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Abstract

This article assesses the technical efficiency of 28 Indian states in delivering elementary education between 2009–2010 and 2020–2021, using the stochastic frontier model developed by Battese and Coelli. The findings indicate that technical inefficiency accounts for 82 per cent of the interstate disparities in elementary education output. Factors such as public expenditure, schooling infrastructure and the presence of qualified teachers positively impact output. However, the effect of public expenditure diminishes beyond a certain threshold. Higher literacy rates, increased urbanisation and a greater proportion of government schools improve efficiency. Conversely, a higher percentage of scheduled caste and scheduled tribe children and the appointment of contractual teachers decrease efficiency. The overall technical efficiency stands at 79 per cent. Efficiency varies widely across states, ranging from 52 per cent to 94.5 per cent. Goa, Haryana and Kerala demonstrate the highest efficiency, while Arunachal Pradesh, Meghalaya and Manipur rank the lowest. Some states have seen improvements in efficiency, while others have experienced declines. These findings suggest that resource-poor states can benefit from increased public expenditure, whereas efficient resource utilisation is crucial for states facing inefficiencies. This article provides essential insights for policymakers to address regional imbalances and enhance elementary education outcomes.

JEL Codes : H52, I21, I22, I28, C14, D24

Keywords

Technical Efficiency Public Expenditure Elementary Education Stochastic Frontier Analysis

1. Introduction

Elementary education, being a merit good, attracts substantial public funding from countries worldwide, and India is no exception. In 2020–2021, India allocated 1.33 per cent of its GDP to elementary education, surpassing the public spending of several neighbouring countries, including China (0.84 per cent), Myanmar (0.78 per cent), Pakistan (0.92 per cent), Sri Lanka (0.44 per cent) and Bangladesh (0.97 per cent). During the same period, Indian states spent an average of ₹36,261 per student per annum (pspa) on elementary education.¹ However, a meticulous examination of input and output dynamics across Indian states reveals pronounced interstate disparities, indicating underlying inefficiencies in the production of elementary education.

States exhibit diverse spending patterns, with some achieving favourable outcomes² through moderate spending, while others grapple with poor outcomes despite higher financial allocations. For example, in 2020–2021, Sikkim and Nagaland spent ₹96,968 and ₹79,071 pspa, respectively. However, the age-specific enrolment ratios in these states were 82 and 78 per cent, respectively. On the other hand, states such as Karnataka, Punjab and Meghalaya attained 100 per cent enrolment with a moderate amount of spending. Similarly, Arunachal Pradesh recorded the lowest retention rate (45 per cent) in 2020–2021, despite an expenditure of ₹71,405 pspa. In contrast, Meghalaya and Assam maintained retention rates of 51 and 65 per cent, respectively, with comparatively lower spending of ₹19,896 and ₹19,531, respectively (Table 1).

Disparities in educational infrastructure are also evident. In 2020–2021, Meghalaya notably surpassed Bihar (seven times more), Uttar Pradesh (four times more) and West Bengal (three and a half times more) in the number of schools per lakh child population. Additionally, significant variations exist in the percentage of government schools across states. Kerala (30 per cent), Uttar Pradesh (55 per cent), Meghalaya (58 per cent) and Goa (59 per cent) reported the lowest percentages of government schools. In contrast, West Bengal (88 per cent), Tripura (86 per cent), Chhattisgarh (85 per cent) and Himachal Pradesh (85 per cent) had the highest proportion of government schools (Table 1).

The Government of India (2017) reveals that several states grappling with low enrolments and an excess of schools and teachers. In 2015–2016, Arunachal Pradesh had 7.3 per cent of primary schools and 13 per cent of upper primary schools with zero enrolment. In Sikkim, 83.3 per cent of primary schools had an enrolment of less than 30, while it was 70 per cent in Jammu and Kashmir and Arunachal Pradesh. Similarly, at the upper primary level, 56 per cent of schools in Jammu and Kashmir, 50 per cent in Nagaland and 43 per cent in Arunachal Pradesh had an enrolment of fewer than 30 students. These findings further suggest inefficiencies in public resource allocation.

The Right to Education Act specifies that having 1 teacher per 35 students is ideal. In 2020–2021, only Bihar reported a shortage of teachers. Conversely, Sikkim, Himachal Pradesh, Nagaland, Jammu and Kashmir, Arunachal Pradesh, Mizoram and Uttarakhand had 3 to 6 teachers per 35 students. Many states also had lower percentages of qualified teachers (i.e., those holding a Bachelor of Education degree or equivalent professional qualification). The states with the lowest percentages were Nagaland (48.38 per cent), Meghalaya (50.16 per cent), Jharkhand (51 per cent), Tripura (56 per cent), Assam (57 per cent), Manipur (66 per cent) and Sikkim (67 per cent) (Table 1). These facts highlight the need to assess the technical efficiency of Indian state governments in providing elementary education.

Table 1.

Status of Elementary Education (EE): Public Expenditure, Schooling Infrastructure and Outputs, 2020–2021

States	Per-student Public Expenditure on EE (in ₹)	Schools per Lakh Child Population (Number)	Government Schools (%)	Teacher per 35 Students (Number)	Teachers with Professional Qualification (%)	Age-specific Enrolment Ratio	Retention Rate (%)
Andhra Pradesh*	23,227	977	72.69	2	76.71	87.81	84.25
Arunachal Pradesh	71,405	1,544	83.19	3	75.50	96.67	44.55
Assam	19,531	1,212	73.81	2	57.36	95.72	65.11
Bihar	10,710	386	80.68	1	69.64	94.66	75.35
Chhattisgarh	25,406	1,191	85.16	2	85.56	90.26	87.82
Goa	25,873	660	58.91	2	93.95	89.76	95.25
Gujarat	32,091	490	74.07	1	91.43	88.21	91.06
Haryana	47,225	604	61.29	2	91.71	94.50	96.91
Himachal Pradesh	59,607	2,111	84.92	4	89.64	98.32	97.41
Jammu and Kashmir*	52,980	1,473	80.01	3	70.52	79.57	67.50
Jharkhand	15,213	725	79.57	1	51.16	92.90	66.68
Karnataka	28,096	777	71.22	1	96.33	100.00	89.95
Kerala	23,363	397	30.39	2	95.70	96.78	100.00
Madhya Pradesh	32,478	984	73.72	2	83.91	85.20	72.96
Maharashtra	28,299	710	61.58	2	96.16	98.18	93.66
Manipur	55,340	1,118	63.11	3	66.71	95.05	52.12
Meghalaya	19,896	2,585	58.25	2	50.16	100.00	50.98
Mizoram	66,954	1,936	73.39	3	76.65	100.00	53.55
Nagaland	79,071	828	72.97	4	48.39	77.72	52.99
Odisha	21,555	1,008	81.84	2	91.20	97.36	82.32
Punjab	20,045	831	67.92	3	78.10	100.00	97.16
Rajasthan	20,100	868	64.12	2	89.23	93.70	73.55
Sikkim	96,968	1,502	67.38	6	67.42	82.23	92.02
Tamil Nadu	37,415	697	63.84	2	90.84	98.66	90.37
Tripura	22,537	1,054	86.44	3	56.42	93.64	85.87
Uttar Pradesh	22,454	675	54.99	1	77.16	93.36	67.51
Uttarakhand	44,851	1,521	72.05	3	85.39	98.94	83.80
West Bengal	12,626	816	87.63	2	83.27	95.75	61.67
Maximum	96,968	2,585	87.63	6	96.33	100.00	100.00
Minimum	10,710	386	30.39	1	48.39	77.72	44.55
Mean	36,261	1,060	70.90	2	78.08	93.39	77.58

Source: (basic data): Public EE expenditure: CAG; schooling infrastructure and outputs: UDISE.

Note: *In this article, the former state of Andhra Pradesh and Jammu and Kashmir is considered.

Technical efficiency refers to the ability of the state governments (here, the decision-making unit) to produce the maximum possible output from a given set of inputs and technology. The education production process of a state is technically efficient if the actual output is equal to the potential output.

Few Indian studies have examined the efficiency of education outcomes at the state level. For example, Mohanty and Bhanumurthy (2020) analysed the efficiency of the education and health sectors across Indian states. Gourishankar and Lokachari (2012) focused on education development and efficiency. Dutta (2012) and Ghose (2017) assessed the efficiency of elementary education outcomes across Indian states for 2007–2008 and 2005–2006 to 2010–2011, respectively. Purohit (2016) studied the efficiency of elementary education outcomes in urban areas for 2012–2013 across 19 states.

The existing Indian studies are confined to a select group of states, rely on cross-sectional data and use Data Envelopment Analysis (DEA).³ However, the DEA methodology suffers from various limitations: (a) it is highly sensitive to variable selection, (b) subject to small sample bias and (c) produces biased estimates in the presence of statistical noise. The stochastic frontier approach (SFA) is relatively stable and is a preferred methodology for policymaking (Coelli et al., 2005; Rassouli-Currier, 2007). SFA is a parametric method used to assess the technical efficiency of decision-making units by considering both random shocks and inefficiencies in the production process.

This article addresses the limitations of existing Indian research by using the stochastic frontier estimation method developed by Battese and Coelli (1995). This method simultaneously estimates the frontier production function and inefficiency effects function, providing a more accurate estimation of technical efficiency compared to the DEA. This article estimates the technical efficiency of 28 Indian states (including former states of Andhra Pradesh and Jammu and Kashmir) from 2009–2010 to 2020–2021 in providing elementary education. It uses the latest data and considers a wider range of explanatory variables to gain a deeper understanding of the topic. It also identifies the determinants of technical inefficiency. This article fills a crucial gap in the literature and offers valuable insights for identifying best practices and developing strategies for optimal public resource allocation, along with pertinent policy recommendations.

This article is structured as follows: The second section provides a brief literature review, the third section discusses the methodology, the fourth section presents empirical results, and the fifth section concludes.

2. Review of Literature

2.1 Empirical Literature on Education Outcome Efficiency

International studies have extensively explored education outcome efficiency. Koku (2015) analysed data from 15 West African countries and found that public expenditure did not significantly impact primary and secondary school enrolment. Instead, per capita GDP emerged as a key positive influencer. Guarini et al. (2020) found a positive effect of both public education expenditure and private wealth on schooling years in 17 regions of Italy. Miningou (2019) developed the Learning Adjusted Years of Schooling index, an education outcome indicator. This article examined the efficiency of 130 countries and found a positive impact of public expenditure on outcomes but a negative impact when considering the square of public expenditure (i.e., the impact of public expenditure on education outcomes appeared to diminish beyond a point).

A significant number of studies favour DEA over SFA due to DEA’s ability to handle multi-input and multi-output scenarios. For example, Campoli et al. (2019) used DEA to determine the efficiency of 27 Brazilian federative units. Dufrechou (2016) compared the efficiency of 11 Latin American countries with 24 high-income countries, using DEA.

Learning outcome data provided by the Program for International Student Assessment (PISA) surveys has been used in several cross-country and country-specific studies. Delprato and Antequera (2021) used the PISA survey data to compare the efficiency of public and private schools in four Latin American countries, namely, Ecuador, Guatemala, Honduras and Paraguay. Salas-Velasco (2020) used it to study the efficiency of public schools in Spain. Ciro and García (2018) measured the efficiency of 37 developed and developing countries in providing secondary education. Cuéllar (2014) compared the efficiency of 15 Latin American countries.

As discussed in the first section, Indian studies on education outcome efficiency are scarce. The few Indian studies that focus on the elementary education sector, treat primary education (grades 1–5) and upper primary education (grades 6–8), separately. One pioneering study by Sankar (2007) measured the efficiency of 27 Indian states in producing educational outcomes such as enrolment, retention, language scores and math scores. Results indicated that both economically disadvantaged states, such as Jharkhand, Uttar Pradesh and Madhya Pradesh, and prosperous states, such as Himachal Pradesh, Tamil Nadu and Kerala, were highly efficient. In contrast, Chhattisgarh, Assam and Gujarat were the least efficient and had lower outcomes.

Dutta (2012) measured elementary education efficiency in Indian states and found that in 2007–2008, Delhi, Kerala and Tamil Nadu excelled in educational outcomes and efficiency, while Bihar, Rajasthan, Madhya Pradesh, Odisha and Uttar Pradesh struggled with lower outcomes and inefficiency due to inadequate inputs.

Purohit (2016) studied the efficiency of primary and upper primary education in urban areas across 19 states in 2012–2013. This article found that Andhra Pradesh, Maharashtra and West Bengal were the most efficient states, while Goa and Uttarakhand were the least efficient. Ghose (2017) estimated technical efficiency scores at both primary and upper primary levels from 2005–2006 to 2010–2011. This article found that Karnataka and Tripura were fully efficient at the primary level, whereas Andhra Pradesh and Kerala were fully efficient at the upper primary level. Bihar, Gujarat, Maharashtra, Tamil Nadu and West Bengal also exhibit high efficiency levels. Purohit (2015) and Ghose and Bhanja (2014) have estimated the district level efﬁciency in enrolments at primary and upper primary levels, in Rajasthan and West Bengal, respectively.

Notably, the Indian studies employed a two-step DEA methodology, which is known for producing biased estimates. These studies are outdated and also lack a comprehensive examination of the entire elementary education sector.

2.2 Empirical Literature on the Determinants of Technical Efficiency (or Inefficiency)

Empirical studies also identify various environmental factors that impact technical efficiency/inefficiency in the education production process. Guarini et al. (2020) emphasised that social capital and quality local governance enhance efficiency. Dufrechou (2016) discovered that economic globalisation had a positive impact on efficiency, while democracy showed a negative association. Additionally, higher income levels led to non-linear efficiency gains. Koku (2015) highlighted the positive impact of corruption control and political stability, on technical efficiency.

Delprato and Antequera (2021) discussed that favourable student-specific factors (such as attending preschool, students’ health, etc.), teacher-specific factors (such as work satisfaction, professional qualification, etc.) and school-specific factors (such as fund availability, enrolment, class size, etc.) had a positive impact on efficiency. Herrera and Ouedraogo (2018) found that increased public expenditure, a higher public-to-private financing ratio, AIDS/HIV prevalence and urbanisation had adverse impacts on efficiency. Inequality and aid dependency showed mixed results, whereas GDP and good governance had a positive impact.

Ciro and García (2018) found that GDP/income and parents’ educational attainment positively impact efficiency. Chakraborty (2009) highlighted that poverty reduces efficiency, and the proportion of minority populations has a positive impact on inefficiency. Salas-Velasco (2020) discussed that private school administration, school autonomy and teacher morale positively impact technical efficiency. Similarly, Kang and Greene (2002) found that private schools in the United States are more efficient in generating education outcomes.

Indian studies by Sankar (2007), Dutta (2012), Purohit (2015, 2016), Ghose (2017), Ghose and Bhanja (2014) and Mohanty and Bhanumurthy (2020) identified factors affecting education outcome efficiency. Population density, literacy rate, school infrastructure and teacher training grants were found to positively impact efficiency, while factors such as student–classroom ratio, urbanisation and income inequality had varying effects.

To summarise, factors such as income, income inequality, poverty, literacy rate, teacher characteristics, infrastructure and governance indicators are expected to impact the efficiency of educational systems. Understanding and addressing these factors are crucial for improving education outcome efficiency. Table 2 presents a summary of the literature review.

Table 2.

Summary of Selective Studies on Efficiency in the Education Sector

International Studies
Author	Method	Area	Outcome	Input	Determinants of Technical (In)Efficiency
Delprato and Antequera (2021)	Simar and Wilson bootstrap DEA	4 LAC, 2017	Scores in math, reading and science	Teacher–pupil ratio, household wealth, school infrastructure variables	Student-specific factors, teacher-specific factors and teaching quality, school-specific factors
Salas-Velasco (2020)	SFA	900 schools in Spain, 2012	Math test score	Teacher–pupil ratio, occupation status/income, school infrastructure, gender	Public/private school, school autonomy, teachers’ morale
D’Elia and Ferro (2021)	SFA	37 universities, Argentina 2005–2013	Number of graduates	Expenditure, students, teachers, region dummy	Proportion of student enrolment to potential enrolment
Guarini et al. (2020)	SFA	19 regions, Italy, 1993–2012	Years of schooling	Public expenditure, private wealth index, regional GDP	Social capital, gender and governance index
Ciro and García (2018)	Simar and Wilson bootstrap DEA	37 countries, 2012–2015	Enrolment rate; performance index (PISA)	Pupil–teacher ratio; public and private spending	GDP, parental education
Campoli et al. (2019)	Slack-based DEA	27 Federal Units, Brazil, 2011–2014	Average years of education, school attendance	Public expenditure, household average income	Not discussed
Dufrechou (2016)	Simar and Wilson bootstrap DEA	35 countries, 1970–2010	Average years of schooling, proportion of population with secondary education	Public education expenditure	GSDP, democracy index, globalisation, regional dummies
Koku (2015)	SFA	15 countries, 2002–2011	Primary and secondary school enrolment	Public expenditure, GDP	Political stability, corruption control
Herrera and Ouedraogo (2018)	DEA and FDH	175 countries, 2006–2016	NER, PISA score, Primary completion rate, literacy rate (total 15 models for 15 outputs)	Public expenditure, adult literacy rate, pupil–teacher ratio	GDP, total public expenditure, public–private finance ratio, HIV/ AIDS, urbanisation, inequality, aid dependency, governance, corruption
Cuéllar (2014)	DEA and FDH	15 LAC; 2000 and 2009	NER, PISA score, primary completion rate, literacy rate	Public expenditure on education	Not discussed

Source: Authors’ compilation.

Note: NER: net enrolment ratio, GER: gross enrolment ratio, PISA: programme for international student assessment.

Table 2.

Continued: Summary of Selective Studies on Efficiency in the Education Sector

Indian Studies
Author	Method	Area	Outcome	Input	Determinants of Technical (In)Efficiency
Sankar (2007)	DEA	27 states, 2002 for input; 2004–2005 for output	Enrolment rate, retention rates, language score, maths score	Distance to school (access), pupil–teacher ratio	Population density, literacy rate
Dutta (2012)	DEA	28 States and Delhi, 2007–2008	Enrolment rate, retention rates	Distance to school (access), pupil–teacher ratio	School infrastructure index, population density, education expenditure and teachers’ training grant, student–classroom ratio
Gourishankar and Lokachari (2012)	DEA	All states and union territories of India, 2006–2007 to 2007–2008	GER, pass percentage	Number of schools and schooling infrastructure and teacher-related variables	Not discussed
Mohanty and Bhanumurthy (2020)	DEA	27 states, 2000 to 2015	GER for school education; GER for higher education	Education expenditure; non-education expenditure	Economic growth, governance quality, mothers’ education
Purohit (2015)	SFA	33 districts in Rajasthan, 2008–2012	Enrolment	Pupil–teacher ratio and infrastructure variables	Female literacy, income and urbanisation
Purohit (2016)	DEA	19 states, 2012–2013	Enrolment in primary and upper primary	Average instruction hours, school grants and infrastructure variables	Access index, availability of tap water, electrification
Ghose and Bhanja (2014)	DEA	20 districts in WB; 2005–2006 to 2010–2011	NER; % of passing students	Schools; PTR; % of teachers graduate and infrastructure variables	Teacher-related indicators, indicators of schooling infrastructure, income, population density, income inequality
Ghose (2017)	DEA	28 states, 7 union territories of India	NER, % of students passing with 60%	Schools per lakh, TPR, classroom–student ratio, % of graduate teachers	Indicators of schooling infrastructure, social indicators, state-specific factors, grants

Source: Authors’ compilation.

Note: NER: net enrolment ratio, GER: gross enrolment ratio.

3. Data and Methodology

SFA is the parametric approach developed by Aigner et al. (1977) and Meeusen and van den Broeck (1977) to measure technical efficiency. It is an extension of the conventional production function. While the conventional production function assumes that producers are fully efficient, and deviations from the production possibility frontier are solely due to random shocks, the SFA specifies the frontier production function (regression model) characterised by a composite error term that can be decomposed into the statistical noise that captures measurement error and a one-sided disturbance term that measures inefficiency.

Over time, various SFA models emerged to estimate time-varying or time-invariant technical efficiency. These models typically employ a two-step process: (a) estimating the stochastic frontier model and technical efficiency scores and (b) using these estimates to identify the determinants of efficiency through Tobit models or OLS. Battese and Coelli (1995) argued that the two-stage approach may yield inconsistent and biased parameter estimates due to (a) potential serial correlation among technical efficiency estimates and/or (b) correlation between the inefficiency term and inputs/output used in the production function.

Battese and Coelli (1995) developed the inefficiency effects model that simultaneously estimates the frontier production function and the inefficiency function, hence solving the problem of the two-step approach. This paper uses the inefficiency effects model to estimate the technical efficiency of 28 Indian states from 2009–2010 to 2020–2021. The elementary education frontier production function can be written as

Y_{i t} = f (x_{i t} ​, β) e^{v_{i t} - u_{i t}},

(1)

where Y_it denotes education outcome, x_it denotes a vector of inputs used in the production of education, v_it is the stochastic error term and v_it ~ iid N (0, σ_v²); and u_it is the inefficiency component. By taking the logarithms of equation (1), we can obtain the SFA model for panel data as

ln Y_{i t} = β_{0} + Σ_{j} β_{j} ln X_{j i t} + v_{i t}_{} - u_{i t} .

(2)

According to Battese and Coelli (1995), u_it follows a truncated normal distribution and time-varying mean, that is, u_it ~ iid N + (m_it, σ_u²). The technical inefficiency term (m_it) depends on a set of environmental factors. The inefficiency model can be expressed as follows:

m_{i t}_{} = δ Z_{i t} .

(3)

As suggested by Jondrow et al. (1982), technical efficiency (TE) can be estimated as the expectation of the truncated error term (u) conditional on composed error term (ε), that is,

T E = E [exp (- u_{i t}) / ε_{i t}] .

(4)

Maximum likelihood estimation is applied to estimate parameters in equations (2) and (3). The likelihood function is parameterised with variances in the model and the variance ratio (γ = σ_u² / σ² and where σ² is the sum variance σ_u² and σ_v²). γ indicates the extent of technical inefficiency variance relative to the total variance, on a scale from 0 to 1. A γ of 0 means that parameters δ are unidentified, and variables in Z are part of the production function. The statistical significance of γ can be tested using the generalised likelihood ratio (LR) test:

LR test statistic = - 2 [L (HR) - L (HUR)],

(5)

where L(HU) and L(HUR) represent the log-likelihood values computed from the restricted model (OLS) and the unrestricted model (SFA), respectively. LR follows a mixed χ² distribution, with degrees of freedom equal to imposed restrictions (Kodde & Palm, 1986).

Usually, SFA models extend the Cobb–Douglas (CD) production function. However, CD production functions are quite restrictive as they assume constant elasticity of substitution. Some studies opt for the trans-log production function because it does not impose restrictions on scale elasticities (Miningou, 2019; Rassouli-Currier, 2007). However, trans-log functions often face multicollinearity issues due to numerous input interaction terms. Quadratic specifications have been explored in a few studies (Kang & Greene, 2002; Pereira & Moreira, 2007; Perelman & Santin, 2011). Best practice involves estimating multiple specifications and selecting the most relevant model based on likelihood ratio tests and information criteria (Chakraborty, 2009; D’Elia & Ferro, 2021; Guarini et al., 2020; Koku, 2015). Since there are only 336 observations in the database used in this study, a functional form that requires the estimation of fewer parameters is more desirable.

This study chooses retention rate as the output variable (Y_it). Research indicates that the retention rate (or completion rate) is a better education outcomes indicator than enrolment/attendance ratios (Cuéllar, 2014; Mehta, 2004; Sankar, 2007; UNESCO, 2009). Retention rate is the percentage of students who finish grade 8. It can be measured as

Retention rate (t) = \frac{(Enrolment in grade 8 (t) - (Repeaters in grade 8 (t)}{(Enrolment in grade 1 (t - 7)}

(6)

Input variables considered in this article are real public expenditure per student, real gross state domestic product (GSDP) per capita, number of teachers per 35 students, number of schools per lakh child population and several schooling infrastructure variables such as the percentage of schools having girls’ toilet, computer, electricity, drinking water and provide midday meals. Teaching quality (measured by the proportion of teachers having professional qualifications such as a bachelor’s in education or an equivalent degree) is also considered. However, data on the proportion of professionally qualified teachers are missing for the years 2009–2010 and 2010–2011.

The inefficiency model includes literacy rate, the proportion of the rural population, the proportion of government schools, the percentage of regular teachers⁴ and the proportion of scheduled caste (SC) and scheduled tribe (ST) children.

The study relies on secondary data from various sources: Expenditure data are sourced from the Finance Account of States, Comptroller and Auditor General of India (CAG) (2022). Retention rate and schooling infrastructure data are compiled from the Unified District Information System on School Education (UDISE) (2015, 2022). Literacy rate and rural population figures are estimated using census data (Government of India [GOI] 2001, 2011). Information on midday meal provision is gathered from the annual work plan and budget documents of the states (GOI, 2022a). The population of elementary schooling age is obtained from the GOI (2022b). GSDP data are compiled from the National Statistical Office (2022).

4. Empirical Results

Table 3 presents the estimated results of equation (2) (frontier models) and equation (3) (inefficiency model). The outcome variable used in this exercise is the retention rate at the elementary level. Specification (1) includes all the input variables for which data are available from 2009–2010 to 2020–2021 for all 28 states. Specification (2) only includes the inputs that were significant in specification (1). Specification (3) includes the proportion of teachers that have a professional qualification⁵ (because data are unavailable for 2009–2010 and 2010–2011). Technical efficiency scores have been estimated based on model (2) as it allows us to track changes in efficiency since 2009–2010.

Table 3.

Maximum Likelihood Estimation of Stochastic Frontier Models and Inefficiency Effects Function (IM)

Variables	All Variables from 2009–2010 to 2020–2021	Final Model (All Significant in 1)	Including Teachers with Professional Degree
Variables	(1)	(2)	(3)
Frontier production function
Log of real per-student expenditure	1.0615***	0.8576***	0.9119***
Log of real per-student expenditure	(0.3343)	(0.3273)	(0.3451)
Square of (log of real per student expenditure)	–0.0614***	–0.0497***	–0.0537***
Square of (log of real per student expenditure)	(0.0176)	(0.0172)	(0.0183)
Log of real GSDP per capita	0.0584**	0.0550*	0.0815***
Log of real GSDP per capita	(0.0283)	(0.0298)	(0.0291)
Log of percentage of schools having functional girl’s toilet	0.0069
	(0.0322)
Log of percentage of schools having functional drinking water	0.0139
	(0.0320)
Log of percentage of schools having functional computer	0.0700***	0.0865***	0.0705***
Log of percentage of schools having functional computer	(0.0260)	(0.0244)	(0.0240)
Log of percentage of schools having functional electricity	0.1089***	0.1278***	0.0951***
Log of percentage of schools having functional electricity	(0.0258)	(0.0244)	(0.0236)
Log of teachers per 35 students	0.1299***	0.1173***	0.1028**
Log of teachers per 35 students	(0.0392)	(0.0397)	(0.0405)
Log of schools per lakh child population	0.0818**	0.0584*	0.0644*
Log of schools per lakh child population	(0.0354)	(0.0306)	(0.0351)
Log of percentage of schools providing midday meals	0.2081*
Log of percentage of schools providing midday meals	(0.1082)
Log of percentage of teacher’s having B.Ed or equivalent qualifications			0.1955***
			(0.0360)
Constant	–1.1514	–1.0619	–2.2812
Constant	(1.4876)	(1.5408)	(1.7061)
Inefficiency model
Log of percentage of population in rural areas	0.1025		–0.4407***
Log of percentage of population in rural areas	(0.1484)		(0.1317)
Log of literacy rate	–1.1794***	–1.1137***	–1.7831***
Log of literacy rate	(0.2181)	(0.2079)	(0.3003)
Log of percentage of teacher’s having regular appointment	–0.0586	–0.0669*	–0.1323***
Log of percentage of teacher’s having regular appointment	(0.0358)	(0.0377)	(0.0308)
Log of percentage of government schools	–0.4303***	–0.3859***	–0.4177***
Log of percentage of government schools	(0.1039)	(0.1052)	(0.1202)
Log of percentage of SC–ST children in child population	0.4350***	0.4432***	0.3991***
Log of percentage of SC–ST children in child population	(0.0439)	(0.0514)	(0.0508)
Constant	5.4930***	5.3897***	10.6368***
Constant	(1.4036)	(1.0813)	(1.8856)
Log likelihood	144.261	142.3935	181.4444
Number of iterations	27	21	28
Gamma (γ)	90.88***	82.42***	32.05***
Observations	336	336	280
Number of states	28	28	28

Source: Authors’ estimation.

Note: Dependent variable: Log of retention rate at elementary level. Standard errors in parentheses. ***P < .01, **P < .05, *P < .1.

Column 1 shows that states’ per-student expenditure (real) has a positive significant impact on the retention rate. However, the square of per-student expenditure (square of log of real per student expenditure) is negative and significant. This implies that additional units of expenditure have a lower impact on the retention rate compared to the previous units of expenditure and the relationship wears off after a certain point.⁶ All the other input variables have a positive coefficient as expected. This indicates that better schooling infrastructure generates better outcomes. However, the percentage of schools having girl’s toilets and drinking water was not significant. Hence, these variables have been dropped in specification (2). The findings of specification (3) are similar to that of specification (2). Additionally, the proportion of teachers with a professional qualification (B.Ed or equivalent) has a positive and significant impact on the retention rate.

The statistical significance of γ indicates the validity of the SFA model. Alternatively, states are inefficient in producing elementary education. According to the γ coefficient, 82.42 per cent of the interstate variation in elementary education output is explained by technical inefficiency (specification 2).

The inefficiency model identifies factors that influence technical inefficiency. Its results are consistent across the three specifications. Literacy rate and the proportion of government schools negatively impact technical inefficiency, suggesting that efficiency improves with higher literacy rates and a greater ratio of government to private schools. The percentage of SC and ST children has a positive effect on inefficiency, suggesting that states that have a higher proportion of ST/SC children are more inefficient. The proportion of the rural population is not significant in specification (1), but specification (3) indicates that urban areas are more efficient compared to rural areas. The appointment of contractual teachers or part-time teachers (instead of regular teachers) has a negative impact on technical efficiency.

Table 4 presents the technical efficiency scores and relative ranking of states. The mean efficiency of states was 76 per cent in 2009–2010, improving to 81 per cent in 2015–2016. Although there was a slight decline in between, it eventually increased to 82 per cent in 2020–2021. The overall efficiency of states during the study period was 79 per cent. Overall, Goa (94.5 per cent) is the most efficient state followed by Haryana (94.1 per cent) and Kerala (94 per cent). Arunachal Pradesh (52 per cent) is the least efficient state followed by Meghalaya (55 per cent) and Manipur (59 per cent). There appear to be wide interstate variations (between 94.5 and 52 per cent) in efficiency.

Table 4.

Technical Efficiency Estimates, Relative Ranks and Mean Efficiency of States Based on the Retention Rate Model

States	2009–2010	2010–2011	2011–2012	2012–2013	2013–2014	2014–2015	2015–2016	2016–2017	2017–2018	2018–2019	2019–2020	2020–2021	Mean
Andhra and Telangana	69.60	74.08	77.24	77.99	75.86	79.08	80.52	81.20	81.21	79.56	89.04	83.92	79.11
Andhra and Telangana	(19)	(14)	(18)	(19)	(21)	(20)	(18)	(18)	(16)	(15)	(10)	(17)	(18)
Arunachal Pradesh	67.78	57.08	60.76	53.76	49.80	48.14	48.28	45.66	45.27	47.36	47.02	53.64	52.05
Arunachal Pradesh	(21)	(24)	(24)	(28)	(28)	(28)	(28)	(28)	(28)	(28)	(28)	(28)	(28)
Assam	67.35	79.70	82.68	81.38	78.97	76.17	70.76	88.95	75.81	78.16	81.10	79.53	78.38
Assam	(23)	(13)	(13)	(18)	(18)	(21)	(22)	(11)	(18)	(17)	(16)	(21)	(19)
Bihar	83.15	84.33	93.50	94.39	94.88	81.96	89.68	90.68	89.76	88.93	94.23	94.24	89.98
Bihar	(10)	(9)	(6)	(6)	(4)	(15)	(9)	(9)	(8)	(10)	(3)	(2)	(6)
Chhattisgarh	80.67	72.59	79.70	76.07	84.51	84.95	85.30	86.08	86.44	76.05	79.21	82.22	81.15
Chhattisgarh	(12)	(15)	(16)	(20)	(14)	(14)	(16)	(15)	(13)	(19)	(18)	(18)	(16)
Goa	96.46	96.63	92.71	94.60	94.55	94.41	94.58	94.33	94.32	94.62	93.60	93.43	94.52
Goa	(1)	(1)	(7)	(4)	(5)	(3)	(2)	(3)	(2)	(3)	(5)	(5)	(1)
Gujarat	69.25	64.05	84.92	84.54	87.18	88.92	91.36	91.83	90.83	92.37	92.51	92.59	85.86
Gujarat	(20)	(21)	(10)	(15)	(12)	(10)	(7)	(6)	(7)	(5)	(6)	(6)	(11)
Haryana	87.25	91.87	95.12	95.37	95.10	95.33	94.92	95.60	95.24	94.74	94.57	94.54	94.14
Haryana	(8)	(4)	(4)	(2)	(3)	(2)	(1)	(1)	(1)	(2)	(1)	(1)	(2)
Himachal Pradesh	93.57	82.94	95.56	94.75	93.22	93.62	92.23	94.13	93.95	93.66	93.90	93.57	92.93
Himachal Pradesh	(3)	(11)	(2)	(3)	(8)	(5)	(5)	(4)	(4)	(4)	(4)	(4)	(4)
Jammu and Kashmir	92.02	96.21	96.24	96.69	96.67	96.09	90.44	82.02	82.62	80.18	78.69	79.85	88.98
Jammu and Kashmir	(6)	(2)	(1)	(1)	(2)	(1)	(8)	(17)	(15)	(14)	(19)	(20)	(7)
Jharkhand	77.49	84.14	84.37	71.64	64.84	69.30	73.79	64.86	69.12	63.18	66.56	69.66	71.58
Jharkhand	(14)	(10)	(11)	(21)	(22)	(22)	(21)	(22)	(20)	(23)	(23)	(23)	(21)
Karnataka	84.76	87.47	85.13	93.51	86.14	87.63	87.50	88.08	89.25	88.05	91.06	91.52	88.34
Karnataka	(9)	(8)	(9)	(7)	(13)	(13)	(12)	(14)	(9)	(12)	(8)	(8)	(9)
Kerala	92.42	91.43	95.47	94.51	94.07	94.34	94.20	94.71	94.31	94.83	94.26	93.62	94.01
Kerala	(5)	(5)	(3)	(5)	(6)	(4)	(3)	(2)	(3)	(1)	(2)	(3)	(3)
Madhya Pradesh	93.27	90.47	82.46	84.74	81.41	80.67	78.70	78.62	78.36	82.86	81.93	83.98	83.12
Madhya Pradesh	(4)	(6)	(14)	(14)	(17)	(18)	(20)	(19)	(17)	(13)	(15)	(16)	(14)
Maharashtra	82.44	81.97	83.53	90.55	88.55	89.40	89.54	90.98	91.34	91.62	92.35	91.33	88.63
Maharashtra	(11)	(12)	(12)	(9)	(11)	(7)	(10)	(8)	(5)	(6)	(7)	(9)	(8)
Manipur	52.41	56.33	59.53	55.18	61.22	60.26	64.87	61.69	60.35	61.42	56.87	60.89	59.25
Manipur	(27)	(25)	(25)	(27)	(23)	(25)	(23)	(24)	(24)	(24)	(26)	(26)	(26)
Meghalaya	35.66	41.42	43.72	60.00	59.82	59.05	61.38	59.20	58.65	58.73	60.66	63.05	55.11
Meghalaya	(28)	(28)	(28)	(26)	(24)	(26)	(25)	(25)	(25)	(25)	(24)	(24)	(27)
Mizoram	67.77	71.26	67.99	61.93	51.32	56.35	56.11	55.66	52.68	54.02	57.41	60.25	59.40
Mizoram	(22)	(17)	(21)	(23)	(27)	(27)	(27)	(26)	(27)	(27)	(25)	(27)	(25)
Nagaland	72.09	72.15	64.17	61.35	59.58	64.83	60.87	54.63	54.44	56.95	54.55	61.18	61.40
Nagaland	(17)	(16)	(23)	(24)	(25)	(23)	(26)	(27)	(26)	(26)	(27)	(25)	(24)
Odisha	71.84	70.13	74.99	84.77	97.33	88.31	86.93	88.12	87.07	90.61	84.88	87.81	84.40
Odisha	(18)	(19)	(19)	(13)	(1)	(11)	(14)	(13)	(11)	(7)	(14)	(12)	(12)
Punjab	88.26	87.60	91.72	89.64	89.47	89.19	89.37	89.12	74.45	77.22	85.40	85.00	86.37
Punjab	(7)	(7)	(8)	(10)	(9)	(9)	(11)	(10)	(19)	(18)	(13)	(15)	(10)
Rajasthan	58.26	43.68	55.06	61.00	58.37	61.84	63.33	64.44	68.01	68.12	71.63	72.61	62.20
Rajasthan	(26)	(27)	(26)	(25)	(26)	(24)	(24)	(23)	(21)	(22)	(22)	(22)	(23)
Sikkim	59.92	51.58	55.00	65.33	77.15	80.77	78.98	72.54	61.93	72.05	80.30	86.43	70.16
Sikkim	(25)	(26)	(27)	(22)	(19)	(17)	(19)	(20)	(23)	(20)	(17)	(13)	(22)
Tamil Nadu	93.68	93.47	94.89	92.79	93.45	92.70	92.12	91.58	87.95	89.12	87.54	89.37	91.55
Tamil Nadu	(2)	(3)	(5)	(8)	(7)	(6)	(6)	(7)	(10)	(9)	(12)	(10)	(5)
Tripura	80.45	65.47	81.81	82.77	76.94	79.16	85.13	82.45	90.90	89.47	90.39	92.38	83.11
Tripura	(13)	(20)	(15)	(16)	(20)	(19)	(17)	(16)	(6)	(8)	(9)	(7)	(15)
Uttar Pradesh	65.66	60.12	66.46	82.19	82.89	89.39	93.42	92.10	86.94	79.32	78.27	82.20	79.91
Uttar Pradesh	(24)	(23)	(22)	(17)	(16)	(8)	(4)	(5)	(12)	(16)	(20)	(19)	(17)
Uttarakhand	73.37	71.17	71.86	88.81	89.13	87.96	87.19	88.64	85.83	88.50	88.59	88.79	84.15
Uttarakhand	(16)	(18)	(20)	(11)	(10)	(12)	(13)	(12)	(14)	(11)	(11)	(11)	(13)
West Bengal	74.42	61.78	79.28	86.77	83.20	81.73	85.92	66.26	67.53	70.44	72.55	85.77	76.30
West Bengal	(15)	(22)	(17)	(12)	(15)	(16)	(15)	(21)	(22)	(21)	(21)	(14)	(20)
Mean	76.12	74.33	78.42	80.61	80.20	80.41	80.98	79.79	78.38	78.65	79.97	81.91	79.15

Source: Authors’ estimation.

Note: Values in the parenthesis are the relative ranks of the states with respect to their technical efficiency scores.

Over time, the relative rankings of states have changed. In 2009–2010, Goa, Tamil Nadu and Himachal Pradesh were the most efficient, while Meghalaya, Manipur and Rajasthan were the least efficient. By 2020–2021, Haryana, Bihar and Kerala emerged as the most efficient, while Arunachal Pradesh, Mizoram and Manipur became the least efficient.

Technical efficiency scores have improved in Uttar Pradesh, Bihar, Gujarat, Haryana, Maharashtra, Meghalaya, Sikkim, Odisha and Rajasthan, while it has declined in Arunachal Pradesh, Chhattisgarh, Jharkhand, Jammu and Kashmir, Mizoram, Nagaland, Madhya Pradesh, Punjab and Tamil Nadu.

An analysis of the relationship between states’ retention rates and their technical efficiency scores reveals that states such as Kerala, Himachal Pradesh, Haryana and Goa exhibit high efficiency and favourable outcome, suggesting efficient resource allocation. Conversely, states such as Arunachal Pradesh, Manipur, Mizoram, Nagaland and Meghalaya demonstrate poor outcomes attributable to inefficient resource allocation. States such as Bihar, Tripura, Uttar Pradesh, Madhya Pradesh, West Bengal and Odisha display above-average efficiency but still experience low output, pointing to potential resource scarcity challenges. On the other hand, states such as Jharkhand, Jammu and Kashmir, Assam and Rajasthan may face a dual challenge of both resource scarcity and technical inefficiency (Figure 1). This analysis highlights that education outcomes can be influenced by a complex interplay of efficiency, resource allocation and existing levels of regional disparities.

Figure 1.

Source: Authors’ illustration.

5. Conclusion

This study measured the technical efficiency of 28 Indian states (from 2009–2010 to 2020–2021) in providing elementary education. Technical efficiency has been measured using the stochastic frontier model for panel data developed by Battese and Coelli (1995), which requires the simultaneous estimation of the elementary education frontier production function and inefficiency effects model. Any deviation from the frontier indicates that there is scope for the state governments to improve education outcome without increasing public expenditure.

The statistical significance of γ validates the SFA model. It reveals that 82.42 per cent of the interstate variation in elementary education output is explained by technical inefficiency. Empirical results show that higher public expenditure positively impacts retention rates, but diminishing returns occur beyond a certain point. To optimise resource allocation, the government should regularly evaluate and adjust budgets based on impact assessments. Prioritising investments in schooling infrastructure and upskilling teachers is crucial for achieving better outcomes. Tailored interventions are essential for addressing inefficiencies in rural areas. Promoting literacy through campaigns and raising awareness about the benefits of education can improve efficiency. The government must foster collaborations with private entities to ensure efficient resource utilisation while expanding access to education. Targeted support for marginalised groups, especially SC and ST children, can improve efficiency. Re-evaluating teacher employment policies in favour of regular appointments and continuous policy monitoring are recommended for sustained improvements.

The estimated overall technical efficiency of states is 79 per cent, indicating that about 21 per cent of states’ potential output is not yet realised. On average, efficiency varied widely (52 to 94.5 per cent) among states, with Goa, Haryana and Kerala being the most efficient, while Arunachal Pradesh, Meghalaya and Manipur were the least efficient. Efficiency improved in Uttar Pradesh, Bihar, Gujarat, Haryana, Maharashtra, Meghalaya, Sikkim, Odisha and Rajasthan. However, it declined in Arunachal Pradesh, Chhattisgarh, Jharkhand, Jammu and Kashmir, Mizoram, Nagaland, Madhya Pradesh, Punjab and Tamil Nadu.

The retention rates and efficiency score patterns indicate that states such as Kerala, Himachal Pradesh, Haryana and Goa exhibit high efficiency alongside positive outcomes. However, Arunachal Pradesh, Manipur, Mizoram, Nagaland and Meghalaya suffer from poor outcomes attributed to inefficient resource allocation. Bihar, Tripura, Uttar Pradesh, Madhya Pradesh, West Bengal and Odisha demonstrate above-average efficiency but yield low outcome, suggesting potential resource scarcity. Jharkhand, Jammu and Kashmir, Assam and Rajasthan appear to confront a dual challenge of resource scarcity and technical inefficiency. These findings are consistent with the research of Sankar (2007) and Dutta (2012).

The study emphasises the need for public policy interventions to improve the performance of the states. Resource-poor states can benefit from increased public expenditure, while inefficient states can achieve substantial improvements through efficient use of existing resources. These findings can offer valuable insights for policymakers and aid in addressing regional imbalances and improving elementary education outcomes.

Footnotes

Declaration of Conflicting Interests

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

Funding

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

Notes

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