Inter-state Disparities of Efficiency in Foreshortening Under-five Mortality Rate in Rural India

Abstract

The present study aims to assess the efficiency of the rural health system to foreshorten the under-five (U5) mortality rates across Indian states. The study further attempts to pinpoint the factors responsible for state-level inefficiency of the rural health system performance. The empirical results reveal that among the Indian states, Kerala is the most-efficient in foreshortening the U5 mortality rate. The results convey that the states with better health indicators may not have efficient health systems. The study concludes that along with investment in the health sector, efficient management of the investment is intrinsic to better health outcomes.

Keywords

Under-five mortality rate stochastic production frontier inefficiency effects model maximum likelihood estimates fixed effects (within) regression Pesaran’s test Hausman Test

Introduction

India is the home of more than 2,000 ethnic groups (US Department of State 2012) that exhibits vast regional diversity concerning culture, lifestyle, religion, language, etc. Naturally, the socio-cultural beliefs are also different from region to region. Starting from the food habits to the level of health, every state is distant from one another. The health statuses of the states differ in every aspect. There are ample studies that show the geospatial differences in health aspects in India (Kumar et al. 2012). Health is one of the barometers of human development. Discrepancies across the Indian states can also be recognised based on the HDI values and ranking. According to UNDP, Human Development Report (2018), Kerala ranks top in terms of HDI (0.779). On the contrary, the least achiever in the list is Bihar with an HDI value of 0.576 and recognised as a medium human development state. Moreover, according to the global healthcare access and quality (HAQ) index, India ranked 145 out of 195 countries in 2016 (Fullman et al. 2018). After the Millennium Development Goals (MDG), India is also among those countries to initiate different health-related schemes to combat maternal and child mortality. Yet, after all these interventions, the maternal mortality ratio was 122 per one 1,000,000 live births in 2015–17. The Infant Mortality Rate in India was 30 per 1,000 live births in 2018, whereas the under-five mortality rate (U5MR) was few deaths ahead at 37 per 1,000 live births in 2018. Restraining U5 mortality is more important than the infant mortality rate, as children between 1 and 5 years are more prone to death. Infants receive better care and nutrition from the mother than the U5 children (Anand and Bärnighausen 2004). Recently, Bora (2020) studied the factors that cause the regional variation in U5 mortality, and suggested a region-specific intervention for the improvement in child survival in India. The states are different concerning the efficient utilisation of healthcare services. Moreover, there are rural–urban discrepancies in the availability of healthcare facilities in India. In fact, rural India is lagging behind the urban when the goal is reducing U5MR. According to sample registration system (SRS) (2016) report, the U5MR in rural and urban Indian was 43 and 25, respectively. Consequently, studies concentrating on the rural health system are essential. This motivates us to further dwell on the rural healthcare scenario of the different states of India, considering U5MR as the output variable. The choice of the output variable and the applied methodology makes it the pioneering attempt of this kind.

The estimation of the efficiency of healthcare is necessary for policy formulation. But investigating the efficacy of the healthcare system is not a very easy process. Healthcare being a purely social sector determining a purely economic production function, which is necessary to assess the efficiency, is a very difficult process. Though the health sector is a social sector with government intervention, where a definite production function is not followed, but researchers like Murray and Frenk (2001) and Evans et al. (2000) measured the healthcare efficiency in their way. The application of the Murray and Frenk (2001) and Evans et al. (2000) model in the Indian context can be found in the work of Kathuria and Sankar (2005). Drèze and Khera (2012) studied the regional pattern in India in terms of human and child deprivation and found that the regions vary for different aspects of social development deprivation. Cavatorta et al. (2015) also evaluated cross-state disparities in child nutrition in rural India.

It is patently true that there exist other factors that differentiate the health attainments for each country and/ or state. With the same level of inputs also, some states may differ in the attainments, and thus there are factors outside health sectors that affect healthcare and health outcomes (Genowska et al. 2015; Rajkumar and Swaroop 2008; Sankar and Kathuria 2004). This further establishes the fact that the states differ in terms of the efficient utilisation of available resources.

With this backdrop, the objective of the present article is twofold; initially, an attempt is made to analyse and compare the efficiency in the performance of rural health system in foreshortening U5MR across Indian states. Then, the article tried to pinpoint the factors responsible for inefficiency in the rural health system performance.

The article is structured as follows: The next section discusses the concept of health system performance and efficiency. After that, econometric models for our analysis are specified. The successive section reveals data information and deals with the variables’ descriptions used for this study. Then, the results are analysed and the possible reason behind these results are discussed. Last, the article concludes with policy implications.

Concept and Methodology

In terms of the neoclassical production function, efficiency is defined as the act of the economic agent to produce specified output at minimum costs. However, when the matter of concern is healthcare, the aftermath is most important. In this circumstance, we need to pinpoint the health agents who are performing preferably than the others and by exploring the constituents that are helping in amplifying their performances. In an attempt to recon the efficiency of different Indian states in abbreviating U5MR, the notion of health system efficiency is elucidated following Murray and Frenk (2001) and Evans et al. (2000). Based on earlier studies, the desired aim (goal) of the health system, in our case foreshortening of U5MR, is measured on the vertical axis as shown in Figure 1.

Figure 1.

Source: Adapted from Murray and Frenk (1999) and Evans et al. (2000).

On the contrary, the inputs to attain the desired outcome are measured on the horizontal axis. The upper line in the figure delineates the maximum possible health aftermath attainable from the given set of health inputs. In literature, it is designated as frontier after Farrell (1957). On the contrary, the lower line in the figure portrays the level of attainable health sequel in the absence of any health system. The principal contrast between the farm output and health system outcome is that in the absence of inputs, farm output would be zero, but the health outcome would not be zero in the absence of any health expenditures, as all individuals in a nation will not die together.

We are presuming that the country and/ or the state has accomplished (x + y) units of health outcomes. The maximum possible attainable health outcome is (x + y + z; see Figure 1). Under this diegesis, Murray and Frenk (2001) and Evans et al. (2000) defined system performance as:

y / (y + z)

(1)

where (y + z) is the potential outcome and y is the level of health outcome achieved.

Thus, Equation (1) can be interpreted as system achieves compared to its potential (Murray and Frenk 1999). There are two alternative methods for measuring the maximum attainable health outcomes from an accessible set of resources, viz., cost-effectiveness analysis (CEA) and production frontier analysis (Sankar and Kathuria 2004). In the frontier framework, technical efficiency is defined as the farm’s capability to produce the maximum possible output from a given set of inputs. It is measured by the ratio of the observed to the maximum achievable outputs. In terms of Figure 1, it means the ratio, (x + (y)/(x + (y + (z). This definition is known as the output-based measure of technical efficiency (Maity 2011). We adopt this definition for measuring the performance of the health system of different states of India in the foreshortening of U5MR.

Econometric Model

In the beginning, we consider a stochastic frontier production function for the panel data,

y_{i t} = f (x_{i t}, β) \exp (V_{it}) T E_{i t}

(2)

where y is the health outcome, x and β stand for the vector of arguments of the production function, viz., access and availability of the health infrastructure inputs, which are directly influencing the health outcomes and the vector of the coefficients, respectively; all the variables being expressed in logarithm.exp(V) is the random error term and the subscript i refers to the particular cross-section, viz., the ith state (i = 1, 2, …, N) and t refers to the tth (t = 1, 2, …, T) time period.

The firm-specific technical efficiency (Kumbhakar 1991), which is assumed to be a random variable, may be written as TE_it = exp _(–_). Since TE ≤ 1, hence U_it ≥ 0, that is, this error is one-sided. So, we can write Equation (2) as:

$y_{i t} = f (x_{i t}, β) \exp (V_{i t}) \exp (- U_{i t})$

(3)

Where x is a (1 × m) vector of explanatory variables is associated with the technical inefficiency of production of firms over time and across cross-section and δ is a (m × 1) vector of unknown coefficients.

V_it is distributed as N(0,σ²) and captures random variation in output due to factors outside the control of the firm (weather, acts of God, etc.) and independently distributed of the U_its. On the contrary, U_its are non-negative random variables associated with the technical inefficiency of production, such that U_it is obtained by truncation (at zero) of the normal distribution with mean,zδ, and variance, σ², that is, V_it ∼ IIDN(0, σ²) and U_it ∼ IIDN(zδ, σ²). Further, estimation of the model is possible by using single equation technique if we assume U_it and V_it are independent of each other and also independent of x.So, the underlying model is normal–truncated normal, as introduced by Stevenson (1980).

Following Battese and Coelli (1995), the technical efficiency of the health sector for the ith state at tth time period, TE, in the stochastic frontier model (3) could be specified in Equation (4).
$T E_{i t} = \exp (- U_{i t}) = \exp (- z_{i t} δ - W_{i t})$
(4)

Equation (4) represents the technical inefficiency effects equation (Battese and Coelli 1995). The regression equation involves an error term W_it, which is the error term of the technical inefficiency effects equation. The random variable W_it is the distribution with zero mean and variance σ². Thus, like the other two error terms, it is also distributed as truncated normal, such that the point of truncation is –zδ, that is, W_it ≥ –zδ. These assumptions are consistent with U_it being a non-negative truncation of the N(z δ, σ²) distribution.

The maximum likelihood estimation technique is the best way to estimate simultaneously the parameters of the stochastic frontier and the technical inefficiency model (Battese and Coelli 1995). Following Battese and Coelli (1993), the likelihood function is expressed in terms of the variance parameters, viz., $σ^{2} = σ_{V}^{2} + σ_{U}^{2}$ and $γ = \frac{σ_{U}^{2}}{σ^{2}}$ , where γ lies between 0 and 1 depending on the dominance of σ and σ, respectively. The maximum-likelihood estimation (MLE) of the equations is obtained by using the FRONTIER-4.1 programme (Coelli 1996).

Data and Variables

This section discusses the data sources and the relevant variables required for the empirical analysis.

Data

The study is based on secondary data. The empirical analysis is conducted by considering 19 bigger states of India over the time period 2008–09 to 2016–17. The selection of the sample period and states are dictated by data availability. A detailed description of the variables, data sources and the earlier studies in support of data identification are provided in Table 1.
Table 1.
Description of Variables of the Frontier Model for Different States of India.

Variable Name Variable Description Variable Category Supported by Earlier Studies Data Source

Under-five mortality rate (U5MR) (y) Probability of a child born to not live up to the age of five years Output Anand and Barninghausen (2004) SRS Bulletin, Office of the Registrar General, India

Number of sub centres (SC) (x₁) The first contact point to provide primary health care Input Sankar and Kathuria (2004) Rural Health Statistics, Ministry of Health & Family Welfare, Government of India, (RHS, MoHFW, GOI)

Number of primary health centres (PHC) (x₂) PHCs provide regular treatment along with child immunisation programme, pregnancy-related care, etc Input Sankar and Kathuria (2004) RHS, MoHFW, GOI

Number of community health centres (CHC) (x₃) This is also a part of providing basic treatment Input Sankar and Kathuria (2004) RHS, MoHFW, GOI

Number of doctors (DOCTORS) (x₄) Medical professionals with relevant degrees Input Sankar and Kathuria (2004) RHS, MoHFW, GOI

Number of nurses (NURSES) (x₅) Trained persons to provide care to the medically ill persons Input Sankar and Kathuria (2004) RHS, MoHFW, GOI

Mean years of marriage (state level data) (MYM) (z₁) The average age of marriage Exogenous Prakash, et al. (2011) Family Welfare Statistics, MoHFW, GOI; Central Statistics Office, Ministry of Statistics and Programme Implementation, (CSO, GOI)

Per Capita NSDP at constant price (PCNSDP) (z₂) NSDP is the state counterpart of a country’s net domestic product Exogenous Barenberg, et al. (2017) CSO, GOI

Gross Enrolment Ratio (GER-1) (z₃), (GER-2) (z₄), (GER-3) (z₅) GER-1, GER-2, GER-3, implies Gross Enrolment Ratio in primary, secondary and senior secondary level. It has been taken as a proxy of literacy rate Exogenous Asafu-Adjaye (2004) Department of School Education and Literacy, Ministry of Human Resource Development, GOI

Rural Gini Coefficient (Gini) (z₆) The rural income inequality is represented by Rural Gini Coefficient Exogenous Asafu-Adjaye (2004) NitiAyog, India

Rural Women Work Force Participation Rate (RWWFPR) (z₇) Participation of women workers in the economy Exogenous Suriyakala, et al. (2016) CSO, GOI

Rural total fertility rate (TFR) (z₈) Total number of children born or likely to be born to a woman in her lifetime Exogenous Suriyakala, et al. (2016) SRS Bulletin, Office of the Registrar General, India

Source: The authors.

Note: SRS; Sample registration system.

Variables

Three types of variables are essential for applying the stochastic production frontier approach to measure health system efficiency (Evans et al. 2001; Sankar and Kathuria 2004). First, we need an output indicator representing the performance of the health sector. Second, we need to specify a comprehensive set of inputs. Finally, we also need to include some non-health variables, recognised as exogenous variables, which affects the health outcome either positively or negatively. The identification of all the variables is accomplished based on the pertinent literature (Anand and Bärnighausen 2004; Asafu-Adjaye 2004; Karpa and Lesniowska 2014; Prakash et al. 2011; Sankar and Kathuria 2004; Suriyakala et al. 2016).

Output Variable

The inter-state comparison of health efficiency can only be pursued if we could identify an appropriate output indicator for the health system. A composite health index delineating all the dimensions of health will be an appropriate health output. Unfortunately, the unavailability of data restricts us from considering such health output. In the absence of a composite health index, we are bound to consider clinical outputs, such as life expectancy at birth (LEB), infant mortality rate (IMR) and U5MR. LEB or disability adjusted life expectancy is a better outcome to represent the health condition (Dubey et al. 2015; Murray and Lopez 1997). The LEB data is available at a gap of 5 years. Accordingly, we cannot form annual panel series. The annual panel series is important for a better understanding of the rural health scenario. Consequently, we have two health yardsticks as output variables for this study, viz., reduction of IMR and foreshortening of U5MR. The MGD emphasised the reduction of IMR while Sustainable Development Goals (SDG) stressed foreshortening U5MR to at least as low as 25 per 1,000 live births by the end of 2030 (SDG-3, WHO n.d.). Earlier studies by Sankar and Kathuria (2004) considered the reciprocal of IMR as heath output. IMR and U5MR are measures of child mortality. In India, the U5MR is 37 per 1,000 live births, whereas it is 30 for IMR in 2018. The children between the age group 1–4 years are more vulnerable to the risk of death than infants, as the infants are better-protected by breastfeeding and other maternal efforts (Anand and Bärnighausen 2004). Hence, keeping these facts in view, we have considered the reciprocal of rural U5MR for different states as the outcome variable to scrutinise the efficiency of the health sector in India.

Input Variables

Apropos inputs, we have two alternatives; either we can use the monetary expenditures on health (such as per-capita expenditures on public health) or the physical inputs. As the study is based on panel data, the non-availability of the data compelled us to consider the physical inputs. The list of the input variables along with their definition is furnished in Table 1.

A perusal of the table reflects that as inputs we have considered only the health infrastructure variables, viz., numbers of Sub-centres, number of Doctors, Nurses, etc. It is worth noting that all the variables were standardised for the total population covered (using the availability of facilities per 1,00,000 population). The same table also discloses the major data sources and the earlier studies based on which the input variables are determined.

Exogenous Variables

It is a well-established fact that improved health is not an exclusive outcome of the health service providers (Murray and Frenk 1999). This is patently true for the inter-state rural health system. Some pioneering studies accentuate the influence of non-health determinants, viz., income, educational level measured differently (Schultz 1963), the mean age of marriage (Prakash et al. 2011), Per Capita NSDP (Barenberg et al. 2017), inequality (Asafu-Adjaye 2004; Karpa and Lesniowska 2014), etc. In the present study, we have considered several non-health variables that have a strong influence on the rural health system efficiency of different Indian states. However, these variables cannot be categorised as the input variables. We recognise these variables as exogenous variables. The list of the exogenous variables, definitions and the supportive earlier studies are mentioned in Table 1. The production function we have considered here is a log-linear version of the Cobb–Douglas production function.

The model to be estimated is presented by Equation (5).
$\begin{matrix} \ln [{(\frac{1}{U 5 M R})}_{i t}] = α_{0} + α_{S C} \ln (S C_{i t}) + α_{p H C} \ln (P H C_{i t}) + α_{C H C} \ln (C H C_{i t}) + \\ α_{D O C} \ln (D O C_{i t}) + α_{N U R} \ln (N U R_{i t}) + (V_{i t} - U_{i t}) \end{matrix}$
(5)

where ln is the natural logarithm (i.e., to the base e).

The technical inefficiency effects are presumed to be defined by the following equation:
$\begin{array}{l} U_{i t} = δ_{0} + δ_{M S Y} \ln (M S Y_{i t}) + δ_{P C N S D P} \ln (P C N S D P_{i t}) + δ_{G E R - 1} \ln (G E R - 1_{i t}) + δ_{G E R - 2} \ln (G E R - 2_{i t}) + \\ δ_{G E R - 3} \ln (G E R - 3_{i t}) + δ_{G i n i} \ln (G i n i) + δ_{W R W F P R} \ln (W R W F P R) + δ_{T P R} \ln (T F R) + W_{i t} \end{array}$
(6)

It is noteworthy that the model is developed by following Battese and Coelli (1995) model. The Equations (5) and (6) are estimated by using FRONTIER 4.1, developed by Coelli (1996).

Results and Discussion

This section discusses the empirical results.

The Scenario of Rural Under-five Mortality Rate of Different Indian States

There are discrepancies across Indian states concerning the reduction of U5MR. Figure 2 shows graphically the achievements of different Indian states in the foreshortening of the U5MR.

Figure 2.
Source: Authors’ own presentation based on SRS data.

The figure reveals that the lowest mean U5MR is obtained for Kerala and the corresponding highest figure is obtained for Madhya Pradesh. The figure discloses that only three Indian states, viz., Kerala, Maharashtra and West Bengal have attained the target set by the ‘SDG’ related to the U5MR up to 2017, that is, 39 per 1,000 live births. It is noteworthy that only Kerala among Indian states is successful in achieving the goal of SDG-3 much before the stipulated time 2030 concerning neo-natal mortality (at least as low as 12 per 1,000 live births) and U5MR (at least as low as 25 per 1,000 live births) (WHO n.d.).

Thus, it is appropriate to investigate the discrepancies in the achievement related to U5MR across Indian states.

Pesaran's Test for Cross-sectional Independence

A comprehensive panel data literature surmises that panel data models are likely to exhibit substantial cross-sectional dependence in the errors (Baltagi 2005). Such interdependencies will not only make the fixed effects and random effects estimators biased, but also inconsistent. Consequently, it is highly endorsed that one should test the independence of the cross-sectional error before proceeding with estimation. The widely accepted test for this purpose was proposed by Pesaran (2006). The Pesaran test result is obtained in the present article by using STATA-12 and the corresponding test result is presented in Table 2.
Table 2.
Pesaran's Test of Cross-sectional Independence.

Pesaran’s Test of cross-sectional Independence Average Absolute Value of the Off-diagonal Elements Probability

–0.155 0.386* 0.8769

Source: Authors’ own calculation based on SRS data.

Note: *Esvidence shows data are cross-sectionally independent.

The result divulges that Pesaran’s test of cross-sectional independence value is −0.155 with a probability 0.8769. The corresponding average absolute value of the off-diagonal elements is 0.386. The CD test result strongly recommends the acceptance of the null hypothesis of no cross-sectional dependence. Thus, we can proceed with rest estimation.

Random-effects and Fixed-effects Regression and Hausman Test

In the present study, as we are dealing with the panel data, we have estimated both the fixed effects (within) (FE) and random effects (RE) generalised least square (GLS) models. The estimated result is presented in Table 3. The descriptive statistics of the variables are presented in ***Table A1.
Table 3.
Random-effects GLS Regression and Fixed-effects (within) Regression of stochastic production frontier function for whole panel.

Variable Random-effects GLS Fixed-effects (within)

Coefficients SE t-ratio Coefficients SE t-ratio

Constant –15.341*** 1.427 –10.75 –16.135*** 1.493 –10.81

SC 0.386*** 0.124 3.11 0.415*** 0.136 3.04

PHC –0.066 0.106 –0.62 –0.011 0.119 –0.09

CHC –0.033 0.066 –0.5 0.024 0.071 0.34

DOCTORS 0.088*** 0.043 2.06 0.122*** 0.043 2.80

NURSES –0.026 0.027 –1.00 –0.018 0.027 –0.65

MYM 1.518*** 0.352 4.31 1.271*** 0.368 3.45

PCNSDP 0.442*** 0.077 5.73 0.515*** 0.085 6.06

GER-1 –0.049 0.102 –0.48 –0.069 0.102 –0.68

GER-2 0.133 0.098 1.35 0.174* 0.096 1.81

GER-3 0.063 0.047 1.36 0.060 0.046 1.31

Gini 0.039 0.113 0.35 –0.065 0.121 –0.53

RWWFPR –0.086*** 0.019 –4.49 –0.075*** 0.019 –3.87

TFR –0.477*** 0.128 –3.71 –0.384*** 0.139 –2.77

R² (Within) 0.843 0.843

R² (Between) 0.511 0.511

R² (Overall) 0.566 0.566

Sigma_u 0.250 0.342

Sigma_e 0.078 0.078

Rho 0.911 0.951

No. of observations 171 171

Source: Authors’ own calculation based on SRS data.

Note: ***, ** and * Significance at 1%, 5% and 10% level, respectively.

A close perusal of the Table 3 discloses that the reduction of U5MR is significantly and positively influenced by the health infrastructure inputs, such as numbers of sub-centres and numbers of doctors. Among the exogenous variables, the table divulges that MYM and PCNSDP positively and significantly, and rural female workforce participation rate and total fertility rate (TFR, rural) negatively and significantly, influence the foreshortening of U5MR. The influence of GER-2 is significant only in the FE model. The possible reasons for the empirical results are discussed in the discussion section. The R² values indicate the superiority of the FE model over the RE model. The model selection is facilitated by the Hausman specification test. The test result is summarised in Table 4.
Table 4.
Hausman Test to Choose Between Random-Effects Model and Fixed-Effects Model.

Variables Coefficients Difference (b – B) χ ₁₃ ² Prob. > χ²

Random effects Fixed effects

SC 0.415 0.386 0.029 60.20* 0.0000

PHC –0.011 –0.066 0.055

CHC 0.024 –0.033 0.057

DOCTORS –0.122 –0.088 –0.034

NURSES –0.018 –0.026 0.009

MYM 1.271 1.518 –0.247

PCNSDP 0.515 0.442 0.073

GER-1 –0.069 –0.049 –0.020

GER-2 0.133 0.174 –0.041

GER-3 0.060 0.063 –0.003

Gini –0.065 0.039 –0.103

RWWFPR –0.075 –0.086 0.011

TFR –0.384 –0.477 0.093

Source: Authors’ own calculation based on SRS data.

Note: *Evidence shows Fixed Effects model is appropriate.

The χ²₁₃ value is 60.20 with the corresponding prob.> χ² = 0.00, validating the appropriateness of FE model here. This result also authorises us to utilise the technical inefficiency effects in a stochastic production function for panel data (Chisholm and Evans 2010).

Efficiency Estimates of Rural Health System for Different States of India

The efficiency scores for different Indian states and their corresponding rankings are discussed in this section. The result is summarised in Table 5.
Table 5.
Efficiency Estimates of Rural Health System for Different States of India.

States\Year
↓ → PME* Ranking

2008–2009 2009–2010 2010–2011 2011–2012 2012–2013 2013–2014 2014–2015 2015–2016 2016–2017

Andhra Pradesh 0.126 0.130 0.153 0.153 0.164 0.171 0.205 0.215 0.229 0.172 14

Assam 0.118 0.124 0.125 0.138 0.160 0.166 0.183 0.217 0.234 0.163 16

Bihar 0.092 0.100 0.109 0.117 0.123 0.127 0.141 0.200 0.233 0.138 18

Chhattisgarh 0.160 0.172 0.188 0.201 0.217 0.219 0.245 0.252 0.263 0.213 12

Gujarat 0.175 0.184 0.194 0.217 0.229 0.242 0.240 0.241 0.270 0.221 9

Haryana 0.192 0.230 0.232 0.273 0.286 0.301 0.314 0.300 0.241 0.263 8

Himachal Pradesh 0.302 0.301 0.302 0.333 0.376 0.394 0.434 0.515 0.580 0.393 3

Jammu and Kashmir 0.230 0.259 0.261 0.286 0.410 0.386 0.452 0.492 0.431 0.356 4

Jharkhand 0.130 0.135 0.143 0.157 0.168 0.175 0.184 0.223 0.239 0.173 13

Karnataka 0.206 0.232 0.260 0.297 0.317 0.322 0.364 0.364 0.363 0.303 7

Kerala 0.917 0.905 0.802 0.905 1.000 1.000 0.925 0.926 0.828 0.912 1

Madhya Pradesh 0.112 0.116 0.125 0.134 0.139 0.147 0.144 0.156 0.165 0.138 19

Maharashtra 0.223 0.245 0.280 0.319 0.319 0.329 0.369 0.356 0.345 0.309 6

Orissa 0.176 0.162 0.202 0.188 0.207 0.213 0.240 0.259 0.274 0.213 11

Punjab 0.228 0.242 0.256 0.298 0.337 0.366 0.429 0.420 0.413 0.332 5

Rajasthan 0.112 0.118 0.130 0.138 0.205 0.174 0.178 0.187 0.199 0.160 17

Tamil Nadu 0.267 0.285 0.347 0.357 0.385 0.415 0.412 0.416 0.666 0.394 2

Uttar Pradesh 0.109 0.119 0.129 0.138 0.158 0.167 0.193 0.222 0.271 0.167 15

West Bengal 0.175 0.188 0.197 0.192 0.197 0.213 0.263 0.272 0.270 0.219 10

Mean Efficiency (yearly) 0.213 0.224 0.234 0.255 0.284 0.291 0.311 0.328 0.343 0.276

Mean Efficiency (overall) 0.276

Source: Authors’ own calculation based on SRS data.

Note: *Panel Mean Efficiency of the states.

The analysis of inter-state relative efficiency of the rural health system is facilitated by considering ‘overall mean efficiency’ (0.276) as the benchmark of comparison (Maity and Neogi 2014). Accordingly, the state for which the efficiency score exceeds the ‘overall mean efficiency’ will be recognised as relatively technically efficient and vice-versa. Based on this benchmark, our observation is that only 7 out of 19 states are technically efficient. It is worth noting that the rankings of the states are pursued by considering panel mean efficiency scores. In the initial period, 2008–09, the most efficient state was Kerala. Importantly, Kerala maintains its position throughout the study period. Kerala upkeeps its top position concerning panel mean efficiency also. The state tops the list with a panel mean efficiency score of 0.912 and having a mean U5MR of 14. The observation regarding the least efficient state divulges that two states are least-efficient in different time periods. Bihar is recognised as the least-efficient state over the periods 2008–09 to 2014–15. Thereafter, Madhya Pradesh became the least-efficient state for the rest of the study period. It is noteworthy that based on the panel mean efficiency score, Madhya Pradesh is recognised as the least-efficient state, preceded by Bihar. The rankings of these two states are 18th and 19th, respectively, among 19 sampled states. Our finding with regards to Kerala was supported by the earlier research conducted by Sankar and Kathuria (2004) and Kathuria and Sankar (2005). As no other study was ever conducted concerning the performances of the rural health system across Indian states, it is impossible to cross-check the result with other studies, except those two mentioned above.

It must be recalled that the state’s ranking based on efficiency score only shows the relative performance of the concerned state and does not designate any hierarchy concerning actual health outcomes. For instance, the relative panel mean efficiency score for Bihar is only 0.138 and the state holds eighteenth position out of 19 states, in the list. However, while considering the actual health accomplishment, Bihar’s position is 13 out of 19 states with a mean U5MR, 59. The efficiency score of the existing health system stipulates that if Bihar could operate its health system as efficiently as Kerala, the state could have reduced the U5MR Rate to 14 (Kerala’s mean U5MR).

Analysis of Stochastic Frontier Model: Factors Affecting Efficiency

The estimated coefficients of Equations (5) and (6), portraying the result of the stochastic production frontier and the inefficiency effects, are analysed in this section. These estimates, together with the estimated standard errors of the maximum-likelihood estimators, given to three significant digits, for the entire study period are presented in Table 6.

Table 6.
Maximum Likelihood Estimates of the Stochastic Production Frontier Function of Health Performance of Different States of India.

Variables Coefficients SE t-Ratio

Constant β ₀ –5.030* 0.321 –15.689

ln(SC) β ₁ 0.870* 0.114 7.643

ln(PHC) β ₂ 0.707* 0.088 8.002

ln(CHC) β ₃ 0.264* 0.061 4.295

ln(DOC) β ₄ 0.192* 0.057 3.347

ln(NUR) β ₅ –0.005 0.035 –0.150

ln(MYM) δ ₁ –3.633* 0.540 –6.733

ln(PCNSDP) δ ₂ –0.331* 0.067 –4.922

ln(GER-1) δ ₃ –0.438* 0.193 –2.266

ln(GER-2) δ ₄ –0.567* 0.162 –3.500

ln(GER-3) δ ₅ 0.047 0.078 0.605

ln(Gini) δ ₆ –0.521* 0.100 –5.239

ln(RWWFPR) δ ₇ 0.113* 0.035 3.222

ln(TFR) δ ₈ 0.576* 0.111 5.190

${\hat{σ}}_{s}^{2}$ 0.043* 0.005 9.133

γ 1.000* 0.000 2,973,447.600

µ 18.973* 2.254 8.418

Log(likelihood) –28.020

LR test 214.543

Source: Authors’ own calculation based on SRS data.

Note: *Significant at 1% level.

Dependent variable: LDU5MR (log of 1/U5MR); no. of observations: 171.

The estimated regression equations are presented below:

Stochastic frontier

$\begin{array}{l} \ln (\frac{1}{U 5 M R}) = - 5.030 + 0.8701 \ln (S C) + 0.707 \ln (P H C) + 0.264 \ln (C H C) + \\ \begin{matrix} (0.321) (0.114) (0.088) \end{matrix} \\ 0.192 \ln (D O C) - 0.005 \ln (N U R) \\ (0.057) (0.035) \end{array}$
(7)

Inefficiency model

$\begin{array}{l} U = - 3.633 \ln (M S Y) - 0.331 \ln (P C N S D P) - 0.438 \ln (G E R - 1) - 0.567 \ln (G E R - 2) + \\ \begin{matrix} (0.540) (0.067) (0.193) (0.162) \end{matrix} \\ 0.047 \ln (G E R - 3) \\ (0.078) \\ - 0.521 \ln (G i n i) + 0.113 \ln (R F W P R) + 0.576 \ln (T F R) \\ (0.100) (0.035) (0.111) \end{array}$
(8)

The absence of multicollinearity is authenticated by ****Table A2. The empirical results concerning production function discloses that the estimated coefficients of ln(SC), ln(PHC), ln(CHC) and ln(DOC) not only have the appropriate sign but are also statistically significant. In fact, ln(SC) and ln(DOC) are also found to be significant in both FE and RE models. Like FE and RE models, the estimated coefficient of the input variable ln(NUR) is statistically insignificant with an unsuitable sign.

Sub-centre is recognised as the first contact point between the primary health care system and the community. Thus, the up-gradation of the first contact point undoubtedly will revamp the health outcome of any area. In rural areas, ASHA, peripheral health workers, especially ANMs and Anganwadi workers, and trained Dais accomplish the role of nurses, and perhaps this is the reason for the insignificant role of ln (NUR).

The estimated coefficients in the inefficiency model are of particular interest to this study. The negative sign of the estimated coefficient of the inefficiency effects variable mean years of marriage (MYM) stipulated that the state with lower MYM are relatively more inefficient than the state with higher MYM. A similar result is also obtained in the FE and RE models. As both the FE and RE models represent input–output relation, consequently, in both models the sign of the estimated coefficient MYM is positive. The positive sign of MYM in the FE and RE models indicate that the states with higher MYM are more successful in reducing U5MR than the state with lower MYM. The result re-establishes customary facts. An early marriage forebodes early motherhood. Under such circumstances, neither the body nor mind of the youngest mother will be ready for parturition. Even after proper health care, the likelihood of maternal mortality as well as U5MR will be escalated. Thus, the state which maintains strict law and order associated with the age of marriage and improves educational provision for girls will certainly be more efficient.

The education is proxied here by three levels of gross enrolment ratio (GER), viz., elementary, lower secondary and senior secondary, in the absence of annual literacy data. The estimated coefficients of the exogenous variables, elementary and lower secondary GER are negative in sign and statistically significant. The inequality in the distribution of income and wealth has a strong implication on the health outcome of any state, including the achievement of the goal of foreshortening the U5MR (Suriyakala et al. 2016). The rural Gini coefficient is considered here to apprehend rural inequality. The negative and the significant value of the estimated coefficient of this exogenous variable stipulates the state with—lower inequality in the distribution of income and wealth, greater is the likelihood of achieving the goal of foreshortening theU5MR. Likewise, the estimated coefficient of the RWWFPR is positive and significant, predicting a higher rural female work participation rate and a higher inefficiency of the state. Surprisingly, we obtained a similar result concerning RWWFPR for both FE and RE models. The estimated coefficient of TFR suggests that the higher value of the TFR escalates the inefficiency of the state.

All the variance parameters are significant at a different level, and the variance parameter (γ) is found significantly different from zero for a half-normal distribution. This indicates the correctness of the assumption of half-normal distribution related to the error terms. The sigma-squares ${\hat{σ}}_{s}^{2}$ is 0.043 and also statistically significant, indicating the correctness of the specified assumptions of the distribution of the composite error term. The ratio of state-specific variability to total variability (γ) is positive and significant, implying that state-specific technical efficiency is important in explaining the total variability of the health system. Besides, the (γ) estimate associated with the sigma-squared of the technical inefficiency effects is relatively large, indicating the viability of the model.

Discussion

Concerning the instruments and personnel of health services, we get similar results for FE, RE and SPF models. In all the three models, the estimated coefficients of the factors representing health personnel and instrument are found to be statistically significant. The results are re-establishing a patent truth that an escalation of the availability of doctors and health facilities enhances the health outcome including reduction of U5MR (Kathuria and Sankar, 2005; Sankar and Kathuria 2004). We obtained a similar conclusion based on the estimated coefficient PCNSDP concerning all the three models utilised in the article. Earlier studies by Sankar and Kathuria (2004) and Kathuria and Sankar (2005) also obtained a similar result. The NSDP includes social sector expenditures that comprise the state’s expenditures on health and education. Consequently, the likelihood of state spending for the health sector development will be low with lower per-capita NSDP. This may affect population health adversely and may result in higher U5MR (Houweling et al. 2005).

The result concerning GER-2 in the inefficiency effects model is similar to that of the FE model. Following the estimated coefficients of the inefficiency effects model, we conclude that the state with higher elementary and lower secondary GERs are more efficient. This may be due to the reason that education may aware citizens of the freely available health facilities including ante-natal and post-natal care, immunisation etc. Consequently, education helps in improving the health status and foreshortening of U5MR (Schell et al. 2007). The estimated coefficient of Gini is significant only in the inefficiency effects model, and the estimated coefficient predicts that lower inequality results in better health outcomes. This may be because lower inequality means all the members of the population, irrespective of their caste and class will be able to get all the facilities provided by the state and central government for human development including health (Odusanya and Akinlo 2021; Ward and Viner 2017). Conventionally, economic independence gives voice to the voiceless along with decision-making power. Thus, a higher rural female work participation rate may sequel in lower U5MR. However, the estimated coefficient of this exogenous variable is paradoxical in our case predicts higher female participation in the workforce, escalates states inefficiency in foreshortening the U5MR, and we obtained a similar result in all the three employed models. This may be because rural Indian women find employment opportunities in the primary and informal secondary sectors, viz., agricultural labourer, construction labourer, hotel and restaurant workers, food processing workers, etc. In these sectors, no employment policies are applied (Nag et al. 2016). The women workers are forced to work under adverse circumstances. In fact, they do not get fully paid maternity and childcare leave (Gopalakrishnan and Brindha 2017). Such employment neither ensures economic independence nor empowerment (Hill 2010; Pearson 2004). We obtained a similar result concerning TFR for all three models. Apparently, higher TFR is the consequence of early age of motherhood, lower birth interval, etc., connoting an escalation of U5MR (Maïga et al. 2015).

Conclusion and Policy Implication

Health and education are the two fundamental pillars of the transformation of human-to-human capital. In fact, health is one of the principal dimensions of HDI. As mentioned earlier, we find the top and lowest HDI states are Kerala and Bihar. On the contrary, Madhya Pradesh is ranked fourth from below with an HDI value of 0.606 and is also recognised as a medium human development state. In a certain sense, our empirical result concerning efficiency scores is supported by UNDP, Human Development Report (2018). Moreover, the positions of the two states, viz., Madhya Pradesh and Bihar are not surprising as the earlier study by Drèze and Khera (2012) also divulged about their underachievement concerning child mortality.

Based on the socio-economic backwardness, the states Bihar, Chhattisgarh, Jharkhand, Madhya Pradesh, Orissa, Rajasthan, Uttaranchal and Uttar Pradesh are clubbed together as the Empowered Action Group (EAG) states (Arokiasamy and Gautam 2008). Converse to the belief, our empirical finding authorised us to argue that all these EAG states are not very poorly performing concerning health outcomes. For example, Jharkhand, the EAG state ranks 13th among 19 Indian bigger states concerning the efficiency scores, which is at a higher position than the non-EAG state Andhra Pradesh. Moreover, the mean U5MR of this state is much better than many other non-EAG states like Gujarat. Consequently, this result is quite opposite to the belief and the paradoxical finding of the study adds a new avenue of discussion in the existing literature.

It is noteworthy that the present study does not consider the participation of the private sector in healthcare services. The superior performances of Kerala and Tamil Nadu may be due to the prevalence of the private healthcare sector, which is absent in the rural areas in Bihar or Uttar Pradesh.

Based on our findings, we suggest the following policy implications:

First, as we have observed that the accessibility and availability of health infrastructure have a positive impact on efficiency, thus, health-related infrastructure such as health institutions, necessary equipment, etc., should be made more readily available. Second, the health personnel and manpower should be given importance as these factors are positively related to controlling mortality. Third, the level of education, particularly the enrolment at all levels, should be stressed as it is patently true that an educated person can efficiently escape controllable mortality. In conjunction with this, education transmits information makes the person aware of the accessibility of the healthcare delivery system free of cost. Fourth, the family planning programme should be implemented carefully to reduce the TFR. Finally, identifying the importance of the health infrastructures as well as health personnel services, we recommend the administrative surveillance to corroborate the proper utilisation of the healthcare system.

The empirical analysis of the study is based on secondary data across Indian states. Accordingly, the selection of states and variables are dictated by data availability. Consequently, we cannot include variables like ST/SC population share, Mother’s health status, Child Stunting, Underweight, Prevalence of Anaemia, Not Fully Immunised, etc., for the present study. This can be viewed as a limitation of this study. Moreover, the efficiency measured by the FRONTIER-4.1 programme that makes the ranking of the states remains invariant over time. This is also another limitation of the study.

Appendix A

Table A1.
Summary Statistics for Output and Input Variables of the Frontier Model

Variable Mean Median Std. Dev. Skewness Maximum Minimum

U5MR 52.05 51 19.64 0.17 98 13

$\frac{1}{U 5 M R}$ 0.02 0.02 0.01 2.42 0.08 0.01

$\ln (\frac{1}{U 5 M R})$ –3.87 –3.93 0.44 0.99 –2.56 –4.58

SC 7,586.68 7,274 4,508.70 1.05 20521 1907

PHC 1,238.30 1,147 789.66 1.34 3692 297

CHC 258.47 217 157.68 1.16 822 70

DOCTORS 1,384.64 1,048 941.46 0.78 3532 271

NURSES 3,337.36 2,491 2,838.95 1.58 13435 376

MYM 21.65 21.5 1.12 0.66 25.2 19.8

PCNSDP 69,525.96 62,145 30,034.01 0.35 143,211 16,902.55

GER-1 103.22 100.89 12.51 1.28 155.3 79.83

GER-2 75.81 74.78 15.18 0.27 120.31 33.9

GER-3 49.89 48.13 18.62 0.29 100.58 7.4

Gini 0.27 0.26 0.06 1.80 0.52 0.19

RWWFPR 37.14 36.43 16.91 0.50 103.95 0.52

TFR 2.45 2.4 0.65 0.62 4 1.7

Source: Authors’ own calculation based on SRS data.

Table A2.
Correlation Diagnostics

Variables ln(x₁) ln(x₂) ln(x₃) ln(x₄) ln(x₅) ln(z₁) ln(z₂) ln(z₃) ln(z₄) ln(z₅) ln(z₆) ln(z₇) ln(z₈)

ln(x₁) 1

ln(x₂) 0.59 1

ln(x₃) 0.48 0.50 1

ln(x₄) 0.55 0.55 0.41 1

ln(x₅) 0.57 0.57 0.53 0.62 1

ln(z₁) –0.47 –0.27 –0.28 –0.12 –0.21 1

ln(z₂) –0.30 –0.22 0.02 –0.18 0.14 0.40 1

ln(z₃) 0.11 –0.07 0.11 –0.15 –0.14 –0.50 –0.38 1

ln(z₄) –0.18 –0.09 0.05 –0.13 0.00 0.47 0.57 –0.35 1

ln(z₅) –0.18 –0.13 0.06 –0.10 0.08 0.47 0.53 –0.46 0.52 1

ln(z₆) –0.11 –0.06 0.04 –0.13 –0.21 0.18 0.03 –0.19 0.30 0.35 1

ln(z₇) 0.03 –0.04 0.30 –0.12 0.09 –0.03 0.41 0.08 0.44 0.40 –0.04 1

ln(z₈) 0.30 0.24 0.08 0.04 –0.12 –0.52 –0.72 0.40 –0.55 –0.50 0.031 –0.31 1

Source: Authors’ own calculation based on secondary data.

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.

ORCID iD

Shrabanti Maity

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Variable Name	Variable Description	Variable Category	Supported by Earlier Studies	Data Source
Under-five mortality rate (U5MR) (y)	Probability of a child born to not live up to the age of five years	Output	Anand and Barninghausen (2004)	SRS Bulletin, Office of the Registrar General, India
Number of sub centres (SC) (x₁)	The first contact point to provide primary health care	Input	Sankar and Kathuria (2004)	Rural Health Statistics, Ministry of Health & Family Welfare, Government of India, (RHS, MoHFW, GOI)
Number of primary health centres (PHC) (x₂)	PHCs provide regular treatment along with child immunisation programme, pregnancy-related care, etc	Input	Sankar and Kathuria (2004)	RHS, MoHFW, GOI
Number of community health centres (CHC) (x₃)	This is also a part of providing basic treatment	Input	Sankar and Kathuria (2004)	RHS, MoHFW, GOI
Number of doctors (DOCTORS) (x₄)	Medical professionals with relevant degrees	Input	Sankar and Kathuria (2004)	RHS, MoHFW, GOI
Number of nurses (NURSES) (x₅)	Trained persons to provide care to the medically ill persons	Input	Sankar and Kathuria (2004)	RHS, MoHFW, GOI
Mean years of marriage (state level data) (MYM) (z₁)	The average age of marriage	Exogenous	Prakash, et al. (2011)	Family Welfare Statistics, MoHFW, GOI; Central Statistics Office, Ministry of Statistics and Programme Implementation, (CSO, GOI)
Per Capita NSDP at constant price (PCNSDP) (z₂)	NSDP is the state counterpart of a country’s net domestic product	Exogenous	Barenberg, et al. (2017)	CSO, GOI
Gross Enrolment Ratio (GER-1) (z₃), (GER-2) (z₄), (GER-3) (z₅)	GER-1, GER-2, GER-3, implies Gross Enrolment Ratio in primary, secondary and senior secondary level. It has been taken as a proxy of literacy rate	Exogenous	Asafu-Adjaye (2004)	Department of School Education and Literacy, Ministry of Human Resource Development, GOI
Rural Gini Coefficient (Gini) (z₆)	The rural income inequality is represented by Rural Gini Coefficient	Exogenous	Asafu-Adjaye (2004)	NitiAyog, India
Rural Women Work Force Participation Rate (RWWFPR) (z₇)	Participation of women workers in the economy	Exogenous	Suriyakala, et al. (2016)	CSO, GOI
Rural total fertility rate (TFR) (z₈)	Total number of children born or likely to be born to a woman in her lifetime	Exogenous	Suriyakala, et al. (2016)	SRS Bulletin, Office of the Registrar General, India

Pesaran’s Test of cross-sectional Independence	Average Absolute Value of the Off-diagonal Elements	Probability
–0.155	0.386*	0.8769

Variable	Random-effects GLS			Fixed-effects (within)
Variable	Coefficients	SE	t-ratio	Coefficients	SE	t-ratio
Constant	–15.341***	1.427	–10.75	–16.135***	1.493	–10.81
SC	0.386***	0.124	3.11	0.415***	0.136	3.04
PHC	–0.066	0.106	–0.62	–0.011	0.119	–0.09
CHC	–0.033	0.066	–0.5	0.024	0.071	0.34
DOCTORS	0.088***	0.043	2.06	0.122***	0.043	2.80
NURSES	–0.026	0.027	–1.00	–0.018	0.027	–0.65
MYM	1.518***	0.352	4.31	1.271***	0.368	3.45
PCNSDP	0.442***	0.077	5.73	0.515***	0.085	6.06
GER-1	–0.049	0.102	–0.48	–0.069	0.102	–0.68
GER-2	0.133	0.098	1.35	0.174*	0.096	1.81
GER-3	0.063	0.047	1.36	0.060	0.046	1.31
Gini	0.039	0.113	0.35	–0.065	0.121	–0.53
RWWFPR	–0.086***	0.019	–4.49	–0.075***	0.019	–3.87
TFR	–0.477***	0.128	–3.71	–0.384***	0.139	–2.77
R² (Within)	0.843			0.843
R² (Between)	0.511			0.511
R² (Overall)	0.566			0.566
Sigma_u	0.250			0.342
Sigma_e	0.078			0.078
Rho	0.911			0.951
No. of observations	171			171

Variables	Coefficients		Difference (b – B)	χ ₁₃ ²	Prob. > χ²
Variables	Random effects	Fixed effects	Difference (b – B)	χ ₁₃ ²	Prob. > χ²
SC	0.415	0.386	0.029	60.20*	0.0000
PHC	–0.011	–0.066	0.055
CHC	0.024	–0.033	0.057
DOCTORS	–0.122	–0.088	–0.034
NURSES	–0.018	–0.026	0.009
MYM	1.271	1.518	–0.247
PCNSDP	0.515	0.442	0.073
GER-1	–0.069	–0.049	–0.020
GER-2	0.133	0.174	–0.041
GER-3	0.060	0.063	–0.003
Gini	–0.065	0.039	–0.103
RWWFPR	–0.075	–0.086	0.011
TFR	–0.384	–0.477	0.093

States\Year ↓ →										PME*	Ranking
States\Year ↓ →	2008–2009	2009–2010	2010–2011	2011–2012	2012–2013	2013–2014	2014–2015	2015–2016	2016–2017	PME*	Ranking
Andhra Pradesh	0.126	0.130	0.153	0.153	0.164	0.171	0.205	0.215	0.229	0.172	14
Assam	0.118	0.124	0.125	0.138	0.160	0.166	0.183	0.217	0.234	0.163	16
Bihar	0.092	0.100	0.109	0.117	0.123	0.127	0.141	0.200	0.233	0.138	18
Chhattisgarh	0.160	0.172	0.188	0.201	0.217	0.219	0.245	0.252	0.263	0.213	12
Gujarat	0.175	0.184	0.194	0.217	0.229	0.242	0.240	0.241	0.270	0.221	9
Haryana	0.192	0.230	0.232	0.273	0.286	0.301	0.314	0.300	0.241	0.263	8
Himachal Pradesh	0.302	0.301	0.302	0.333	0.376	0.394	0.434	0.515	0.580	0.393	3
Jammu and Kashmir	0.230	0.259	0.261	0.286	0.410	0.386	0.452	0.492	0.431	0.356	4
Jharkhand	0.130	0.135	0.143	0.157	0.168	0.175	0.184	0.223	0.239	0.173	13
Karnataka	0.206	0.232	0.260	0.297	0.317	0.322	0.364	0.364	0.363	0.303	7
Kerala	0.917	0.905	0.802	0.905	1.000	1.000	0.925	0.926	0.828	0.912	1
Madhya Pradesh	0.112	0.116	0.125	0.134	0.139	0.147	0.144	0.156	0.165	0.138	19
Maharashtra	0.223	0.245	0.280	0.319	0.319	0.329	0.369	0.356	0.345	0.309	6
Orissa	0.176	0.162	0.202	0.188	0.207	0.213	0.240	0.259	0.274	0.213	11
Punjab	0.228	0.242	0.256	0.298	0.337	0.366	0.429	0.420	0.413	0.332	5
Rajasthan	0.112	0.118	0.130	0.138	0.205	0.174	0.178	0.187	0.199	0.160	17
Tamil Nadu	0.267	0.285	0.347	0.357	0.385	0.415	0.412	0.416	0.666	0.394	2
Uttar Pradesh	0.109	0.119	0.129	0.138	0.158	0.167	0.193	0.222	0.271	0.167	15
West Bengal	0.175	0.188	0.197	0.192	0.197	0.213	0.263	0.272	0.270	0.219	10
Mean Efficiency (yearly)	0.213	0.224	0.234	0.255	0.284	0.291	0.311	0.328	0.343	0.276
Mean Efficiency (overall)	0.276

Variable	Mean	Median	Std. Dev.	Skewness	Maximum	Minimum
U5MR	52.05	51	19.64	0.17	98	13
$\frac{1}{U 5 M R}$	0.02	0.02	0.01	2.42	0.08	0.01
$\ln (\frac{1}{U 5 M R})$	–3.87	–3.93	0.44	0.99	–2.56	–4.58
SC	7,586.68	7,274	4,508.70	1.05	20521	1907
PHC	1,238.30	1,147	789.66	1.34	3692	297
CHC	258.47	217	157.68	1.16	822	70
DOCTORS	1,384.64	1,048	941.46	0.78	3532	271
NURSES	3,337.36	2,491	2,838.95	1.58	13435	376
MYM	21.65	21.5	1.12	0.66	25.2	19.8
PCNSDP	69,525.96	62,145	30,034.01	0.35	143,211	16,902.55
GER-1	103.22	100.89	12.51	1.28	155.3	79.83
GER-2	75.81	74.78	15.18	0.27	120.31	33.9
GER-3	49.89	48.13	18.62	0.29	100.58	7.4
Gini	0.27	0.26	0.06	1.80	0.52	0.19
RWWFPR	37.14	36.43	16.91	0.50	103.95	0.52
TFR	2.45	2.4	0.65	0.62	4	1.7

Variables	ln(x₁)	ln(x₂)	ln(x₃)	ln(x₄)	ln(x₅)	ln(z₁)	ln(z₂)	ln(z₃)	ln(z₄)	ln(z₅)	ln(z₆)	ln(z₇)	ln(z₈)
ln(x₁)	1
ln(x₂)	0.59	1
ln(x₃)	0.48	0.50	1
ln(x₄)	0.55	0.55	0.41	1
ln(x₅)	0.57	0.57	0.53	0.62	1
ln(z₁)	–0.47	–0.27	–0.28	–0.12	–0.21	1
ln(z₂)	–0.30	–0.22	0.02	–0.18	0.14	0.40	1
ln(z₃)	0.11	–0.07	0.11	–0.15	–0.14	–0.50	–0.38	1
ln(z₄)	–0.18	–0.09	0.05	–0.13	0.00	0.47	0.57	–0.35	1
ln(z₅)	–0.18	–0.13	0.06	–0.10	0.08	0.47	0.53	–0.46	0.52	1
ln(z₆)	–0.11	–0.06	0.04	–0.13	–0.21	0.18	0.03	–0.19	0.30	0.35	1
ln(z₇)	0.03	–0.04	0.30	–0.12	0.09	–0.03	0.41	0.08	0.44	0.40	–0.04	1
ln(z₈)	0.30	0.24	0.08	0.04	–0.12	–0.52	–0.72	0.40	–0.55	–0.50	0.031	–0.31	1