Education System Performance among Indian States: A Public Expenditure Efficiency Analysis using Linear Programming Methods

Deepa Sankar, Education Economist,

SASHD

Introduction Education and health care, and within these, elementary education and public health, are considered as merit goods which provide both private and social benefits. Any democracy ruled by welfare oriented governments cannot shy away from the provision of these services, whether the private sector exist or not in these sectors. Education and health systems1 deserve highest preference in any endeavor that aims at enhancing the human development and building social capital in the country. The principal goals of a health or education system should be to provide better health or enhanced education in a responsive way and with a reasonable fiscal allocation. How well the education / health systems accomplish these goals (performance) is reflected through actual health and education outcomes attained in relation to its potential, given the endowments / inputs made through health and educational allocations and infrastructure created. Until recently, the discourses on system performance centered on just outcomes/output achieved (such as enrolment rates and completion rates in the case of education and infant mortality rates and expectancy of life or a combined index in the form of Human Development Index) without really bothering about various inputs used and structures created and their efficient use. Taking these analytical gaps into consideration, World Bank (1999) and WHO (2000) made early attempts to measure health system efficiency and performance. In education, applications of DEA to measure the efficiency of educational production have extensively been reported in literature, beginning with the introductory paper of DEA (Charnes et al., 1978), which introduced the DEA methodology by demonstrating it in a school setting2. The basic point of such estimates – whether in health or in education systems – were that DMUs differ in outcomes in spite of using similar inputs due to their differential performance, of which efficiency levels are an important factor.

This paper is an attempt to measure the relative “efficiency” of public education systems to improve educational outcomes. It looks at the efficiency with which the Indian administrative Decision Making Units (DMU) – whether it is states or districts or sub-districts - translate educational inputs to desired education outcomes, and in the process, the factors that facilitated the efficiency with which the process happened. Such as analysis (that examines the outcomes attained in the context of the level of investments

1 An education system could be defined as all those organizations, organizations and services that are channeled to the improvement of education level of the people of the society, and a health system is the same that is aimed at providing health services to the people of the country. 2 See Annex 1 for a brief review of the literature related to efficiency estimations in education related sectors. DEA was originated from Farrell (1957) seminal work and was popularized by Charnes, Cooper and Rhodes (1978),

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(in physical and human infrastructure and other inputs) and the process of attaining the outcomes (the efficiency of the system)), should aid the DMUs to plan appropriate investment strategies to achieve (a) higher levels of overall outcomes without increasing its resource inputs if possible; or (b) if that is not possible, to address the question of the adequacy of the resources in the sector; and (c) to identify exogenous determinants of its efficiency and work upon that. In the context of evidence – based, decentralized micro planning, there is more and more recognition for the fact that the differences in efficiency (which is also an outcome of the capacity) are related to the differences in the way the education infrastructure and facilities are provided and managed.

The paper is organized into the following sections. In the next section, a description about the education sector policy is provided followed by a description about the current scenario in the country, especially highlighting the inputs and outputs. In section 2, the concept of education sector performance and efficiency is discussed. The section also describes the methodology for arriving at indicators related to education sector performance / efficiency. In this section, models for analysis are specified and discussed. A brief description of data and sources are given along with this section. In the fourth section, the results on the efficiency estimates, followed by a discussion on the determinants of efficiency are provided. In the fifth and final section, the insights from the exercise are discussed, and the conclusions are made.

Section 1. Country and Sector Scenario: A brief note on India’s elementary education sector development In large federal structures like that of India, how (efficiently and effectively) these services are delivered depends on who provides them. Both education and health care are subjects in the concurrent list of the Indian Constitution and hence both Union and state governments have a claim on the provision of these services. However, traditionally, the major responsibility of providing social services such as health and education lied primarily with the state governments. Sadly, different states started off at different levels of provision and outcomes, and expanded with different degrees of intensity and efficiency, reflecting the differential capacities, willingness and resulting financial inputs. This has resulted in vertical and horizontal imbalances in inputs and outputs/outcomes in these sectors. Thus, there were divergence in the performances of states in health and education service delivery and outcomes.

Traditionally states like Kerala and Himachal Pradesh have been ahead of other states in terms of the percentage of children attending schools, and more significantly, attending age-appropriate grades and finally, completing the stages expected of their age. On the other hand, states like Bihar and Uttar Pradesh have been traditionally laggards. The proportion of over-age children and under-age children attending grades have also been high in laggard states. Naturally, grade- to- grade promotion rates as well as stage to stage transition rates have been low in laggard states while they have been high in better off states.

Till 1980s, the major discourse in elementary education in the country was centered on how to expand access and schooling facilities, especially in rural areas. In 1990s, the discussion moved mainly to issues related to universal enrolment and retention. The issues related to quality and learning outcomes and completing elementary education

cycle has got the attention of late. The investment policies of the Central and state governments are often guided by these concerns and priorities.

In 1990s, the fiscal crisis hit the economy which led to a series of economic reforms, important among which were steps initiated to reduce the fiscal deficit and contain growth in public expenditure, especially in social sectors. This affected the states’ ability to allocate more resources to education and health sectors. The National Education Policies envisage that the states spend at least 6 percent of the state domestic product (SDP) on education sector. However, such a stipulation has turned out to be useless given the differential levels of SDPs of different states and the growth in that. For example, Bihar spends around 6 percent of the SDP on education and the overall SDP of Bihar has been growing at a stagnant rate. In contrast, Punjab, with one of the highest levels of SDP, which has grown many folds over the last few decades, spends less than 3 percent on education, but Punjab’s per child expenditure is many times more than that of Bihar. There are various aspects that decide the expenditure levels of education. While some of the states have resorted to cost-effective alternatives to teacher appointments (teacher salaries accounts for the largest share of non-plan expenditure, which accounts for more than 90 percent of the total revenue expenditures on education), while many other states continued with regular teachers. At the same time, the vertical gaps between the centre and states in terms of revenue generating capacities were also increasing.

Thus, these horizontal and vertical gaps in the abilities of financing among different states and between Centre and States had led to a rethinking on the strategies of making more funds available to the states, especially for providing in the social sectors. There was also an increased recognition of the need to transfer substantial volume of funds from Central government to state governments due to the differential revenue-generating capacity of Indian states and the varying backlog of educational needs among states. Thus, various Centrally Sponsored Schemes (CSS) were brought in with the purpose of helping the states with additional funds.

However, in its early incarnations, various CSS in education sector did not add much value in the sense that many state governments started substituting the CSS for their own allocations for plan expenditure in the sector. In mid-1990s, District Primary Education Program (DPEP) was started in selected districts wherein the project was expected to create access and infrastructure and provide quality inputs in addition to the existing expenditure in the sector. The Sarva Shiksha Abhiyan (SS), India’s flagship elementary education program that started in 2001 was an extension of the DPEP that was implemented in primary sector in half of the districts to the entire elementary cycle of eight years with all 600 districts in the country covered. Both these programs have been helping the Indian states to increase the access, infrastructure and human capital in the sector.

However, the efforts have not been uniform across states, and the input differentials still continue. For example, in Bihar, the student classroom ratio (SCR) was 84 in 2004 while in Himachal Pradesh, this was merely 18. One may argue that this may be the result of the way population is dispersed. However, it is any way expected that certain minimum facilities should be made available to students following certain desirable norms. This type of differences in inputs could also result in differential outcomes. For example, while Himachal Pradesh has hardly half a percent of the children in the age group of 6-14

years out of school while in Bihar, such low inputs have resulted in having at least 10 percent of the corresponding age group children not enrolled in school.

For the given inputs, the outcomes of Bihar might look “more efficient” than that of Himachal Pradesh, especially since they are catering to the children who any way would have accessed the education system, how much ever low the quality of inputs, while in Himachal Pradesh, additional efforts have already been taken place to reach the “most difficult to reach” category of people. Hence, this analysis of efficiency should be careful enough to distinguish between “efficient systems” that achieved or nearing the goals of better outcomes from those “efficient systems” which happens to be efficient only because of their low inputs, and hence in no way are at the desirable levels of outcomes.

Section 2. Concept and Methodology

The Concept The efficiency analysis of education sector here takes a conceptual framework that is most commonly used for production function of firms. Here, the educational institution (as variously defined) is seen as analogous to a firm transforming inputs into outputs through a production process. To do such review of the functioning of public sector provision, three main criteria of performance should be examined: efficiency, efficacy and equity. For the Central and state governments, there are several questions that they would like to seek answers to using these three criteria.

- How could one find out whether the states/ districts / sub-districts are performing efficiently? Is there any scope for these DMUs to improve outcomes without increasing inputs by being efficient? What are the resource gaps even if operating on the efficiency frontier in terms of the outcomes achieved and the goals?

- What are the exogenous factors that affect the performances of the DMUs in terms of educational attainment in the most efficient way? Which are the factors that could be altered during the immediate time period or medium term and what are the factors that need long gestation period?

Efficiency: Efficiency basically involves “more outputs for less inputs” – investigates the possible resource savings for given outputs or more outputs for the same inputs. An efficient education system is the one that achieves maximum outputs for its given inputs or the one that achieves its goals with the least cost. Farell (1957)’suggested that the efficiency of a DMU consists of two components: (a) technical efficiency and (b) allocative efficiency. His definition of technical efficiency, i.e., the ability to produce the maximum possible output from a given set of inputs, is similar to what one would like to define education sector performance. This is because both tend to measure the relationship between observed output and the maximum attainable output for the observed inputs, i.e., what the system achieves, compared to its potential. Within the context of education, technical efficiency may then refer to the physical relationship between the resources used (say, capital, labor and equipment) and some education outcome (Worthington, 2001).

On the other hand, the allocation efficiency is a measure which reflects the ability of a DMU to use the inputs in optimal proportions, given their respective prices. Total

economic efficiency is a combined measure of technical and allocative efficiencies. In this paper, the focus is only on the measurement of technical efficiency and not on the allocative or economic efficiencies.

Efficacy analysis involves measuring the distance between the actual/observed outputs and ideal/desirable outputs or goals. Equity criterion looks at the fairness in the distribution of outputs/outcomes of the allocation of resources (using primarily the Gini measure of inequality). Given the resource constraints, for a government who wants to act on the welfare goals to produce social services, the concern is, more than saving resources, to produce maximum outcomes or improve performance, or allocate more resources. The provision of public/ merit goods by government involves using the productive potentials of physical and human resources optimally (efficiently, effectively and equitably) to achieve maximum/ better outputs. The challenge for the education sector reforms in the country is to find a way to measure comparative education sector performance of different states/ districts/ sub-districts so as to facilitate identifying the comparatively better performer.

Methodology In the past, a stream of international research that compared performance of public sector and education sector in detail have already suggested the existence of inefficiencies in producing the desired outcomes3. At the same time, another track of research in education performance included the analysis of the determinants of schooling quality /performance using linear model techniques, including resource allocations or the inputs, as well as other determining factors of outcomes. Some of these studies showed positive correlations between the level of resources allocated for schools (translating into various school inputs, including PTRs) and student performances4, while some other studies find little or no correlation between the two5. However, some of these studies found the positive influence of variables not related to school inputs and exogenous to the schooling systems, such as the parental education levels.

In this paper, the attempt is to bring in the levels of performance and the determinants of performance by estimating a semi-parametric model of the education production process using a two-stage approach. In a first stage, the output efficiency score for each DMU is estimated using the mathematical programming approach known as DEA, relating education inputs to outputs. The methodology of DEA is a mathematical programming technique used to evaluate the relative efficiency of DMUs, derived from analyzing empirical observations obtained from DMUs. Relative homogeneity of organizational units such as states, districts, sub-district units provide instances for implementation of the DEA methodology. In a more general manner, DEA is most useful in cases multiple outputs are produced through the transformation of multiple inputs, and the input-output transformation relationships are not known (Charnes et al., 1978).

3 See for example, studies by Afonso, Schuknecht and Tanzi (2005) for public expenditure in the OECD, St. Aubyn (2003) for education spending in the OECD and Gupta and Verhoeven (2001) for health and education in Africa. 4 see Barro and Lee, 2001 5 Hanushek and Kimko (2000) and Hanushek and Luque (2003)

In a second stage, these efficiency scores are explained using regression analysis. Here, the factors that could affect the efficient production of educational outcomes – such as the role of parental education, density of population and hence the economies of scale of operation etc – mainly the exogenous and environmental variables are explained. These are, however, of a fundamentally different nature from input variables, in so far as their values cannot be changed in a meaningful spell of time by the DMU (Afonso and Aubyn, 2002) The frontier in the DEA approach is constructed using linear programming methods, the term “envelopment” stemming from the fact that the production frontier envelops the set of observations. (Afonso and Aubyn, 2002). DEA assumes the existence of a convex production frontier. The advantage of DEA is that given its non-parametric basis, it allows substantial freedom to specify inputs and outputs, the formulation of the production correspondence relating inputs to outputs, and so on. This is seen as especially useful in education production function where the usual axioms of production activity breakdown (i.e., profit maximization). The programming approach may then offer useful insights into the efficiency of these types of services (some assumptions regarding the production technology are still made regardless, such as that relating to convexity). Simulation studies (see, for instance, Banker et al., 1988) have indicated that the piecewise linear production frontier formulated by DEA is generally more flexible in approximating the true production frontier than even the most flexible parametric function form (Worthington, 2001).

Another positive feature of DEA is that it allows the calculation of technical efficiency measures that can be either input or output oriented. Input oriented technical efficiency measure ask question as to “how much can input quantities be proportionately reduced without changing output quantities produced?” Output oriented technical efficiency measure asks the question as to “how much can the output quantities be proportionately increased without altering input quantities used?”. The two measures provide the same results under constant returns to scale but give different values under variable returns to scale. Nevertheless, both output and input-oriented models will identify the same set of efficient/inefficient producers or DMUs. Following the analytical methodology used by Afonso and Aubyn (2005) for their pioneer study on the cross country efficiency of secondary education provision in 25 OECD countries, the methodology used in the current effort is described below. Consider p inputs and q outputs for n DMUs (States). yi is the column vector of the outputs and xi is the column vector of the inputs for the i-th State. The (p×n) input matrix is defined as X and (q×n) output matrix is represented by Y. The linear programming model then assumes that for a given State (the DMU) maximize efficiency:

Max λ, δi δi Subject to δiyi≤ Yλ xi≥ Xλ

n1’ =1

λ≥ 0………………….. (1)

In problem (1), δi is a scalar satisfying 1 ≥ δ i. It is the efficiency score that measures technical efficiency of the i-th unit as the distance to the efficiency frontier, the latter being defined as a linear combination of best practice observations. With 1 > δ i, the decision unit is inside the frontier (i.e. it is inefficient), while 1 =δi implies that the decision unit is on the frontier (i.e. it is efficient). The vector λ is a (n×1) vector of constants, which measures the weights used to compute the location of an inefficient DMU if it were to become efficient. The inefficient DMU would be projected on the production frontier as a linear combination of its peers using those weights. The peers are other DMUs that are more efficient and therefore used as references. n is a n-dimensional vector of ones. The restriction 1 ' 1 = λ n imposes convexity of the frontier, accounting for variable returns to scale. Dropping this restriction would amount to admit that returns to scale were constant. The problem (1) has to be solved for each of the n DMUs in order to obtain n efficiency scores (Afonso and Aubyn, 2005).

Non-discretionary inputs and the DEA/Tobit two-steps procedure

In the efficiency analysis using DEA (as described above) include only those variables that are direct inputs into the system and is provided by the DMU (state’s education departments). However, social sector outcomes do not only depend on the provision or inputs. There are various other factors that come in the way of the attainment of outcomes. Especially in a country as heterogeneous as India, the household and individual factors, especially those relating to the variances in social, economic, cultural and political aspects do have some influence on the social sector outcomes. These are nondiscretionary inputs and not really within the control of the concerned departments’ activities.

Since the analysis of efficiency and non-efficiency using DEA methods do not take into account these influences, usually two –stage models are suggested and used in the literature to deal with such situations.

Let zi be a (1× r) vector of non-discretionary outputs. In a typical two-stage approach, the following regression is estimated: ^ δ i = zi β +εi , ……………(2) where δˆi is the efficiency score that resulted from stage one, i.e. from solving (1). β is a (r×1) vector of parameters to be estimated in step two associated with each considered non-discretionary input. The fact that 1 ≥ δˆi has led many researchers to estimate (2) using censored regression techniques (Tobit), although others have used OLS (Afonso and Aubyn, 2005).

Figure 1 illustrates the basic idea behind a two-stage approach. In a simplified one output and one input DEA problem, A, B and C are found to be efficient, while D is an inefficient DMU. The output score for unit D equals (d1+d2)/d1, and is higher than one. However, unit D inefficiency may be partly ascribed to a “harsh environment” – a

number of perturbing environmental factors may imply that unit D produces less than the theoretical maximum, even if discretionary inputs are efficiently used. In our example, and if the environment for unit D was more favourable (e. g. similar to the sample average), then we would have observed Dc. In other words, unit D would have produced more and would be nearer the production possibility. The environment corrected output score would be (d1c+d2c)/d1c, lower than (d1+d2)/d1, and closer to unity.

Source: (Afonso and Aubyn, 2005). Estimation of Efficiency using various input-output models: Empirical Analysis

Models used to estimate the efficiency are described below.

Model 1: Panel data, DEA and Malmquist Index In this model, using panel data for two time periods of mid 1990s and 2004-05, it was attempted to measure productivity change using DEA program and the Malmquist Total Factor Productivity (TFP) Index. Following Farel et al (1994) specifications as outlined in Coelli T.J (1996), an output –based Malmquist productivity change index was estimated:

mo (yt+1, xt+1,yt, xt) = [(dto (xt+1, yt+1)/dt

o (xt,yt))*(dt+1o (xt+1, yt+1) / dt+1

o (xt,yt))]1/2

This represents the productivity of production point (xt+1, yt+1), relative to the production point (xt, yt). A value greater than one indicates positive TFP growth from period t to t+1. This index is in fact the geometric mean of two output based Malmquist TFP indices.

The two points of time used in this model are the mid-1990s and 2004-05. First period marks the major change in terms of policies in financing education sector in India, as the

DPEP programs were started. The inputs are taken from the Sixth All India Education Survey (for 1993) and Seventh All India Education Survey (for the year 2002) while the output indicators are from the NSS rounds (52nd round of 1995-96 and 61st round of 2004-05). There is a lag of 2 years between the input indicators used and the outcome indicators considered. This was considered appropriate given the fact that in social sectors, time lag in transforming inputs to outcomes is inevitable. The inputs taken into consideration were the (a) percentage of habitations that have access to primary schools within the prescribed norms, (b) percentage of habitations that have access to upper primary schools within the prescribed norms; (c) Teachers available per students at primary level and (d) teachers available per students at the upper primary level.

Model 2: DEA using VRS In this model, the standard technical efficiency estimation of DMUs (here the States) for a particular period of time using output oriented, with VRS model is considered. The inputs and outputs used in this model are same as the previous model, except that only the latest period is taken into consideration here.

Model 3. Modifying Model 2 with learning achievement indicators This model again is the same as model 2, and major modification is that the outcomes include learning scores also, taken from the Annual Status of Education Report (2006) of PRATHAM, for the year 2006. This again confirms with our assumptions about lags involved, in this case, from attendance to learning outcomes.

Model 4 & 5. Modifications of the models 2 and 3 by converting inputs and outputs into indices In these two models, basically the modifications are merely in terms of converting the multiple input and output indicators into single input and output indices. One important aspect to note here is that there is a difference in using the indicators as such and that of cumulated indices. While indicators are not relative measures, indices are, and hence the relative inputs and output indices show the relative provisions and their relative productivity indices.

Model 6. Output Oriented Technical Efficiency Estimation for 19 major states using data from District Information System for Education (DISE) In this model, the input and output indicators are used from the school based data system, DISE. Here again, the input and output indicators used are summarized into input index and output index and used. The data is taken from the Education Development Index used by Jhingran and Sankar (2006) for their paper on the Education Development Index. Here, the input index has got three sub-dimensions: (a) Access index which is a cumulative index of access to schools and availability of schools and the proportionate ratio of primary and upper primary schools; (b) Infrastructure Index using indicators related to school facilities such as classroom availability, drinking water facilities in schools, toilet facilities in schools etc; (c) Teacher Index, mainly reflecting teacher availability. The Output index also has three sub-dimensions: (a) outcome index using enrolment and completion rates; (b) equity index using gender parity measures; and (c) Learning outcomes using the ASER (2006) learning levels index. All the model specifications are given in table below.

Table 1

Models Model 1 Model 2 Model 3 Model 4 Model 5 Model 6

Model CRS and VRS CRS and VRS CRS and VRS CRS and VRS CRS and VRS CRS and VRS

Orientation Output oriented Output oriented Output oriented Output oriented Output oriented Output oriented

No of states 29 states 29 States 27 States 29 states 27 states 19 states No. of time

periodds 2 1 1 1 1 1

Periods referring to:

(a) 1993 for inputs; 1995-96 for outputs; (b) 2002 for inputs ; 2004-05 for outputs

2002 (for inputs) 2004-05 (outputs)

2002 (for inputs) 2004-05 (outputs)

2002 (for inputs) 2004-05 (outputs)

2002 (for inputs) 2004-05 (outputs) 2004-05

Source of data AIES for inputs

NSS 52nd & 61st rounds for outputs

7th All India Education Survey for inputs

NSS 61st rounds for outputs

7th AIES for inputs NSS 61st rounds and

ASER survey for outputs

7th AIES for inputs NSS 61st rounds for

outputs

7th AIES for inputs NSS 61st rounds & ASER for outputs

District Information System for

Education (DISE) No of inputs 4 4 4 1 1 3 No of outputs 4 4 5 1 1 3

Input variables

1. 1.% of habitations with access to primary within 1Km distance

2. % of habitations with access to upper primary within 3km distance

3. Teacher Pupil ratio- primary

4. Teacher Pupil Ratio - UP

1. 1.% of habitations with access to primary within 1Km distance

2. % of habitations with access to upper primary within 3km distance

3. Teacher Pupil ratio- primary

4. Teacher Pupil Ratio - UP

1. % of habitations with access to primary within 1Km distance

2. % of habitations with access to upper primary within 3km distance

3. Teacher Pupil ratio- primary

4. Teacher Pupil Ratio –Upper Primary

Input index using the variables of (a) Access to primary schools; (b) access to upper primary schools; (c) TPR at primary; and (d) TPR at upper primary

Input index using the variables of (a) Access to primary schools; (b) access to upper primary schools; (c) TPR at primary; (d) TPR at upper primary; and

(a) Access Index (b) Infrastructure Index © Teacher Index

Output/ Outcome variables

1. Enrolment Rates in primary 2. Enrolment Rates in Upper

Primary 3. Completion Rates in

primary 4. Completion Rates in Upper

Primary

1. Enrolment Rates in primary

2. Enrolment Rates in Upper Primary

3. Completion Rates in primary

4. Completion Rates in Upper Primary

1. Enrolment Rates in primary

2. Enrolment Rates in Upper Primary

3. Completion Rates in primary

4. Completion Rates in Upper Primary

5. Learning levels

Output index using the variables of (a) enrolment at primary; (b) enrolment at Upper Primary; (c) Completion of primary ; and (d) Completion of upper primary

Output index using the variables of (a) enrolment at primary; (b) enrolment at Upper Primary; (c) Completion of primary ; and (d) Completion of upper primary; (e) Learning levels of children

(a) Outcome Index (b)Equity Index (c) Learning

outcome index

Treatment of Slacks Malmquist DEA Multi-stage DEA Multi-stage DEA Multi-stage DEA Multi-stage DEA Multi-stage DEA

Estimations using Model 1 The aim of the analysis here is to measure the productivity change (efficiency change) and decompose the change into technical efficiency change and technological change. The summary statistics for the data used is given in the table below. Table 2: Model 1: Summary Statistics for the data for two years used in the analysis for 29 states

Indicators Year Mean SD Maximum Minimum 1995-96 79.99 13.05 100.00 49.98 Primary -

Enrolment rates 2004-05 91.64 6.98 100.00 68.71 1995-96 64.51 17.69 95.95 19.40 Primary

Completion rates 2004-05 77.05 13.77 98.01 49.72 1995-96 78.31 11.62 95.82 56.75 Upper primary

Enrolment 2004-05 88.31 7.48 99.30 74.48 1995-96 41.61 14.97 75.13 4.39 Upper Primary

Completion rates 2004-05 61.56 15.89 94.78 25.82 1993 82.88 11.02 98.62 47.05 Primary Access

2002 85.54 9.42 100.00 51.62 1993 75.52 14.82 100.00 28.35 Upper primary

access 2002 78.01 13.82 100.00 31.17 1993 3.68 2.60 15.00 1.09 TPR - Primary

2002 3.62 1.64 8.33 1.20 1993 4.18 2.47 14.29 1.24 TPR - Upper

Primary 2002 4.23 1.81 9.09 1.37 The results of the estimations are given below. The analysis shows that in most of the states, the total factor productivity change from mid – 1990s to 2004-05 have been positive, while in some other states like Arunachal Pradesh, Delhi, Haryana, Himachal Pradesh, Meghalaya and Sikkim, the productivity change have been negative. Basically this denotes that where the TFP change have been positive, the efficiency of the states improved while in states with TFP change is less than 1, the efficiency deteriorated. But improvements in state specific efficiencies do not mean that the states reached the efficient most position. States like Chattisgarh, Goa, and Karnataka registered improved efficiency changes during the decade, but they were still below the efficiency envelopment. In these states, for the given inputs (access to schooling facilities and teacher facilities), the states could still improve their outcomes with respect to enrolments and completion rates. In other states, if their outcomes are poor, the only way to improve them is by investing more since these states have no scope for improvement in outcomes given the current level of inputs. The issue is specifically serious in states like Arunachal Pradesh, Bihar, Jharkhand, MP, Rajasthan, UP and to a large extent, West Bengal and to some extent in some North – Eastern States like Meghalaya, Manipur and Tripura where the levels of outcomes are extremely poor and still poses no scope for improvement using the current level of inputs (resulting from the assets already created in the education sector and the current level of flow of funds into the sector). See table below.

Table 3: Panel Data DEA results for Education Production efficiency Year 1 Year 2 MALMQUIST INDEX SUMMARY OF FIRM MEANS

Technical Efficiency

change (CRS)

Technological

change

Pure technical efficiency

change (VRS)

Scale Efficien

cy change

Total Factor productivity

change

vrs te vrs te effch techch pech sech tfpch 1 AP 0.939 0.962 0.981 1.156 1.024 0.958 1.134 2 Arunachal 1.000 1.000 1.000 0.898 1.000 1.000 0.898 3 Assam 0.928 0.928 0.983 1.076 1.000 0.984 1.058 4 Bihar 1.000 1.000 1.000 1.161 1.000 1.000 1.161 5 Chhattisgarh 1.000 0.975 0.987 1.156 0.975 1.012 1.141 6 Delhi 1.000 1.000 0.950 1.010 1.000 0.950 0.960 7 Goa 1.000 0.978 1.069 1.029 0.978 1.093 1.101 8 Gujarat 0.811 0.925 1.331 1.136 1.141 1.167 1.512 9 Haryana 1.000 0.975 0.954 0.927 0.975 0.979 0.884 10 HP 1.000 1.000 0.988 0.997 1.000 0.988 0.985 11 J&K 0.839 0.943 1.150 1.061 1.125 1.022 1.220 12 Jharkhand 1.000 1.000 1.000 1.165 1.000 1.000 1.165 13 Karnataka 0.978 0.961 0.973 1.206 0.983 0.990 1.173 14 Kerala 1.000 1.000 1.000 1.199 1.000 1.000 1.199 15 MP 0.789 0.871 1.088 1.057 1.104 0.985 1.149 16 Maharashtra 1.000 1.000 1.000 1.208 1.000 1.000 1.208 17 Manipur 0.938 1.000 1.365 0.968 1.066 1.280 1.321 18 Meghalaya 1.000 0.971 0.817 1.009 0.971 0.841 0.824 19 Mizoram 0.940 1.000 1.188 1.038 1.064 1.116 1.233 20 Nagaland 0.977 1.000 1.407 0.940 1.024 1.374 1.322 21 Orissa 0.901 0.971 1.077 1.193 1.078 0.999 1.285 22 Punjab 0.974 0.967 0.943 1.126 0.993 0.949 1.062 23 Rajasthan 0.761 0.947 1.243 1.027 1.244 0.999 1.277 24 Sikkim 0.963 0.984 1.025 0.975 1.022 1.003 0.999 25 TN 1.000 1.000 1.000 1.286 1.000 1.000 1.286 26 Tripura 0.872 0.973 1.183 0.954 1.116 1.060 1.128 27 UP 1.000 1.000 1.109 1.047 1.000 1.109 1.161 28 Uttaranchal 0.865 0.934 1.058 0.980 1.081 0.979 1.038 29 West Bengal 0.937 1.000 1.106 1.146 1.067 1.036 1.267 Mean 0.945 0.975 1.060 1.069 1.034 1.026 1.133

Explaining efficiency from Model 1 To explain differential efficiency, the variables used in this particular model were: (a) literacy rates of the state; (b) density of population; (c) Road length per square kilometer; (d) percentage of population below poverty line; (e) percentage of urban population. The correlation matrix of these variables is given below. The high t-statistics for the constant term indicates that a large part of the inefficiency cannot be explained by the variables used in the regression. One of the reasons for the inability to explain the inefficiencies could be the fact that various DMUs – whether with low outputs or high outputs are found to be efficient. This camouflages the influence of various environmental factors

(some of them as specified in this) on the outcome levels itself. The regression analysis shows that of these variables used, the important variable that explained the efficient production of educational outcomes of the states in India was the density of population and literacy rates. More the density of population, more the concentration of child population and hence the economies of scale in terms of provision of inputs results. This in turn, makes the states with high density of population more efficient. While density of population is highly correlated with geographical features and population growth, it is beyond the control of the states’ education ministries. On the other hand, literacy rate is also important. The role of literacy in educational outcomes is historically established and this variable is something that the state could try to change through concentrated efforts in the medium term period.

Table 4: Correlation matrix of variables used in second stage regressions for PANEL DATA vrste % urban

population % Literacy rate

Density of population

Road length per sq.km

% Pop BPL

Per capita SDP

Vrste 1.0000

% urban population 0.0179 1.0000

% Literacy rate 0.2617 0.3933 1.0000

Density of population 0.2674 0.0790 -0.0294 1.0000

Road length per sq.km 0.2019 0.1679 0.3776 0.5651 1.0000

% Pop BPL -0.0879 -0.5669 -0.4298 -0.1323 -0.2277 1.0000

Per capita SDP 0.2371 0.6180 0.4545 0.0275 0.3015 -0.7077 1.0000

Table 5: Tobit estimations for explaining efficiency Estimation model 1 Estimation model 1 Coef T stat Coef T stat

Literacy rate .0022466 2.28* .0017194 1.63 % of urban population -.0001921 -0.14 Density of population .0001564 2.71** .0001468 2.13**

Road Length -.0025291 -0.11 % of pop. BPL .0016513 1.44 Per Capita SDP -3.99e-07 -0.13 Dummy _ year 2 .0456531 1.83* .025636 1.09

Constant .7274942 7.86*** .8218124 12.56*** _se .071746 .0742089

No of observations 58 58 Log likelihood 24.621966 22.96332

LR chi2(6) 14.59* 11.28* * indicates significance at 90% confidence interval; ** indicates significance at 95% confidence interval and *** indicates at 99%

Estimations using Models 2 & 3 While the panel data DEA estimation of efficiency using Malmquist index and TFP changes is useful to measure the changes in efficiency, for any current day policy it is important to understand the situation for the present day. The role of one time -period estimation emerges from this. While some people look at the outputs in terms of enrolments and completion only, while others see the merits of the education systems through the learning achievement levels of the children. While model 2 estimates efficiency using only enrolments and completion rates outcomes, model 3 also includes the learning achievement levels. Hence, the comparative results are given here together.

Table 6: Summary Statistics for the data used in the analysis for states

Model 2 No of states: 29

Model 3 No of states: 27

Mean SD Maxm Min Mean SD Max Min Primary –

Enrolment Rates 91.10 7.20 98.98 68.71 90.76 7.34 98.97 68.71

Upper Primary – Enrolment Rates 86.91 7.18 98.26 74.48 86.35 7.13 98.25 74.47

Primary Completion rates 74.35 13.57 98.01 49.72 74.73 13.65 98.00 49.71

Upper primary completion rates 58.62 15.46 94.78 25.82 59.58 14.59 0.94 39.46

Language learning achievement score 75.54 10.31 92.00 54.75

Out

puts

Maths learning achievement score 70.63 12.33 89.75 45.25

Primary Access 85.42 9.22 100.00 51.62 85.16 9.00 94.58 51.61 Upper Primary

Access 76.34 13.07 100.00 31.17 75.46 12.71 95.52 31.16

Teacher Pupil Ratio-primary 3.59 1.70 8.33 1.20 3.46 1.47 8.33 1.20

Inpu

ts

Teacher Pupil Ratio Upper

primary 4.31 1.94 9.09 1.37 4.24 1.95 9.09 1.37

The results of the efficiency estimations using model 2 and model 3 is presented in the table below. Clearly, one of the important points that comes out from this comparative analysis of two models – one using only the basic outputs while the other including higher level outcomes indicators also among the outputs – is that the specification of the model and the indicators used becomes an important parameters in deciding the efficiency levels. A state like AP which was not among the efficient most states while only the basic outputs were considered became one among the most efficient when the learning achievement indicators were included in the outcome measures. However, most other states have similar ranking under both models, hence the analysis and interpretation becomes easier. Here again, not all states at the frontier which are considered as efficient have higher outcomes as the efficiency scores are mere reflections about the scope for improvements given the inputs. These results need to be analyzed in the context of the output slacks and consequently, the output targets the states could have achieved if they

were as efficient as the most efficient states, especially peers. See table 8 for these results.

Table 7: EFFICIENCY ESTIMATION RESULTS States MODEL 2 MODEL 3

crste vrste scale Peers Rank crste vrste scale Peers Rank AP 0.917 0.962 0.953 drs TN 9 0.951 1.000 0.951 drs 1

Arunachal 1.000 1.000 1.000 1 1.000 1.000 1.000 1

Assam 0.908 0.928 0.979 drs Delhi, Kerala, TN 14 0.908 0.929 0.977 drs RJ, Kerala 13

Bihar 1.000 1.000 1.000 1 1.000 1.000 1.000 1

Chhattisgarh 0.971 0.975 0.996 drs Bengal,

Jharkhand, TN

5 0.982 0.987 0.995 drs Bengal,

Jharkhand, Arunachal,

3

Delhi 0.950 1.000 0.950 drs 1

Goa 0.866 0.978 0.886 drs TN 3 0.866 0.982 0.882 drs TN,

Mizoram, Kerala

4

Gujarat 0.876 0.925 0.947 drs TN 15 0.925 0.958 0.966 drs TN, MH, Bengal, Kerala

9

Haryana 0.954 0.975 0.979 drs Bengal, Bihar, Delhi 4 0.960 1.000 0.960 drs 1

HP 0.988 1.000 0.988 drs 1 0.988 1.000 0.988 drs 1

J& K 0.848 0.943 0.899 drs HP, TN, Kerala, 12 0.848 0.945 0.898 drs Manipur,

HP, Kerala, 11

Jharkhand 1.000 1.000 1.000 1 1.000 1.000 1.000 1

Karnataka 0.947 0.961 0.986 drs Kerala, TN 10 0.959 0.976 0.983 drs Kerala, Bengal, TN 8

Kerala 1.000 1.000 1.000 1 1.000 1.000 1.000 1

MP 0.846 0.871 0.972 drs Bengal,

Jharkhand, TN,i

16 0.967 0.994 0.972 drs Kerala,

Meghalaya, Bengal

2

Maharashtra 1.000 1.000 1.000 1 1.000 1.000 1.000 1

Manipur 0.891 1.000 0.891 drs Meghalaya 1 0.891 1.000 0.891 drs 1

Meghalaya 0.817 0.971 0.841 drs Arunachal, TN 7 0.903 1.000 0.903 drs 1

Mizoram 0.935 1.000 0.935 drs 1 0.935 1.000 0.935 drs 1

Nagaland 0.925 1.000 0.925 drs 1 0.925 1.000 0.925 drs 1

Orissa 0.963 0.971 0.991 irs Jharkhand, Kerala, TN 7 0.969 0.977 0.992 irs

Kerala, Jharkhand,

TN 7

Punjab 0.917 0.967 0.949 drs TN, Bengal, Delhi 8 0.923 0.981 0.942 drs Bengal,

Kerala, TN 5

Rajasthan 0.943 0.947 0.996 drs Jharkhand, Kerala, TN 11 0.943 0.947 0.996 drs Jharkhand,

Kerala, TN 10

Sikkim 0.845 0.984 0.859 drs HP,

Mizoram, Manipur,

2

Tamil Nadu 1.000 1.000 1.000 1 1.000 1.000 1.000 1

Tripura 0.926 0.973 0.952 drs Arunachal, Kerala, HP 6 0.926 0.978 0.947 drs Arunachal,

Kerala, HP 6

Uttar Pradesh 0.989 1.000 0.989 drs 1 0.989 1.000 0.989 drs 1

Uttaranchal 0.909 0.934 0.972 drs TN, Kerala 13 0.909 0.937 0.970 drs Kerala, Bengal, TN 12

West Bengal 1.000 1.000 1.000 1 1.000 1.000 1.000 1

Table 8: COMPARISON OF ACTUAL OUTPUTS TO EFFIECIENT OUTPUT TARGETS FOR STATES GIVEN THEIR INPUTS SUMMARY OF OUTPUT TARGETS ( If the state were at the efficient points):

SUMMARY OF ACTUAL OUTPUTS MODEL 2 MODEL 3

vrste %

Enrolment rates

% Completion rates

% Learning levels % Enrolment

rates

% Completion rates

% Enrolment rates

% Completion rates

% Learning levels

State M 2 M 3 Pry U.Pry Pry U.Pry Lang_ score

Math_ score Pry U.Pry Pry U.Pr

y Pry U.Pry Pry U.Pry Lang_scor

Math_ score

AP 0.962 1.000 95.2 79.3 81.9 62.9 73.40 75.40 99.0 93.7 95.5 81.1 95.20 79.30 81.90 62.90 73.40 75.40

Arunachal 1.000 1.000 75.8 84.5 56.3 40.6 67.15 69.40 75.8 84.5 56.4 40.6 75.80 84.40 56.30 40.60 67.15 69.40

Assam 0.928 0.929 91.6 89.7 75.6 56.5 67.80 63.85 98.7 96.7 96.4 89.3 98.90 96.50 97.00 89.50 77.81 71.33

Bihar 1.000 1.000 68.7 74.5 49.7 46.5 70.35 64.20 68.7 74.5 49.7 46.5 68.70 74.50 49.70 46.50 70.35 64.20

Chhattisgarh 0.975 0.987 88.2 79.8 74.2 50.0 69.05 58.65 90.5 85.9 76.8 61.8 89.30 84.90 75.20 57.30 69.95 62.51

Delhi 1.000 94.5 93.6 80.4 65.4 94.5 93.6 80.4 65.4

Goa 0.978 0.982 96.8 91.0 91.5 71.4 88.65 84.90 99.0 93.7 95.5 81.0 98.60 98.10 94.60 89.10 90.53 86.47

Gujarat 0.925 0.958 91.6 82.4 85.7 68.8 72.50 62.30 99.0 93.7 95.5 81.0 95.60 90.50 89.50 73.50 75.71 67.29

Haryana 0.975 1.000 89.9 87.4 78.4 56.6 78.90 71.95 92.2 89.7 80.4 66.4 89.90 87.40 78.40 56.70 78.90 71.95

HP 1.000 1.000 98.5 96.0 87.4 71.3 80.05 74.55 98.4 96.0 87.4 71.3 98.50 96.00 87.40 71.30 80.05 74.55

J&K 0.943 0.945 92.8 90.7 75.5 61.8 73.00 76.80 98.4 96.1 86.6 73.7 98.20 97.00 85.00 75.40 83.58 81.29

Jharkhand 1.000 1.000 80.3 77.6 54.6 43.1 70.35 64.50 80.3 77.6 54.6 43.1 80.30 77.60 54.60 43.10 70.35 64.50

Karnataka 0.961 0.976 95.1 84.8 88.8 71.7 67.25 54.70 99.0 93.7 95.5 81.2 97.50 93.00 92.90 78.80 68.93 61.09

Kerala 1.000 1.000 98.9 98.3 98.0 94.8 92.00 86.95 98.9 98.3 98.0 94.8 98.90 98.30 98.00 94.80 92.00 86.95

MP 0.871 0.994 84.7 80.2 69.6 47.6 83.40 81.80 97.2 92.1 91.2 75.5 93.20 88.50 81.10 62.80 88.85 82.27

Maharashtra 1.000 1.000 94.3 88.3 91.7 79.7 83.60 72.00 94.3 88.3 91.7 79.7 94.30 88.30 91.70 79.70 83.60 72.00

Manipur 1.000 1.000 97.0 96.4 60.2 51.6 74.80 81.80 97.0 96.4 60.2 51.6 97.00 96.40 60.20 51.60 74.80 81.80

Meghalaya 0.971 1.000 91.6 86.9 50.9 40.9 90.15 89.75 94.2 94.7 61.1 51.3 91.60 86.90 50.90 40.90 90.15 89.75

Mizoram 1.000 1.000 97.9 97.9 85.5 74.8 89.85 88.85 97.9 97.9 85.5 74.8 97.90 97.90 85.50 74.80 89.85 88.85

Nagaland 1.000 1.000 97.5 94.2 73.9 72.6 81.20 83.20 97.5 94.2 74.0 72.6 97.50 94.20 73.90 72.60 81.20 83.20

Orissa 0.971 0.977 87.9 75.8 76.9 62.2 70.25 60.75 91.4 87.6 79.2 67.1 91.10 87.40 78.70 65.80 71.89 64.95

Punjab 0.967 0.981 92.9 87.2 78.3 62.5 75.20 65.45 96.1 90.2 88.7 69.6 94.70 89.40 86.50 67.50 76.69 68.76

Rajasthan 0.947 0.947 84.1 76.9 63.1 43.9 58.70 55.40 88.9 86.2 74.1 64.4 88.90 86.20 74.10 64.40 73.60 67.45

Sikkim 0.984 96.7 95.3 57.8 25.8 98.3 96.8 85.6 74.7

TN 1.000 1.000 99.0 93.7 95.5 81.0 54.75 45.95 99.0 93.7 95.5 81.0 99.00 93.70 95.50 81.00 54.75 45.95

Tripura 0.973 0.978 94.7 90.6 64.8 39.5 84.40 76.80 97.4 96.5 90.9 81.1 96.90 96.50 91.40 83.20 86.33 81.72

UP 1.000 1.000 84.3 78.4 60.2 51.4 54.95 45.25 84.3 78.4 60.2 51.4 84.30 78.40 60.20 51.40 54.95 45.25

Uttaranchal 0.934 0.937 92.4 87.9 76.1 62.7 81.65 74.60 98.9 95.9 96.7 87.7 98.60 97.30 97.10 91.80 87.15 81.53

W.Bengal 1.000 1.000 89.1 81.3 73.3 42.3 86.25 77.50 89.1 81.3 73.3 42.3 89.10 81.30 73.30 42.30 86.25 77.50

The comparison of actual outputs already attained by the states and the project outputs- i.e, the outputs the states might have generated if they were operating at the efficient levels – shows the scope for improvement for the same inputs. For example, a state like Chhatisgarh, given their level of inputs, could have attained a age specific enrolment rate at primary of around 90 percent, an improvement of at least 2 percentage points from its current levels. Same is the case with other outcomes. Similar is the case with MP which could have also improved its outcomes by a few percentage points had it been utilizing inputs at the most efficient frontiers. On the other hand, a state like Bihar, for its given inputs is at the maximum attainable outcome levels. There is no scope for improvements given the current levels of inputs. Similarly, Kerala and HP are also at the efficient frontiers, but with much better outcome levels for all indicators. Clearly, these outcomes have been achieved by creating the appropriate measures of inputs and using them efficiently.

Once again, it comes out clearly that there are three ways to achieve the social sector goals: (a) If the outcome and efficiency levels are both poor, the state need to invest more in the sector as well as improve the efficiency of production; (b) if the outcomes are poor, but the state is operating at an optimal efficiency levels, then there is a need to invest much larger inputs and see how technological changes could be brought in; (c) if the outcomes are better and still states are inefficient, the states should see how they could raise the outcome levels further or divert resources within the sector to achieve other related outcomes (for example, if the state is at the best possible output levels in terms of enrolments and completion rates, quality may be an issue, or the learning levels may be an issue where they could focus their resources better. Or else, if the elementary sector outputs are all achieved and still there is some inefficiency in the use of resources, then the focus of expansion could be the secondary level inputs.)

States that are at different levels of outcomes and efficiency levels in both the models are given in table 9. Rajasthan is one state that comes out poorly in terms of both efficiency as well as outcomes. Contrast this with all other laggard states – like Bihar, Jharkhand and UP. These states, though at the bottom in terms of outcomes, turns out to be efficient in terms of using up the inputs to produce outcomes. At first, it might look as if Rajasthan is indeed doing badly in both measures. However, it is important to see why Rajasthan’s efficiency scores are so poor compared to UP and Bihar’s. This will come out in the second stage estimation of efficiency. One aspect could be that given the concentration of population in states like Bihar and UP, whatever is provided can have an economies of scale factor while in Rajasthan, given the dispersed population and area, the inputs in terms of access to schools are not sufficient enough to obtain the desired outcomes, nor efficiency of producing outcomes that are achieved by even laggards like Bihar and UP. On the other hand, Uttarakhand (formerly Uttaranchal) and Karnataka, even with better outcomes, turns out to be highly inefficient. In Uttarakhand, because of the hilly terrains, the efficiency factor may be affected, but in Karnataka, the inefficiency scores show the scope for further improving outcomes are not exploited fully. The fact that Karnataka’s peers are Kerala and TN also gives it a tough measurement of efficiency. Even Goa is in the ‘middle’ efficient category of states, and turns out to be inefficient in comparison to its peer state Tamil Nadu. States like Kerala and HP are efficient ones along with Bihar and Jharkhand, but in terms of outcomes, both categories of states are at two extreme ends.

Table 9: Models 2 and 3: Where do the states stand in terms of efficiency and outcomes?

Outcomes Low (q1) Low

Middle (q2) Middle High (q3)

High (q4)

Low (q1)

Rajasthan, Assam, Gujarat, MP (model 2),

J&K, Karnataka (model 2), Uttaranchal

Low-Middle (q2)

AP (model 2), Chhatisgarh, Haryana, Meghalaya, (model 2), Orissa, MP (model 3)

Punjab, Tripura, Karnataka (model 3)

Goa (model 3)

Middle High (q3)

Goa (model 2), Sikkim

Eff

icie

ncy

scor

es

High (q4)

Arunachal, Bihar, Jharkhand, UP

Meghalaya (model 3), Manipur (Model 3), West Bengal

AP (model 3) Delhi, Maharashtra, Manipur, Nagaland, TN (model 3)

HP, Kerala, Mizoram, TN (model 2)

Similar to the results of the tobit regressions carried out for model 1, for this model also, a tobit regression was carried out to see whether the efficiency level variations across states could be explained by any of the known environmental factors. The results yielded similar inferences as got from the previous model – a lot of the efficiency remains unexplained, while the economies of scale in operation in densely populated areas are coming out significantly.

Table 10: Tobit estimations for explaining efficiency Estimation model 1 Estimation model 1 Coef T stat Coef T stat Coef T stat

Literacy rate .0017741 1.44 .0015214 1.16 .0018371 1.06 % of urban population

-.0001135 -0.10

Density of population

.0000906 1.94* .0000824 1.76* .0001683 2.58

% of pop. BPL .0010229 1.18 Per Capita SDP -1.57e-06 -0.70 Teacher absence .0010465 0.65

Constant .8225101 9.23*** .8780028 11.17*** .7729171 5.49*** _se .0422351 .0742089

No of observations

29 29 20

Log likelihood 21.409921 20.649686 17.467118 LR chi2(6) 6.24 4.72 10.78**

Estimations using Model 4 and 5 Estimating efficiency for states with varying efficiency scores yielded mixed results. In the next stage, the previous two models (model 2 and model 3) were modified to represent single input and output by converting input and output variables into indices. The graph 1 below shows the input index-output index combinations for various states. As in the case of model 2 and 3, the difference between model 4 and 5 is basically the inclusion of learning outcomes in the output index in model 5 while model 4 do not take into account learning outcomes.

Graph for Model 4

AP

AR'CHL

ASAM

BHR

CHGARH

DELHI

GOA

GUJHAR

HP

JK

JHKND

KARNT

KERL

MP

MH

MNPR

MGHLYA

MZRM

NGLD

ORSA

PNJB

RJSTN

SKM

TN

TRPRA

UP

UK

BENGL

0.2

.4.6

.81

Out

put i

ndex

.2 .4 .6 .8Input Index

Input and Output Index for Education Efficiency estimation

Unlike the previous estimations, here the actual outcomes and actual inputs are not used. An index scales the states from the best to the worst. As a result, the where the state is in interms of the relative provision and relative outcomes achieved decides the efficiency of the states. The summary statistics is provided in table 11. Table 11. Summary Statistics for the data used in the analysis for 29 states

Model 4 Model 5 Mean SD Max Min Mean SD Max Min

Input Index 0.5176 0.1295 0.7874 0.1728 0.5890 0.12897 0.8316 0.2233 Output Index 0.5621 0.2197 0.9990 0.0749 0.5336 0.215682 0.9992 0.1091

Table 12 : EFFICIENCY ESTIMATES USING OUTPUT ORIENTED VRS ESTIMATION MODEL 4 MODEL 5

State crste vrste scale Peers Rank crste vrste scale Peers Rank

AP 0.556 0.571 0.972 drs Kerala 17 0.525 0.560 0.937 drs Kerala, TN 16

Arunachal 0.715 1.000 0.715 irs Arunachal 1 0.654 1.000 0.654 irs Arunachal 1

Assam 0.497 0.595 0.836 drs Kerala 15 0.582 0.608 0.957 drs Kerala, TN 11

Bihar 0.098 0.103 0.952 irs Kerala, Arunachal 28 0.134 0.138 0.972 drs TN,

Kerala 24

Chhattis’h 0.500 0.513 0.975 irs Kerala, Arunachal 19 0.506 0.516 0.982 drs Kerala,

TN 17

Delhi 0.566 0.717 0.790 drs Kerala 8 Goa 0.586 0.788 0.744 drs Kerala 6 0.665 0.796 0.836 drs Kerala 5

Gujarat 0.537 0.615 0.872 drs Kerala 11 0.548 0.587 0.934 drs TN, Kerala 12

Haryana 0.517 0.572 0.905 drs Kerala 16 0.546 0.583 0.936 drs TN, Kerala 13

HP 0.707 0.833 0.849 drs Kerala 4 0.836 0.881 0.949 drs TN, Kerala 2

J& K 0.536 0.634 0.846 drs Kerala 10 0.569 0.608 0.937 drs Kerala, TN 11

Jharkhand 0.392 0.448 0.875 irs Kerala, Arunachal 23 0.359 0.377 0.951 irs TN,

Arunachal 21

Karnataka 0.640 0.695 0.920 drs Kerala 9 0.665 0.697 0.953 drs Kerala, TN 7

Kerala 1.000 1.000 1.000 Kerala 1 0.930 1.000 0.930 drs Kerala 1

MP 0.369 0.374 0.988 drs Kerala 25 0.400 0.429 0.933 drs Kerala, TN 20

Maharashtra 0.798 0.802 0.994 irs Kerala, Arunachal 5 0.783 0.829 0.944 drs Kerala,

TN 4

Manipur 0.565 0.612 0.923 drs Kerala 13 0.585 0.620 0.944 drs TN, Kerala 9

Meghalaya 0.345 0.380 0.907 drs Kerala 24 0.431 0.462 0.932 drs Kerala, TN 19

Mizoram 0.581 0.852 0.682 drs Kerala 3 0.729 0.856 0.852 drs Kerala 3 Nagaland 0.462 0.741 0.623 drs Kerala 7 0.551 0.719 0.766 drs Kerala 6

Orissa 0.544 0.563 0.966 irs Kerala, Arunachal 18 0.553 0.561 0.986 drs TN,

Kerala 15

Punjab 0.488 0.615 0.795 drs Kerala 12 0.578 0.615 0.940 drs Kerala, TN 10

Rajasthan 0.335 0.344 0.974 irs Kerala, Arunachal 27 0.305 0.305 1.000 Kerala,

TN 23

Sikkim 0.335 0.492 0.680 drs Kerala 22

TN 0.981 0.997 0.984 irs Kerala, Arunachal 2 1.000 1.000 1.000 TN 1

Tripura 0.474 0.513 0.925 drs Kerala 20 0.546 0.578 0.944 drs Kerala, TN 14

UP 0.363 0.371 0.978 irs Kerala, Arunachal 26 0.342 0.351 0.975 irs TN,

Arunachal 22

Uttaranchal 0.524 0.608 0.862 drs Kerala 14 0.602 0.642 0.938 drs TN, Kerala 8

West Bengal 0.482 0.493 0.978 irs Kerala,

Arunachal 21 0.475 0.505 0.941 drs Kerala, TN 18

This type of efficiency estimation clearly throws out just one or two efficient points (states, here in the case of model 4 that did not include learning achievement levels, are Kerala and Arunachal; and in the case of model 5, Kerala and Tamil Nadu). These points then become the peers for all other states for comparison. In the case of model 4, it shows that given the access and teachers provided, most states which had the state of Kerala as the primary peer, could have been where Kerala is in terms of outcomes related to enrolment and completion rates had they been “efficient”. On the other hand, if the learning levels are also included in the outcome measures, the outcome targets achieved would have shown the inter-state disparities. However, states like Bihar turns out to be somewhat inefficient in these estimations. The revealing aspect of these indices – based efficiency estimates is that it shows that even the states like Bihar and UP shows scope for improvement, taken in relative terms.

Table 13: Summary of Output targets at the efficient levels MODEL 4 MODEL 5

State

Actual Output index

SUMMARY OF OUTPUT (Index)

TARGETS:

Actual Output index

SUMMARY OF OUTPUT

(Index)TARGETS AP 0.571 0.999 0.5340 0.954 Arunachal 0.252 0.252 0.2293 0.229 Assam 0.594 0.999 0.5180 0.852 Bihar 0.075 0.725 0.1091 0.79 Chhattisgarh 0.431 0.841 0.3899 0.756 Delhi 0.716 0.999 Goa 0.787 0.999 0.7949 0.999 Gujarat 0.615 0.999 0.5686 0.969 Haryana 0.571 0.999 0.5593 0.959 HP 0.832 0.999 0.7847 0.89 J&K 0.633 0.999 0.5809 0.956 Jharkhand 0.217 0.484 0.2204 0.584 Karnataka 0.695 0.999 0.6064 0.87 Kerala 0.999 0.999 0.9992 0.999 MP 0.374 0.999 0.4189 0.977 Maharashtra 0.769 0.959 0.7594 0.916 Manipur 0.612 0.999 0.5662 0.914 Meghalaya 0.380 0.999 0.4556 0.985 Mizoram 0.851 0.999 0.8549 0.999 Nagaland 0.741 0.999 0.7186 0.999 Orissa 0.445 0.791 0.4161 0.742 Punjab 0.614 0.999 0.5779 0.94 Rajasthan 0.287 0.834 0.2144 0.702 Sikkim 0.492 0.999 TN 0.889 0.891 0.7013 0.701 Tripura 0.512 0.999 0.5294 0.915 UP 0.317 0.855 0.2237 0.637 Uttaranchal 0.608 0.999 0.6075 0.947 West Bengal 0.422 0.856 0.4692 0.929

Further analysis using outcome – efficiency matrix for states (table 14) show that those states with low outcomes also have lower efficiency while the states with high outcomes also have higher efficiency. This result is somewhat contrary to what was coming out from the previous analysis using absolute units of inputs and outputs. Interestingly, in the case of some states, the inclusion of learning achievement levels in the outcome index has reduced their efficiency position. See for example the case of Uttarakhand or Chattisgarh and Orissa.

Table 14: Model 4 and 5: Where do the states stand in terms of efficiency and

outcomes? Outcomes

Low (q1) Low Middle (q2)

Middle High (q3)

High (q4)

Low (q1)

Bihar, Jharkhand, MP, Meghalaya, Rajasthan, UP, West Bengal

Sikkim,

Low-Middle (q2)

Chhatisgarh (model 5); Orissa (model 5)

AP, Assam, Chhatisgarh (model 4), Haryana, Orissa (model 4), Tripura,

Uttarakhand (model 4)

Middle High (q3)

Delhi, Gujarat, J&K, Karnataka, Manipur, Punjab, Uttarakhand (model 5)

Nagaland Eff

icie

ncy

scor

es

High (q4)

Arunachal, Goa, HP, Kerala, MH, Mizoram, TN,

Explaining efficiency in the case of models 4 and 5. The analysis of efficiency using the vrs te of models 4 and 5 shows that literacy rates in the states is the significant explanatory factor. If the factors that contribute to the differential literacy levels are traced, then the unpacking of the schools systems efficiency / inefficiencies could also be traced.

Table 15. Explaining Efficiency Coef T stat Coef T stat Coef T stat Coef T stat Literacy rate .0133349 4.21*

** .01166 2.96*** .01151 3.03*

** .02054 6.39***

Density of population

-.0001614 -1.26

Per capita SDP 6.40e-06

0.77

Schools with more than 2 teachers

.00319 0.92

% urban population

.000995 0.24

Constant -.2384288 -1.08 -.244570

-1.07 -.24881 -1.11 -.81068 -2.80**

R-sq 0.4374 0.4155 0.4215 0.7776

Estimations using Model 6 In this model, the DEA estimations were carried out for information emerging from DISE, but which were converted into various sub-dimensional indices for inputs and outputs. The results do not vary much, showing similar trends as those in model 4 and 5. See the summary statistics, DEA estimations, output targets at efficient productions and summary results in tables 16-19. Table 16. Model 6: Summary Statistics for the data used in the analysis for 19 states

Mean SD Maximum Minimum EQUITY INDEX 0.566 0.195 0.908 0.156 OUTCOME INDEX 0.538 0.274 0.995 0.014 LEARNING INDEX 0.504 0.259 1.000 0.010 ACESS INDEX 0.320 0.128 0.593 0.117 INFRASTRUCTURE INDEX 0.560 0.221 0.915 0.098 TEACHER INDEX 0.394 0.252 1.000 0.000

Table 17. Model 6

crste vrste scale Peers Rank AP 0.850 0.916 0.927 drs Kerala, West Bengal, TN 2

ASSAM 0.512 0.621 0.825 drs Kerala, TN, HP, MP 10 BIHAR 1.000 1.000 1.000 Bihar 1

CHHATTIS GARH 0.771 0.791 0.975 drs MP, Kerala, Jharkhand 8

GUJARAT 0.626 0.814 0.769 drs Mp, Bengal, Kerala, TN 6 HARYANA 1.000 1.000 1.000 HARYANA 1

HP 0.733 1.000 0.733 drs HP 1 JHARKHAND 1.000 1.000 1.000 JHARKHAND 1 KARNATAKA 0.847 0.905 0.936 drs Kerala, TN 4

KERALA 1.000 1.000 1.000 KERALA 1 MP 1.000 1.000 1.000 MP 1

MAHA RASHTRA 0.849 0.916 0.926 drs Kerala, TN, HP, MP 3

ORISSA 0.799 0.846 0.944 drs Kerala, TN, Jharkhand, MP 5 PUNJAB 1.000 1.000 1.000 PUNJAB 1

RAJASTHAN 0.685 0.774 0.885 drs TN, Kerala, UP 9 TAMIL NADU 1.000 1.000 1.000 TAMIL NADU 1

UP 1.000 1.000 1.000 UP 1 UTTAR

ANCHAL 0.629 0.813 0.774 drs Kerala 7

WEST BENGAL 1.000 1.000 1.000 WEST BENGAL 1

Table 18. Model 6

SUMMARY OF ACTUAL OUTPUTS SUMMARY OF OUTPUT TARGETS:

EQUITY INDEX

OUTCOME INDEX

LEARNING INDEX

EQUITY INDEX

OUTCOME INDEX

LEARNING INDEX

AP 0.16 0.70 0.60 0.776 0.764 0.655 ASSAM 0.50 0.28 0.41 0.805 0.876 0.660 BIHAR 0.24 0.01 0.44 0.240 0.010 0.440

CHHATTIS GARH 0.43 0.27 0.35 0.543 0.490 0.724

GUJARAT 0.65 0.56 0.45 0.799 0.853 0.553 HARYANA 0.60 0.54 0.64 0.600 0.540 0.640

HP 0.81 0.90 0.69 0.810 0.900 0.690 JHARKHAND 0.37 0.11 0.44 0.370 0.110 0.440 KARNATAKA 0.68 0.82 0.28 0.826 0.906 0.472

KERALA 0.91 0.99 1.00 0.910 0.990 1.000 MP 0.59 0.61 0.82 0.590 0.610 0.820

MAHA RASHTRA 0.73 0.69 0.70 0.797 0.862 0.764

ORISSA 0.58 0.48 0.40 0.685 0.682 0.504 PUNJAB 0.38 0.76 0.52 0.380 0.760 0.520

RAJASTHAN 0.54 0.39 0.17 0.697 0.652 0.457 TAMIL NADU 0.77 0.85 0.12 0.770 0.850 0.120

UP 0.46 0.25 0.01 0.460 0.250 0.010 UTTAR

ANCHAL 0.74 0.59 0.72 0.910 0.990 1.000

WEST BENGAL 0.62 0.40 0.81 0.620 0.400 0.810

Table 19

Model 6: Where do the states stand in terms of efficiency and outcomes? Outcomes

Low (q1) Low Middle (q2)

Middle High (q3)

High (q4)

Low (q1)

Chhatisgarh Assam, Gujarat, Rajasthan

Low-Middle (q2)

AP, Orissa Karnataka,

Middle High (q3)

Eff

icie

ncy

scor

es

High (q4)

Bihar, Jharkhand, UP,

Haryana, Maharashtra, MP, Punjab, TN, Bengal

HP, Kerala,

Summary: Explaining Efficiencies in Elementary education system in India In this paper, an attempt was made to estimate the efficiency of producing elementary education outcomes at the states level using the non-parametric technique of DEA. The efficiency estimates were examined using various parameters and various models. The data used were mainly physical inputs and outcomes. In social sectors like health and education it is difficult to attribute the financial allocations as inputs to estimate efficiency as the financial requirements vary across states to generate the inputs and structures. The analysis shows that not all states with better outcomes are efficient states. Similarly, not all states that seem to be efficient are better off states in terms of education. For example, most of the laggard states in terms of educational outcomes –Bihar, Jharkhand, UP and MP – shows that they are operating at the efficient most frontiers. This is coming out in all efficiency estimations using absolute input and output values (the exception being the efficiency estimations using single input and single output which are calculated as relative indices).

What are the implications of such results wherein the educationally backward states appearing as “efficient”? The concept “efficiency” here basically means that the state is using the inputs fully to produce outputs, and there are no further improvements that they can make with the same set of inputs. So, in no way the efficiency estimates are signs that these states are better than others. States like Himachal Pradesh, Tamil Nadu and Kerala which have relatively high educational outcomes in the country are also operating at the efficient frontiers. For such states, the output oriented efficiency estimates show limited scope for further improvement since they have already reached the highest levels. On the other hand, the laggard states’s problem is that they have low outcomes, but their problem is that given their current input levels, they have limited scope for improving their outcomes and catching up with the better off states. For such states, it is very important that adequate inputs are created – either by investing more finances in education sector by the states or using the existing centrally sponsored schemes better. The analysis of efficiency using single input and output indices (which scales states in a comparative mode) shows that lower outcomes and lower efficiencies are cumulative.

The factors that contribute to the “efficiency scores” largely remain unexplained – basically because of the paradox of education outcome wise lagging states showing better “efficiency”. However, some of the regressions showed the role of density of population, a proxy to look at concentration factor and hence the scope for economies of scales to operate, as significant, while in the index-based efficiency regressions, the literacy rates came out strongly. This could be an indicator that the variable literacy rates camouflages other variables. If one is able to decompose the factors that contribute to better literacy rates, those factors could as well facilitate explaining differential efficiency in education production function.

One of the possible reasons for the factors that contribute to efficiencies or inefficiencies coming out strongly in this analysis is the level of analysis. At the state level, a lot of variations and the factors that contribute are hidden. These factors may come out in an analysis of district level education production performances.

Overall, the main message of this analysis is as follows: (a) There are states that have higher levels of educational outcomes and hence the focus should be not on increasing investments, but making them efficient; (b) there are states that are laggards in terms of educational outcomes, but given their resource allocations and structures created, they are catering to the educational needs of the people in a better way. In such states, it is important that the outputs should be improved. Given their limited scope for improvement in the current levels of inputs and investments, it is important to increase allocations for the education sector in such sector till the desirable outcomes are arrived at.