structure, at both state and district levels. The grassroots-level service delivery is offered at the block—which is a sub-district level administrative and developmental unit in most states of India—and sub-block levels. Each block has one or more VDs including a block-level veterinary dispensary (BVD), which is headed by the block veterinary officer (BVO), who is also the administrative head of any other dispensary in the block. Other dispensaries in the block are run by a veterinary assistant surgeon (VAS) or an additional veterinary assistant surgeon (AVAS). VDs in turn have many livestock aid centres (LACs) under their jurisdiction. The LACs usually located at the panchayat level are headed by a livestock inspector (LI). The state of Odisha has 2,939 LACs functioning for service delivery (GoO 2010, 4). These three veterinary institutions directly deliver various services of the department—treatment, surgery, gynaecological and obstetrical services, disease diagnosis service, breeding services like providing artificial inseminations (AI), disease preventive measures like vaccinations—apart from other services such as de-worming, castration and insurance facilitating services like ear tagging for identification, issuing health certificate and post-mortem if insured animals die. The institutions also offer various extension services like training on animal husbandry management, feeding and fodder development. Gomitras are personnel who are trained in providing AI services at the doorstep of farmers and are usually placed in LACs. BVDs also have a mobile veterinary unit (MVU) with a veterinary doctor and an attendant and are provided with a vehicle (a car or a van) to travel to various villages. The MVUs, which are equipped with various equipment for providing AI and treatment, travel to various villages based on a planned schedule to offer such services at the grassroots.

Veterinary service delivery is offered through various inputs of staff and materials such as veterinary doctors, LIs, VDs, LACs, medicines and vaccines and produces several outputs such as treatment, vaccination, AI of animals and farmers’ trainings. Many of the inputs and outputs cannot be measured in monetary terms or in any other common form, thus making it difficult to measure efficiency using any direct ratio or a weighted average. Data envelopment analysis (DEA) is the technique which was developed for measuring efficiencies of such programmes of governments and not-for-profit organisations and can be used here. The technique does not require any common denominator like money and can use whatever units in which particular inputs or outputs are measured as long as all measures of a particular variable are expressed in the same unit for all decision-making units (Charnes, Cooper and Rhodes 1978; Ramanathan 2003).

This article is organised as follows. A brief review of literature on DEA and ranking is given in the next part followed by research design including the techniques used, rationale, objectives and locations for this study, data, models and methods, a brief data description, findings of DEA efficiencies and ranking of VDs, summary of findings, discussion of results, concluding remarks and limitations of the study, followed by references.

Literature Review

M. J. Farell (1957) proposed the concept of economic efficiency being the product of technical efficiency and allocative efficiency. The concept of measuring efficiency using an operation research technique called DEA was first proposed by Charnes, Cooper and Rhodes (1978), a method with ‘possible uses in evaluating public programs’ which have a collection of decision-making units (DMUs) with common inputs and outputs (with positive values for each DMU). They developed the technique for measuring total efficiency combining both technical efficiency and scale efficiency, referred to as CCR Model which assumes constant returns to scale (CRS). Banker, Charnes and Cooper (1984) developed the technique for measuring technical efficiency separately without combing scale efficiency called as BCC model which allows for variable returns to scale (VRS). Ali and Seiford (1990) established the conditions under which DEA models are translation invariant, which affords a solution to the problems of scaling and zero values on DEA.

One of the earlier literatures on application procedures for DEA is by Golany and Roll (1989), which discussed various aspects of the application including DMUs and factors among others. Boussofiane, Dyson and Thanassoulis (1991) focused on key issues in practice in applying DEA. Another important paper in the category is of Dyson et al. (2001), which considers various aspects of application including minimum number of DMUs to be used to have discrimination in efficiency scores. Podinovsky and Thanassoulis (2007) recommend weighting of individual factors to aggregate them as one of the methods of reducing the number of factors and argue that it is equivalent to using weight restrictions in the multiplier model. A more recent paper is the one by Cook, Tone and Zhu (2014).

The concept of cross-efficiency and cross-efficiency matrix was first introduced by Sexton, Silkman and Hogan (1986). The paper defined cross-efficiency as the efficiency score derived by calculating the score based on optimal input and output weights of other DMUs. Andersen and Peterson (1993) developed a model for ranking efficient DMUs, which later became known as super efficiency model. Doyle and Green (1996) developed the concept of cross-efficiency further and coined the term Maverick DMU and Maverick Index.

Friedman and Sinuany-Stern (1997) developed a method for comparison between individual DMUs and the ranking of all DMUs, both efficient and inefficient, with the use of canonical correlation analysis (CCA). The paper also recommends a non-parametric statistical test to validate the classification by DEA and the ranking by CCA using Mann-Whitney rank sum test. Sinuany-Stern and Friedman (1998) developed a method using discriminant analysis to provide common weights for multiple inputs and outputs that discriminate optimally between efficient and inefficient DMUs. The method, termed as discriminant DEA of ratios (DR/DEA), calculates the ratio of weighted outputs and inputs to be used as a metric for ranking DMUs. Friedman and Sinuany-Stern (1998) developed a combined ranking method for ranking DMUs in the DEA context based on three ranking methods, the CCA, the DR/DEA and the ranking based on cross efficiency method (CE/DEA). Adler, Friedman and Sinuany-Stern (2002), in a review of various ranking methods, divided the methods into six somewhat overlapping areas. The first area is based on the use of cross-efficiency matrix, the second on super efficiency methods, the third on number of DMUs for whom a particular efficient DMU is a peer, the fourth on various multivariate statistical techniques, the fifth area on ranking of inefficient DMUs based on proportional measures of efficiency and the sixth on combining multiple criteria decision methodologies with DEA.

Cinca and Molinero (2004) argue that the selection of DEA model is problematic and that the estimated efficiency of any DMU will depend on the inputs and outputs included in the model and the total number of inputs and outputs. Stressing the importance of selecting a parsimonious specification and to avoid models that assign high efficiency values to DMUs that operate in unusual ways (mavericks), the paper proposed a new method for model selection. The paper suggests the use of PCA for analysing the efficiency scores obtained from various model specifications and for producing DMU rankings. Each model (data model) may be used as a variable, and each efficiency score of individual DMUs may be taken as observations of the variable for running the PCA. The paper advocates the use of factor loading on each model of first principal component (PC) for estimating its importance and factor scores of first PC of DMUs to rank them. Also individual components may be used to describe the nature of efficiency measurement of each model. The paper demonstrates the method by applying PCA on efficiency scores of 18 DMUs from 21 DEA models.

There are several studies done on measurement of efficiency of dairy farms in various countries. Zibaei, Kafi and Bakhshoodeh (2008) study the context by which veterinary services may affect the technical efficiency of 840 Iranian dairy farms. The study uses DEA to estimate the regional frontier and meta frontier-level technical efficiencies. Gaspar et al. (2009) analyse technical efficiencies of livestock farming systems in Extremadura, Spain, using input-oriented both CRS and VRS models. Kelly et al. (2012) use DEA to measure efficiencies of a sample of Irish dairy farms and compare key production characteristics of efficient and inefficient units using ANOVA and identify longer grazing season, higher milk quality standard, higher likelihood of participation in milk recording and greater land quality associated with more efficient dairy farms, apart from using less input per unit of output and higher production per cow and per hectare. Kelly et al. (2013) estimate the technical and scale efficiencies of pasture-based Irish dairy farms using DEA. The study also shows that increased farm size, intensification and dairy specialisation are associated with higher efficiency. Aldeseit (2013) uses DEA to measure technical efficiency of dairy farms in Jordan and finds that the farms are not operating at optimal scale size.

Although there are many studies in the animal husbandry domain, we could find no study measuring efficiency of VDs or of ranking them. The current study differs from the above-mentioned studies in important ways. First, all those studies are on efficiency of for-profit units undertaking some economic activity unlike VDs which are service-oriented government-sponsored units. Values of the outputs of veterinary services are not readily measurable, especially in the absence of a competitive market for the same, making it more difficult to measure efficiencies. Veterinary services are one of the inputs to the animal husbandry activities, and their cost to a dairy unit, for example, is readily measurable as the amount paid for the services and the costs of purchase of materials like medicines and vaccines, if any. Hence, measuring the efficiency of VDs is altogether of a different kind compared to efficiency measurement of any animal husbandry unit.

The term ‘ranking’ in this study refers to arranging the DMUs, VDs in this case, in terms of their performance in a descending order with the best performing VD at the top and worst performing VD at the bottom. DEA results produce efficiency scores for each DMU between 0 and 1. The DMUs which get an efficiency score of 1 are considered efficient and others as inefficient. As the scores of all efficient DMUs are equal to 1, they cannot be ranked using this score alone. Hence, an additional method of ranking is required in this case. Several studies exist in the literature where efficiency measurement using DEA and ranking using a related method are done in the not-for-profit domain. Hollingsworth and Harris (2002) use DEA and super efficiency to measure cost and production efficiency of local government programmes for childhood immunisation in urban and rural parts of Australia. The study ranks the programmes using super efficiency scores. Ramanathan (2005) studied the operations efficiency of 20 hospitals in the Sultanate of Oman using DEA and ranked the efficient hospitals using the super efficiency model. Singh (2016) measured the performance of states under the Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) using DEA and ranked the states using cross-efficiency approach. Visbal-Cadavid, Martínez-Gómez and Francisco (2017) assessed the efficiency of public universities in Columbia using DEA. The universities are also ranked in the study using Pareto efficient cross-efficiency model. Mirmozaffari and Alinezhad (2017, 217–22) used cross-efficiency and two-stage DEA for efficiency measurement and ranking of 12 heart hospitals in Iran.

Khan and Gulati (2019) used DEA and double bootstrapping approaches to measure financial, operational and social efficiency measures and ranked micro finance institutions (MFIs) in India using bias corrected efficiency scores obtained from bootstrapping. Puertas and Marti (2019) used cluster analysis and DEA to measure the contribution of universities towards sustainability and developed a ranking scheme which they called ‘GreenMetric’ to rank universities.

Most of these studies are comparable to the current study as they are public programmes where assessment of market values of outputs is difficult and hence measurement of efficiency needs a method like DEA. Ranking of DMUs is done based on one of the available methods. The DEA and PCA method, not used in any of these studies, fulfils two objectives at the same time—selecting most important factors or input and output variables among several available input and output variables and ranking all DMUs, both efficient and inefficient.

Research Design

DEA for Efficiency Measurement

DEA is a methodology for measuring the performance efficiency of organisational units called DMUs. This technique aims to measure how efficiently a DMU uses the resources available to generate a set of outputs. DMUs can include manufacturing units, schools, bank branches, hospitals or even practising individuals like doctors or lawyers. Most of these DMUs are non-profit organisations where the measurement of performance is difficult as a lot of inputs used by such organisations and a lot of outputs produced by them cannot be measured using a common denominator like money. Efficiencies of DMUs estimated using DEA are relative with respect to the best performing DMU. DEA is a non-parametric technique and does not require the assumption of the nature of a distribution (Ramanathan 2003).

Stochastic frontier analysis (SFA) developed by Meeusen and van den Broeck (1977) and Aigner, Lovell and Schmidt (1977) is another frontier technique of measuring efficiency. However, it is a parametric technique and requires specification of the functional form of the production function. Given the limited knowledge about the production function of veterinary service delivery, the technique is not considered in this study.

Rationale for the Study

The 10-year ‘Perspective Plan ARD Sector 2010–20’ has a total outlay of nearly ₹22.516 billion (around $322 million) out of which veterinary service delivery itself has a 39% share of ₹8.696 billion (around $124 million). The plan has delivery of ‘efficient veterinary services at the door step of the farmers’ as one of its missions (GoO 2010), and thus measurement of efficiency of veterinary service delivery is of practical importance. There is also a growing awareness among people about need for accountability and transparency in public programmes and public spending, which makes it important to measure the efficiency of service delivery by veterinary institutions in Odisha.

The method of DEA was proposed with the intention of measuring the efficiencies of programmes in the not-for-profit sector like those of governments and NGOs. However, while the use of DEA has increased manifold in the for-profit sector, its application in the intended sectors like animal husbandry has been negligible. Therefore, this study attempts to demonstrate the use of DEA in this less explored application on a government programme/department providing veterinary services. Also, the department at various levels (like district, sub-division and block levels) attempts to evaluate performances of VDs and ranks them periodically with the help of various outputs (most of which are used in this study also) individually. Hence, using a more comprehensive method like DEA for the purpose should be highly desirable.

Hence, a study is conducted with the following research questions and objectives.

It tries to answer the research questions of ‘Can DEA be used to measure the efficiency of VDs?’ and ‘Can meaningful and useful interpretations be made by this?’ and sets out with the following objectives:

Measuring the relative efficiencies of VDs of the study location using DEA, based on various inputs and outputs identified as relevant and identify peers for inefficient dispensaries.

Measure optimal levels of inputs/outputs for VDs identified as inefficient to make them efficient and identify their current returns to scale (RTS) properties.

Rank all the VDs based on their efficiencies for benchmarking.

The study is conducted in two parts. The first part examines input and output variables for their suitability in applying DEA (and makes suitable modifications wherever required) and uses basic DEA models to measure technical and scale efficiencies, finds input/output projections of inefficient DMUs for achieving efficiency, identifies RTS properties, thereby covering the first two objectives, and ranks DMUs using super efficiency and cross-efficiency. The second part of the study, which is the subject of this article, uses the not-so-commonly used PCA on DEA efficiency scores to rank DMUs based on the method proposed and demonstrated in Cinca and Molinero (2004).

This article tries to look at two aspects in specific to understand the role of different variables in the models in determining the efficiencies of VDs using PCA and rank the VDs based on DEA average efficiency (AE) and PCA.

Locations for the Study

Two ecosystems of the state where animal husbandry and animal production are more advanced, the coastal Odisha and the western Odisha are selected for this study. In particular, six districts from the two ecosystems are selected. The term ‘ecosystem’ is used here with its general meaning to represent two separate regions geographically, climatically and socio-culturally. The two ecosystems are selected as they are more advanced in animal husbandry and animal production compared to other parts of the state. The districts included in the study are Balasore with 21 VDs, Cuttack with 25 VDs (final 23 VDs) and Jagatsinghpur with 12 VDs of the coastal ecosystem and Bargarh (19 VDs), Jharsuguda (9 VDs) and Sambalpur (17 VDs) of the western ecosystem.

Models and Methods

This study uses the input-oriented version of the basic model of CCR (Charnes, Cooper and Rhodes 1978), which produces more discriminating efficiency scores for measuring technical efficiencies of VDs under various combinations of inputs and outputs. The choice of input or output orientation does not make a difference in this study because this study uses the efficiency scores alone which will be the same for individual DMUs under both input- and output-oriented CCR models. To rank the VDs, PCA, a multivariate statistical technique, is used in addition to average of DEA efficiency scores.

DEA in Detail

DEA is a linear programming-based technique to measure the relative efficiency of various units called DMUs. Each unit (DMU) would have used various inputs in different quantities to produce various outputs in different quantities.

Efficiency may be defined as a ratio of output to input and its measurement will be simple if one type of input is used to produce one type of output. Efficiency can then be measured as the ratio between the quantity of output to the quantity of input. Similarly, if all inputs and outputs can be expressed in terms of their monetary values, a similar ratio can be used to measure efficiency. In these cases, the unit which gets a higher value for this ratio can be considered to have higher efficiency and vice-versa. However, if the numbers of inputs or/and outputs are more than one and there are no common denominator like money to measure all inputs and outputs, then a simple ratio is not possible and one may have to devise some weighting scheme to find weighted input and weighted output to find such a ratio. In such a situation, how to assign weights to different inputs and outputs will be debatable. The problem may be compounded when the units of measurement of each of the inputs and outputs are different. If devising a weighting scheme is possible with reasonable accuracy, the ratio of weighted outputs to weighted inputs can be considered as efficiency. DEA uses linear programming to solve such a problem of assigning weights to different inputs and outputs such that the weighted ratio of outputs to inputs is maximised for the unit being studied, at the same time ensuring that no unit including the one being studied will get a ratio value of more than one using the same weights. This ratio will vary between 0 and 1. A unit will be considered as efficient if it gets a ratio of 1 and inefficient otherwise. Such a linear programming problem is run for each of the units to find their respective efficiencies. (Charnes, Cooper and Rhodes 1978; Ramanathan 2003).

CCR Input-oriented Model

The CCR model (Cooper, Seiford and Tone 2007) may be expressed in matrix form—by taking the input values in matrix form as ‘X’, output values in matrix form as ‘Y’ and the input multipliers as a row vector ‘v’ and output multipliers as a row vector ‘u’—as follows:

(LP 1) Max uy_o

Subject to

vx_o = 1

uY – vX < = 0

v > = 0, u > = 0,

Where y_o is the column vector of outputs and x_o is the column vector of inputs for DMUo.

The dual of the above primal LP problem, DLP 1, known as ‘envelopment’ form in DEA literature, with a real variable θ and a non-negative vector λ = (λ₁, λ₂, …, λ_n)^T of variables, can be formulated as follows:

(DLP 1) min θ

Subject to the constraints

θx_o - X λ > = 0

Y λ > = y_o

λ > = 0.

This DLP 1 tries to guarantee at least an output level as given in y_o of DMU_o while reducing the input vector x_o proportionally to a value as small as possible. Hence, this method is called as the input minimisation or input-oriented model. In applications of DEA, like in this study, the dual form of the LP (DLP 1) is solved as this will reduce the computational effort and to make interpretation more straight forward. This model is used in this study to find efficiencies of VDs under all the data models.

Principal Component Analysis

PCA is a dimension reduction tool that can be used to reduce a large set of variables to a small set that still contains most of the information available in the large set. It is a multivariate procedure that transforms a number of correlated variables into a smaller number of uncorrelated variables called PCs. Factor loadings are simple correlations between the variables and the factors, while factor scores are composite scores estimated for each respondent on the derived factors (Malhotra and Dash 2016).

Decision-making Units

Decision-making happens at various levels of veterinary service delivery among which BVDs and VDs are the most critical levels. Most of the planning and target setting occurs at the block level and most of the responsibility for achieving the target happens at the VD level. As VDs are considered as the focal points for delivery of veterinary services, VDs are the DMUs for this study, as most of the performance monitoring and assessment of the department occurs at this level. There are three types of VDs under the two ecosystems. One type is the block-level VDs which have a VD and a MVU. The second type is the sub-block-level VDs which do not have an MVU. Each of these VDs have a few LACs under itself. The third type of VDs is the district-level veterinary polyclinics which have doctors specialised in medicine, surgery and gynaecology. They also have other infrastructural facilities which are not there in the first two types of VDs. Under the study area, there was only one such unit during the period for which data was collected (2016–17). This particular VD is excluded from the analysis as this is not comparable with other VDs, while the other district-level VDs where polyclinics were not established during the period for which data was collected are retained in this study. Thus, typically, VDs in this study, considered as DMUs, have one VD with or without a MVU and some LACs under their jurisdiction.

Variables and Data Models Used

The variables involved in the delivery of veterinary services included the following:

Input factors such as technical staff; institutional infrastructure; equipment related to treatment, breeding, vaccination, gynaecology and obstetrics; diagnostic services and surgery; and supplies like medicines and semen straws.

Environmental factors like type and number of different animals and the competitive environment for offering veterinary services.

Output factors such as numbers of various services provided like treatments, AI, number of progenies born from AI services, vaccinations, surgeries, castrations, de-worming, animal health camps conducted, training and exposure visits for farmers, and various programme implementation outputs.

In the initial stage, 60 input variables and more than 12 output variables were identified as per the procedure laid down in Golany and Roll (1989), and data were collected on these for 103 VDs of the 6 districts for the year 2016–17 from the respective VDs and the respective SDVO or CDVO offices. From the data collected and based on discussions with the veterinary doctors of the VDs (Bowlin et al. 1985, as cited in Golany and Roll 1989), it was observed that the most important differentiating inputs were the staff and type of institution such as district-level VD, block-level VD or sub-block-level VD. The staff included veterinary doctors, para-veterinary staff called livestock inspectors (LIs), non-salaried trained staff called Gomitras, and support staff. If each of the institutional components or staff components are to be considered as separate input variables, they should have positive values for each DMU. However, many of these variables have zero values for many DMUs. Given the difficulties about zero-valued factors (inputs and outputs) in DEA (Ali and Seiford 1990; Charnes, Cooper and Rhodes 1978), it is decided to have only positive values in the analysis. In addition, to minimise the number of factors to increase discrimination in efficiency scores, a weighting scheme is used (Podinovsky and Thanassoulis 2007) with suitable weights to quantify the staff of a VD based on the salaries and wages of the respective employees with weights of 10:5:4:3 for veterinary doctors, LIs, Gomitras and support staff, respectively. Based on the investment made to set up a veterinary institution, weights were assigned to different types of institutions such as a VD, MVU and LAC using weights of 8:3:1, respectively.

Based on discussions with the veterinary doctors (Bowlin et al. 1985m as cited in Golany and Roll 1989), seven important output variables are identified. Four of them—the number of treatments done, number of AIs done, number of progeny born and number of vaccinations done—are most important, and all of the VDs had some positive values for them. The number of progeny born, which is an outcome rather than an output variable and represents AIs done nine months back and the success rate of AIs done, is considered as an alternative output variable to AI in this study. Although it is an outcome variable, it is used as a proxy to combination of number AIs done and success rate of AIs done, as most veterinary doctors with whom the authors discussed, expressed that progeny is also an important output apart from AI. The values of the other three output variables—castrations, number of man-days of training given to farmers and number of animals insured—had zero in many VDs. Given the difficulties about zero-valued factors (inputs and outputs) in DEA (Ali and Seiford 1990; Charnes, Cooper and Rhodes 1978), it is decided to have only positive values in the analysis. This required a weighting scheme to construct one output variable out of these three variables. A suitable weighting scheme is devised based on a survey of farmer users of these services and a single output variable ‘CIT’ is constructed using weights of 1:1.2:1.3 for castration, insurance and farmers’ training, respectively. Thus, five output variables were identified finally as treatment, AI, progeny born, vaccination and CIT, representing weighted castration, insurance and training. One VD which had zero value for CIT is excluded from the analysis. Thus, finally this study has 101 VDs as DMUs.

Among the environmental variables, the animal population in the jurisdiction of a VD is observed to be the most critical and included indigenous (native) cattle, crossbred or exotic cattle, buffaloes, sheep, goat, pigs, dogs and poultry. These are combined into three broad categories of large animals, small animals and poultry and used as environmental input variables. Another representative population variable of importance is the breedable animal population which is the count of indigenous cattle, crossbred/exotic cattle and buffaloes which have attained puberty and are potential candidates for AI. Thus, four different environmental variables are considered.

After arriving at two input variables, four environmental input variables and five output variables, various data models are devised to find efficiencies of VDs as described in a subsequent section. The minimum requirement of number of DMUs, which is at least twice of m × n (Dyson et al. 2001), where ‘m’ is the number of inputs and ‘n’ is the number of outputs, is abundantly satisfied in this study. With 101 DMUs, the present study has more than 2.5 times the minimum required number for models with the maximum number of factors: (2 + 3 inputs × 4 outputs) × 2 = 40.

Descriptive Statistics of Inputs and Outputs

Table 1 presents the descriptive statistics of inputs including the environmental input variables ecosystem-wise. The average number of weighted staff units per VD for coastal VDs is 57.5, while that for western VDs is 41.8 and the overall average for all 101 VDs put together is 50.5, though both the ecosystem VDs have comparable number of weighted institutional units. The large animal and poultry populations are higher for coastal compared to western VDs, while the small animal population are comparable.

Table 1.

Descriptive Statistics of Inputs of VDs (In Numbers).

Ecosystem	Statistic	Staff	Institutions	Large Animals	Breedable Animals	Small Animals	Poultry
Coastal (N = 56)	Mean	57.5	28.6	28,799	11,349	13,604	43,469
	SD	33.6	13.4	17,866.3	10,274.0	8,731.4	57,848.4
	Minimum	13	11	1,410	200	1,036	397
	Maximum	168	57	72,105	46,824	34,866	253,531
Western (N = 45)	Mean	41.8	25.6	18,859	4,338	13,506	26,853
	SD	24.8	11.8	10,304.9	2,959.9	9,549.0	26,284.1
	Minimum	8	11	3,794	750	2,456	4,231
	Maximum	101	60	45,646	16,271	41,989	158,061
Total (N = 101)	Mean	50.5	27.2	24,370	8,225	13,560	36,066
	SD	30.9	12.7	15,714.3	8,612.4	9,058.4	47,046.8
	Minimum	8	11	1,410	200	1,036	397
	Maximum	168	60	72,105	46,824	41,989	253,531

Source: Field data collection from offices of VDs/ BVO/SDVOs/CDVOs of respective districts.

The descriptive statistics of outputs produced by the studied VDs is presented in Table 2. The VDs of the coastal ecosystem have performed better than VDs of western on an average in the case of all five outputs. The relative variation in AIs between all VDs and progeny between western VDs are considerably higher compared to those of other outputs. In general, the higher staff and animal population in coastal VDs appear to have enabled them to produce higher outputs compared to western VDs.

Table 2.

Descriptive Statistics of Outputs of VDs (In Numbers).

Ecosystem	Statistic	AI	Progeny	Treatment	Vaccination	CIT
Coastal (N = 56)	Mean	4,069	1,600	23,603	73,654	2,260
	SD	4,444.8	1,479.7	19,767.6	46,915.6	1,280.9
	Minimum	320	70	1,965	3,878	260
	Maximum	27,054	7,223	86,522	196,290	4,955
Western (N = 45)	Mean	1,354	1,029	9,426	52,372	1,255
	SD	1,505.9	1,486.8	6,478.5	42,363.3	925.3
	Minimum	82	45	1,544	2,000	339
	Maximum	7,656	7,673	26,731	220,900	5,460
Total (N = 101)	Mean	2,860	1,346	17,287	64,172	1,812
	SD	3,701.7	1,502.7	16,838.3	45,970.1	1,237.3
	Minimum	82	45	1,544	2,000	260
	Maximum	27,054	7,673	86,522	220,900	5,460

Source: Field data collection from VDs/BVOs/SDVOs/CDVOs.

Correlation between different inputs, among different outputs and between inputs and outputs were found as required for variable selection in DEA (Golany and Roll 1989) and are presented in Table 3. The correlations between all inputs and outputs are positive and significant as required for using the data in DEA. The variables with their respective codes are given as row heading while only the variable codes are given as column headings to keep the table compact.

Table 3.

Pearson’s Correlation Coefficients Between Inputs and Outputs.

Input / Output

Statistic

Weighted staff (I1)

Sig (2t)

Weighted Institutes (I2)

0.857^**

Sig (2t)

0.000

Large animals (I3)

0.575^**

0.541^**

Sig (2t)

0.000

Small animals (I4)

0.410^**

0.444^**

0.711^**

Sig (2t)

0.000

Poultry (I5)

0.590^**

0.523^**

0.512^**

0.405^**

Sig (2t)

0.000

Breedable animals (I6)

0.620^**

0.623^**

0.641^**

0.421^**

0.617^**

Sig (2t)

0.000

AI (O1)

0.645^**

0.656^**

0.490^**

0.337^**

0.497^**

0.701^**

Sig (2t)

0.000

0.001

0.000

Progeny (O2)

0.654^**

0.689^**

0.415^**

0.280^**

0.408^**

0.632^**

0.861^**

Sig (2t)

0.000

0.005

0.000

Treatment (O3)

0.703^**

0.523^**

0.564^**

0.303^**

0.467^**

0.529^**

0.547^**

0.481^**

Sig (2t)

0.000

0.002

0.000

Vaccination (O4)

0.663^**

0.601^**

0.627^**

0.560^**

0.494^**

0.612^**

0.653^**

0.539^**

0.643^**

Sig (2t)

0.000

CIT (O5)

0.611^**

0.523^**

0.597^**

0.456^**

0.382^**

0.550^**

0.414^**

0.389^**

0.661^**

0.646^**

Sig (2t)

0.000

Source: Author’s own calculations.

Notes: *Pearson’s correlation coefficient; **Correlation is significant at the 0.01 level (2-tailed).

Efficiencies of VDs Based on Various Combinations of Inputs and Outputs

In the current study, two input variables, four environmental input variables and five output variables are used. A total of 138 different data models are generated based on all combinations of these inputs, outputs and environmental inputs by following the below mentioned rules:

Staff is used as a single input or in combination with institutions as two inputs, leading to two different models. Institutions alone are not used as single input because staff is the most important critical input, and it will be absurd to exclude staff from any model.

Four outputs are used with one output case, two outputs case, three outputs case or four outputs case. In all such combinations where AI is used as an output, number of progeny born is used in an alternative output.

Based on the presence or absence of environmental variables, three forms of models are devised: (a) models with no environmental variables; (b) models with three environmental variables of large animals, small animals and poultry referred to as AP; and (c) models with three environmental variables of breedable animals, small animals and poultry referred to as BP.

Using the above rules, models are devised as follows—4 single output combinations, 6 two output combinations, 4 three output combinations and 1 four output combination—thus making it a total of 15 models. When a single input of staff is used, we have 15 models, and when we use both staff and institutions, we have another 15 models, thus making it 30 models. For each of these, we have three different forms of environmental variables, making it 30 × 3 = 90 models. Out of these 90, AI is used in 48 models which can be replaced by its alternative progeny to devise another 48 models—for a total of 138 data models.

AE, Ranking Based on AE and Number of Times Efficient

Use of arithmetic mean (average) of efficiency (AE) scores based on weights assigned to optimise each and every DMU is done often to obtain what is called as cross-efficiency or average cross-efficiency in DEA literature for ranking DMUs (Adler, Friedman and Sinuany-Stern 2002; Doyle and Green 1984; Sexton, Silkman and Hogan 1986). The current study uses AE scores obtained from different data models as one of the methods for ranking VDs.¹ Efficiency scores of VDs are found for all of the VDs under each of the 138 models using input-oriented CCR model and the AE for each VD is found out. The descriptive statistics of the AE scores based on these 138 models are presented in Table 4, along with ranking of VDs based on AE and number of times individual VDs are efficient among the 138 models.

Table 4.

Descriptive Statistics of AE, Ranks Based on AE and Number of Times Efficient Out of 138 Models.

Ecosystem	Statistic	AE	Ranks Based on AE	Number of Times Efficient
Coastal (N = 56)	Mean	0.604	41.3	18.8
	SD	0.153	26.7	27.5
	Minimum	0.220	1	0
	Maximum	0.896	94	102
Western (N = 45)	Mean	0.458	63.1	12.5
	SD	0.205	28.0	22.7
	Minimum	0.0649	2	0
	Maximum	0.883	101	96
Total (N = 101)	Mean	0.539	51.0	16.0
	SD	0.191	29.3	25.5
	Minimum	0.0649	1	0
	Maximum	0.896	101	102

Source: Author’s own calculations.

Note: Efficiencies calculated using OSDEA software.

The AE is the AE score of individual VDs obtained from each of the 138 data models. Coastal VDs perform better with an AE score of 0.604, while western VDs have a lesser AE of 0.458 for an overall average of 0.539 for all the 101 VDs put together. The rankings of VDs based on AE scores also suggest a better performance by coastal with a lower average rank compared to western. Of the 101 VDs, 48 are efficient in one or more of the models, of which 32 are of coastal group and 16 are of western group. No ranking is attempted here as only 48 VDs can be ranked using number of times efficient. Coastal VDs do better in this with a higher average number of times efficient and also the highest of 102 times efficient among the 138 models going to them.

Analysis of AE Scores of Data Models Used

Further analyses of efficiency scores of VDs based on 138 data models are done. Individual VDs’ efficiencies are taken as variables, and each of the models are taken as observations for this analysis. The AE here are the average score of all 101 VDs for a particular model, unlike the VD-wise analysis presented in the previous section. The descriptive statistics of AE and number of efficient VDs for each of the data models are given in Table 5. Thus, the AE of all VDs based on 138 models is 0.539, and the average number of efficient VDs per model is 11.67.

Table 5.

Descriptive Statistics of AE and Number of Efficient VDs Under Various Models.

Statistic	AE	Efficient Number
Mean	0.539	11.67
N	138	138
SD	0.152	8.97
Minimum	0.201	1
Maximum	0.799	38

Source: Author’s own calculations.

The influence of presence or absence of each of the input/output variables is studied using non-parametric Mann-Whitney rank sum test to test whether significant differences existed in AE scores and number of efficient VDs of different models with and without a particular variable. Non-parametric tests are used here, as the DEA efficiency scores are considered as non-parametric and use of a parametric test like 2-independent sample t-test is not allowed. Friedman and Sinuany-Stern (1997) also use a non-parametric statistical test to validate the classification by DEA and the ranking by CCA using Mann-Whitney rank sum test in their study on ranking of DMUs using CCA. Table 6 presents a summary of the test results for different models discussed earlier. The table has listed results for only those variables where there is significant difference (p < 0.05) in efficiency scores between models with them and models without them, due to space constraints. As is evident, the efficiency scores are influenced by the presence or absence of each of these input/output variables. The AE and average number of efficient units are also given in the table. The higher values of these for the models with the respective variables compared to models without them show that the presence of these variables has significantly increased the efficiency scores and number of efficient VDs (p < 0.05).

Table 6.

Summary of Mann-Whitney Rank Sum Test for Test of Difference of Efficiency Scores and Number of Efficient VDs, With or Without Given Variables.

Variable	Institutions		Vaccination		CIT		AP**	BP***
Test for	Average Eff.	Efficient VDs	Average Eff.	Efficient VDs	Average Eff.	Efficient VDs	Efficient VDs	Average Eff.	Efficient VDs
Models with*	69	69	72	72	72	72	46	46	46
Models without	69	69	66	66	66	66	92	92	92
Average with	0.574	14.0	0.625	16.4	0.601	13.7	13.2	0.601	17.4
Average without	0.505	9.32	0.446	6.47	0.472	9.52	10.9	0.509	8.80
Mean rank with	59.7	60.1	43.9	47.0	53.5	59.2	64.0	60.8	56.6
Mean rank without	79.3	78.9	93.0	90.1	84.2	79.0	80.4	86.9	95.3
Man-Whitney U	4,118	4,150	686	893	1,321	1,695	1,614	1,314	928
Z	–2.89	–2.75	–7.20	–6.33	–4.50	–2.91	–2.27	–3.62	–5.38
Sig (2-tailed)	0.004	0.006	0.000	0.000	0.000	0.004	0.023	0.000	0.000

Source: Author’s own calculations.

Notes: *number of models with the given variable; **AP = animal population with large animals; ***BP = animal population with breedable animal population.

Thus, the presence or absence of outputs, AI or progeny and treatment has not changed the efficiency scores or number of efficient VDs per model significantly (p < 0.05), while the presence of institutions, vaccination, CIT and environmental variables—with the exception of models with AP where only number of times efficient is significant and not AE—has significantly increased the AE scores and number of efficient VDs (p < 0.05).

PCA for Prioritising Variables

Cinca and Molinero (2004) devised a method for the use of PCA of efficiency scores obtained under different data models and used the first PCA component score for ranking DMUs. In this study, each of the 138 models are used as a variable, and efficiency scores are used as individual observations for finding PC. Based on an eigenvalue criterion of >1, nine components are extracted as given in Table 7. The first component explains 61% of variation in efficiency scores, second component about 12% and so on. All the nine components put together explain 97.48% of variation.

Table 7.

PCs with Eigenvalues >1.

Component	Initial Eigenvalues
	Total	% of Variance	Cumulative %
1	83.887	60.788	60.788
2	16.647	12.063	72.851
3	13.070	9.471	82.322
4	9.206	6.671	88.993
5	4.686	3.395	92.388
6	2.447	1.773	94.162
7	2.021	1.464	95.626
8	1.406	1.019	96.645
9	1.152	0.835	97.480

Source: Author’s own calculations.

Different input/output models may be analysed using the first factor loading (Cinca and Molinero 2004). Table 8 presents the highest and lowest factor loadings for first PC and sum of all nine PCs and the data models that obtained these loadings. Based on the first PC, models with more number of input/output variables along with animal population received higher loading, while those with less number of inputs and outputs and progeny as one of the outputs received lower loadings. However, based on sum of all factor loadings, models with progeny as one of the variables and without animal population obtained the maximum loading, while those with vaccination and CIT and one of the animal populations (BP or AP) received the lowest loading, thus rendering it difficult to make any interpretations based on top and bottom ranks alone. Looking at both the factor loadings, it may be suggested that use of AP does better than use of BP as environmental variables. Vaccination and CIT along with either AI or progeny figure in all top models under first factor loading, while treatment and progeny appear in all top models based on all factor loading, suggesting that all four outputs are important. However, whether to use AI or progeny does not get a conclusive answer. As institutions figure in four of the top five models based on first factor loading and in two of the top five models based on all factor loadings, its use as input appears appropriate. Models are represented in Table 8 conveniently by the first letter of each of the input/output factors present in the model.

Table 8.

Models Ranked Based on Their First Factor Loading and Sum of All 9 Factors Loading.

		First PC		All 9 PCs
Ranks		Factor Loading	Model	Factor loading	Model
	1	0.930	SIAVO AP*	1.980	SIPT
	2	0.930	SIPTVO AP	1.970	SPT
	3	0.928	SIPVO AP	1.959	SPTV
	4	0.928	SIATVO AP	1.949	SPV
Top ranked models	5	0.926	SATVO AP	1.851	SIPTV
	138	0.455	SP	–0.447	SVO BP
	137	0.463	SIP	–0.407	STVO BP
	136	0.538	SP BP	–0.204	SVO AP
	135	0.545	SIP BP	–0.197	SIVO BP
Bottom ranked models	134	0.550	SP AP	–0.178	SITVO BP

Source: Author’s own calculations.

Notes: *S = Staff, I = Institutions, A = AI, P = Progeny, T = Treatment, V = Vaccinations, O = CIT, AP = Animal Population with large animals, small animals and poultry, BP = model with breedable animal population instead of large animal population.

Test of differences of factor loadings of different models is done using Mann-Whitney rank sum test. To understand the importance of each of the input/output variable, test has been conducted to look at differences in factor loadings of first PC between with and without a particular variable. The test results are presented in Table 9 for only those variables where significant differences (p < 0.05) existed.

Table 9.

Summary of Mann-Whitney Rank Sum Test for Test of Difference of Factor Loadings of First PC of Different Models with or Without Given Variables.

Variable	AI	Vaccination	CIT	AP
Number of models with	48	72	72	46
Number of models without	90	66	66	92
Mean rank with	89.50	83.35	89	81.93
Mean rank without	58.83	54.39	48.58	63.28
Rank sum with	4,296.00	6,001.00	6,384.50	3,769.00
Rank sum with out	5,295.00	3,590.00	3,206.50	5,822.00
Man-Whitney U	1,200.00	1,379.000	995.500	1,544.000
Z	–4.292	–4.250	–5.884	–2.584
Sig (2-tailed)	0.000	0.000	0.000	0.010

Source: Author’s own calculations.

The presence or absence of the four variables—AI, vaccination, CIT and AP—have shown significant differences (p < 0.05) in factor loadings of models for first PC. Comparing these results with Table 6, where tests of differences are found between AE and number of times efficient, institutions and BP become less important and AI becomes important. However, vaccination and CIT are shown as important variables in both the methods whether AE or factor loadings of first PC on models.

PCA for Ranking the VDs

Table 10 presents the descriptive statistics of factor scores of VDs and ranks based on them for first factor and sum of all nine factors. Coastal VDs perform better than western VDs with higher average factor scores and lower average factor ranks.

Table 10.

Descriptive Statistics of Factor Scores of VDs and Ranks Based on Them.

Ecosystem	Statistics	Factor1 Score	Sum of All Factors Score	F1 Rank	All Factors Rank
Coastal (N = 56)	Mean	66.30	61.72	41.30	42.11
	SD	16.591	17.518	26.664	26.774
	Minimum	23.94	22.6521	1	2
	Maximum	96.80	95.7229	94	94
Western (N = 45)	Mean	50.4422	46.468240	63.07	62.07
	SD	22.458	22.525	28.175	28.795
	Minimum	7.19	5.6161	2	1
	Maximum	96.08	96.0805	101	101
Total (N = 101)	Mean	59.2372	54.927050	51.00	51.00
	SD	20.883	21.215	29.300	29.300
	Minimum	7.19	5.6161	1	1
	Maximum	96.80	96.0805	101	101

Source: Author’s own calculations.

Table 11 presents the VD-wise factor scores and ranks along with AE scores, ranks based on them and number of times particular VDs are found to be efficient. Tirtol VD (V46) of coastal ecosystem gets the first rank based on AE and first factor score, while Kesaibahal (V98) gets first rank based on all factors score. Balasore (V9) in coastal gets the top position in number of times efficient by being efficient in 102 out of the 138 models. Dehurda (V1), Machchagoan (V56) and Kolabira (V79) also figure in the list of top five ranks based on one or the other ranking method.

Table 11.

VD-wise AE, Number of Times Efficient, PCA Factor Scores and Ranks Based on Them.

DMU Code	DMU Name	AE	Efficient Number	Factor1 Score	All Factors Score	Rank AE	Rank F1	Rank All F9
V1	Dehurda	0.880	60	95.765	95.218	3	3	3
V2	Kamarda	0.611	0	67.168	65.818	40	40	30
V3	Baliapal	0.780	24	85.177	85.068	8	9	9
V4	Langaleswar	0.752	12	81.803	84.391	13	15	10
V5	Jaleswar	0.651	8	71.193	69.424	28	29	28
V6	Raibania	0.488	0	53.328	52.736	65	66	57
V7	Basta	0.729	15	79.522	80.727	20	20	13
V8	Remuna	0.544	0	59.479	57.988	53	54	44
V9	Balasore	0.869	102	94.550	90.267	5	5	6
V10	Rasalpur	0.638	0	70.147	62.627	32	32	32
V11	Rupsa	0.749	5	82.224	74.170	14	13	17
V12	Gopalpur	0.542	0	59.300	57.504	54	55	47
V13	Khantapada	0.619	0	68.292	57.931	36	36	45
V14	Soro	0.725	24	79.226	73.278	21	21	20
V15	Khaira	0.520	0	57.115	51.628	58	58	60
V16	Simulia	0.553	0	60.619	56.357	46	49	51
V17	Balikhanda	0.644	0	70.420	70.171	30	31	27
V18	Nilagiri	0.668	24	73.590	61.330	25	25	36
V19	Ayodhya	0.358	0	39.400	35.705	88	88	86
V20	R.B.Pur	0.617	0	67.827	61.453	37	39	35
V21	Oupada	0.376	0	41.609	35.477	85	84	87
V22	Nayabazar	0.379	0	41.837	39.237	83	83	79
V23	Kissannagar	0.396	0	43.529	41.513	80	80	76
V24	Kalapada	0.747	56	81.772	73.912	15	16	18
V25	Niali	0.302	0	33.097	33.418	91	91	89
V26	Mahanga	0.625	0	68.453	72.628	35	35	22
V27	Salipur	0.518	0	56.653	57.112	59	60	48
V28	N.Koili	0.755	59	82.682	90.138	12	12	7
V29	Tangi	0.546	1	60.548	46.827	52	50	68
V30	Choudwar	0.486	0	54.034	45.846	66	64	71
V31	Baranga	0.603	0	66.589	58.613	42	42	43
V32	Phulnakara	0.541	48	60.912	37.997	55	47	83
V33	Athagarh	0.517	6	56.862	52.824	60	59	56
V34	Gurudijhatia	0.630	46	68.601	58.841	34	34	41
V35	Tigiria	0.492	0	54.159	48.962	63	63	66
V36	Badamba	0.731	50	80.973	65.381	19	17	31
V37	Manibandha	0.546	0	60.216	53.067	51	51	55
V38	Gopapur	0.771	65	85.233	71.900	10	8	23
V39	Narsinghpur	0.494	1	54.323	48.796	62	62	67
V40	Kamaladiha	0.734	16	80.511	73.456	17	19	19
V41	Kanapur	0.790	83	86.377	76.514	7	7	16
V42	Baideswar	0.638	36	69.707	71.803	31	33	24
V43	Subarnapur	0.551	1	60.645	51.487	48	48	61
V44	D. Banki	0.764	23	84.306	72.797	11	11	21
V45	Raghunthpur	0.483	1	52.783	54.787	67	68	53
V46	Tirtol	0.896	87	96.798	95.723	1	1	2
V47	Tulanga	0.714	1	77.924	81.430	22	22	12
V48	Hazipur	0.393	0	43.027	38.860	81	81	80
V49	Jagatsinghpur	0.687	32	75.135	71.791	24	24	25
V50	Alipingal	0.775	79	84.570	82.462	9	10	11
V51	Kujang	0.549	1	60.087	58.792	49	52	42
V52	Paradeep	0.220	0	23.943	22.652	94	94	94
V53	Nuagaon	0.374	0	40.804	42.025	86	87	74
V54	Erasama	0.635	47	70.577	57.914	33	30	46
V55	Balikuda	0.446	1	49.724	34.615	75	74	88
V56	Machhagaon	0.805	36	87.909	93.168	6	6	4
V57	Ambabhana	0.410	0	44.697	44.591	78	78	72
V58	Dunguri	0.400	0	44.054	38.014	79	79	82
V59	Attabira	0.597	23	65.108	77.558	43	43	15
V60	Kadobahal	0.695	48	75.768	85.536	23	23	8
V61	Bargarh	0.454	1	49.322	52.644	74	75	58
V62	Barpali	0.492	0	53.625	54.253	64	65	54
V63	Bhatli	0.499	0	54.796	50.828	61	61	63
V64	Bheden	0.472	0	51.261	56.769	70	72	50
V65	Papanga	0.552	0	59.899	68.318	47	53	29
V66	G.Turum	0.250	0	27.197	26.863	93	93	92
V67	Bijepur	0.126	0	13.961	10.164	97	97	97
V68	Gaisilet	0.118	0	13.134	9.780	98	98	98
V69	Jharbandh	0.135	0	15.120	10.767	95	95	95
V70	Padampur	0.065	0	7.195	5.616	101	101	101
V71	Melchamunda	0.286	0	31.835	23.720	92	92	93
V72	Paikmal	0.100	0	10.975	9.645	99	99	99
V73	Mandosil	0.479	0	53.242	42.285	68	67	73
V74	Sohela	0.072	0	7.785	7.106	100	100	100
V75	Kuchipali	0.131	0	14.651	10.753	96	96	96
V76	Jharsuguda	0.547	24	61.036	49.914	50	46	65
V77	Brajrajnagar	0.617	0	68.004	62.566	38	37	33
V78	Laikera	0.659	47	73.004	60.860	26	26	38
V79	Kolabira	0.878	96	95.735	90.680	4	4	5
V80	Arda	0.747	25	81.895	77.781	16	14	14
V81	Bagdehi	0.473	0	51.931	50.063	69	69	64
V82	Belpahar	0.604	14	66.884	59.563	41	41	40
V83	Lakhanpur	0.583	47	64.886	55.818	44	44	52
V84	Kanaktora	0.657	1	72.740	61.260	27	27	37
V85	Sambalpur	0.333	0	36.150	38.093	89	89	81
V86	Burla	0.466	0	51.569	46.104	72	71	69
V87	Hirakud	0.371	0	41.334	31.521	87	86	90
V88	Rengali	0.304	0	33.516	30.560	90	90	91
V89	Laida	0.420	0	46.680	39.792	77	77	78
V90	Jujomura	0.383	0	42.366	36.495	82	82	85
V91	Dhama	0.377	0	41.573	37.376	84	85	84
V92	Kuchinda	0.732	43	80.900	70.384	18	18	26
V93	Jamankira	0.532	1	58.450	51.170	56	56	62
V94	Fasimal	0.525	0	57.661	52.065	57	57	59
V95	Bhojpur	0.470	0	51.850	46.023	71	70	70
V96	Bamra	0.458	0	50.777	41.278	73	73	77
V97	Garposh	0.433	0	47.960	41.541	76	76	75
V98	Kesaibahal	0.883	71	96.076	96.081	2	2	1
V99	Rairakhol	0.576	36	63.790	56.979	45	45	49
V100	Charmal	0.645	48	71.669	60.025	29	28	39
V101	Naktideul	0.615	36	67.837	61.871	39	38	34

Source: Author’s own calculations.

Comparison of AE and PCA for Ranking VDs

As can be seen from the annexure, the ranking of VDs based on the three methods of AE, first factor score and all factors score using PCA are comparable. To test the level of similarity among these ranking methods, Spearman’s rank correlation coefficients are found as presented in Table 12. All the three ranking methods have very high and significant (p < 0.01) correlations among the ranking of VDs produced by them.

Table 12.

Rank Correlation Between Ranking Based on AE, F1 and F9 (N = 101 for All Pairs).

	Rank Type	Statistics	F1 Rank	All Factors Rank	AE Rank
	F1 Rank	Correlation	1.000
	All factors Rank	Correlation	0.951^*	1.000
		Sig. (2-tailed)	0.000
Spearman’s rho	AE Rank	Correlation	0.999^*	0.960^*	1.000
		Sig. (2-tailed)	0.000	0.000

Source: Author’s own calculations.

Note: * Correlation is significant at the 0.01 level (2-tailed).

Summary of Results, Discussions and Concluding Remarks

Summary of Results

The technical efficiencies of service delivery of 101 VDs belonging to two ecosystems of Odisha, India, are found using CCR input-oriented model for 138 different data models. The different data models are designed using two input variables, four environmental variables and five output variables in various combinations. The AE of each VD based on 138 efficiency scores and the number of times individual VDs are efficient out of 138 models are presented and discussed. VDs of the coastal ecosystem overall fared better than VDs of the western ecosystem. Ranking of VDs based on AE is also attempted in this study. Further analysis to understand the role of individual factors reveals that the presence of institutions, vaccination, CIT and combinations of animal population variables—AP or BP—has significantly increased the AE and number of efficient VDs under a particular model. Coastal VDs of Dehurda (V1), Balasore (V9), Tirtol (V46) and western VDs of Kolabira (V79) and Kesaibahal (V98) obtained the top five ranks using AE.

Use of factor loadings of first PC for prioritising different data models has given top five ranking for models with more number of input/output variables along with animal population (AP), while those with less number of inputs and outputs and progeny as one of the outputs received lowest five ranking. However, the use of factor loadings of all nine PCs gives contrasting results in terms of top five and bottom five ranks. Mann-Whitney rank sum test as test of differences in factor loadings of first PC between presence and absence of particular variables in models shows AI, vaccinations and CIT (output variables) and AP (environmental input variables) as significant, implying that their presence has given models higher factor loading compared to models in which they are absent. This fact may be interpreted as use of AP (with large animals, small animals and poultry) instead of BP (with breedable animals, small animals and poultry) to be more appropriate and use of AI as an output instead of progeny as more appropriate.

PCA is used in this study as a second method of ranking VDs. Nine PCs are identified which explained nearly 97.5% of the variation in efficiency scores under 138 models. Ranking of VDs is done using the first PC and using the sum of all nine PCs. Coastal VDs of Dehurda (V1), Balasore (V9) and Tirtol (V46) and western VDs of Kolabira (V79) and Kesaibahal (V98) obtained the top five ranks based on first PC, while Machchgoan (V56) replaced Balasore (V9) for the top five ranks based on the sum of all PCs. Spearman’s rank correlation shows a high correlation between ranking based on AE and ranking based on PCs. The first PC and AE have higher correlation compared to those between AE and all PCs and first PC and all PCs.

Discussions

Governments spend considerable amounts of money in providing different services to the public, many of which are on subsidised basis. Given that tax payers’ money is being used for this, it is imperative that such programmes operate efficiently. However, efficiency measurements of such programmes are hardly done in practice. Veterinary service delivery is one such example. Although veterinary services contribute immensely to the development of the animal husbandry sector, efficiency of service delivery is not measured comprehensively. In the studied areas, for example, VDs are ranked based on their performance in individual output achievements, like number of vaccinations done during a year. Such a process would give multiple ranks to each VD based on multiple outputs. Hence, there is need for a comprehensive method of measuring efficiency and ranking VDs based on it.

Overall, the study demonstrates two important aspects. The first is that though efficiency of veterinary service delivery cannot be expressed in the form of a quantitative production model, it can be measured reasonably well using DEA and ranked using the method used in this article. The second point is that useful interpretations like importance of various factors in determining the efficiency of veterinary service delivery can be identified as demonstrated, and useful measures can be taken to improve efficiency. The study also uses PCA as a method for ranking based on DEA efficiency scores and finds that the results have high correlation with ranking based on AE. Thus, using PCA does not produce significant differences in ranking compared to using AE scores itself, though some additional interpretations are possible using PCA. The studies discussed earlier used super efficiency or cross-efficiency for ranking DMUs alone, while the use of DEA and PCA has the additional advantage of facilitating in the selection of important factors (input and output variables) to be used in DEA apart from ranking.

Concluding Remarks

The most important factors as identified by the model are AP consisting of large animal, small animal and poultry (as environmental input variables), AI, vaccination and CIT (as output variables). In conclusion, it can be stated that any model to measure efficiency of VDs should essentially include these variables. The second point is that use of DEA and PCA offers a comprehensive method for ranking VDs for any decision-making instead of a multiple ranking system using multiple outputs.

Some of the limitations of the study include the following.

DEA efficiency scores do not include an error term to represent random effect and hence are considered as biased by many researchers.

There is a limitation on data details. For example, the number of different types of animals treated in a year is not available; instead, only the total number of treatments done during the year is available. This figure may favour those VDs which cater to a higher sheep, goat and poultry population compared to those with predominantly large animal population as treatments given to small animals and poultry are usually many at a time, while those for large animals are usually one at a time.

The study has used CCR input-oriented model alone for measuring technical efficiencies of VDs. As some of the models use environmental variables also, which are not under the control of management of VDs, non-controllable or non-discretionary variable models are appropriate for models with such variables. However, to maintain uniformity in all models for comparison, only CCR input-oriented model is used in the case of all the 138 data models.

Using the same data, some more data models are possible which has not been done in this study. Such models include models without staff as an input variable (69 models possible), use of individual animal populations of large animals, breedable animals, small animals and poultry in various combinations (several hundred models possible), among others.

Footnotes

Acknowledgments

The author would like to thank the Animal Husbandry and Veterinary Services Department of Odisha for providing the data for this study. Thanks also to Prof. L. K. Vaswani, Prof. R. N. Subudhi and Dr Sailabal Debi for their guidance, comments and suggestions during various stages of this research. The author also acknowledges all the help and cooperation extended by his colleagues in completing this study. The author takes complete responsibility for any errors or omissions in this study.

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author received no financial support for the research, authorship and/or publication of this article.

Notes

Orcid iD

Ganesha H.S.

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