Introduction:
Efficiency in resource utilization in healthcare sector has been analysed by a number of empirical studies.[1,2] There has been a focus both at a unit level and the aggregate level. These analyses pertain to hospitals, nursing homes, Health Maintenance Organizations (HMOs) and district health authorities.[3-9] Generally either of the methods, namely, non-parametric or parametric is employed. Data envelopment technique is popular in the former. Among the latter type, an idealized yardstick is developed which is used to evaluate economic performance of health system. These methods provide a production possibility frontier depicting a locus of potentially technical efficient output combination that an organization or health system is capable of producing at a point of time. An output combination below this frontier is termed as technically inefficient.[10-12] Some of the exhaustive reviews also provide us in detail the steps followed and empirical problems that have been faced by the researchers.[13,3] Yet, there are a very few studies in the developing countries’ context. In the Indian context focus mostly has remained either the all-India rural or urban sector or the analysis has been carried out up to the state level aggregates only. So far, a district level analysis has been attempted for a few states including Assam, Orissa, Punjab, Maharashtra, Karnataka, West Bengal and Madhya Pradesh.[14-16] We extend our analysis in this paper to focus on efficiency of the health care system at sub-state level (i.e., district level) in India using Tamil Nadu state and its district level data. We explore the reasons for relative performance of different districts with Data Envelopment Analysis.
Tamil Nadu is, one of the high income Indian states and with its above national average income at INR per capita 58360 at constant prices, fourth next to Gujarat and Harayana (Table 1). Situated in the southern part of India with capital city as Chennai, covers an area of 130,058km2(50,216 miles), and is the eleventh largest state in India and a population above 72 million (72,147,030). The state is bordered by the states of Karnataka, Kerala, Andhra Pradesh and union territory of Puducherry. In terms of literacy (2011 census), growth in literacy (between the years 2001-2011) and per capita health expenditure the state occupies a rank of 3, 15 and 5 respectively among the major Indian states (Table 1). In 2013, with an IMR of 21, 24 and 17 at aggregate, rural and urban level, the state is second lowest mortality state next to Kerala in the country (Table 2).
Table 1: Rank of Tamil Nadu among major Indian states in terms of Per capita income, literacy and public expenditure on health |
State |
2012-13 (NSDP capita INR at Constant prices) |
Rank* |
Literacy Rate (%) - 2011 Census |
Rank |
Decadal Difference (%) |
Rank |
Per Capita Total Public Expenditure on Health 2009-10 |
Rank |
Andhra Pradesh |
39645 |
9 |
67.41 |
17 |
7.19 |
12 |
459 |
9 |
Assam |
22273 |
17 |
73.18 |
11 |
9.93 |
7 |
715 |
2 |
Bihar |
14356 |
19 |
63.82 |
19 |
16.82 |
1 |
210 |
19 |
Chhattisgarh |
28087 |
13 |
71.04 |
12 |
6.38 |
17 |
380 |
15 |
Gujarat |
59157 |
3 |
79.31 |
5 |
10.17 |
6 |
480 |
7 |
Haryana |
64052 |
2 |
76.64 |
8 |
8.73 |
9 |
483 |
6 |
Jammu & Kashmir |
30035 |
12 |
68.74 |
15 |
13.22 |
4 |
1073 |
1 |
Jharkhand |
27010 |
14 |
67.63 |
16 |
14.07 |
2 |
264 |
18 |
Karnataka |
43266 |
8 |
75.6 |
9 |
8.96 |
8 |
468 |
8 |
Kerala |
55643 |
5 |
93.91 |
1 |
3.14 |
19 |
580 |
4 |
Madhya Pradesh |
24867 |
16 |
70.63 |
13 |
6.89 |
14 |
312 |
17 |
Maharashtra |
65095 |
1 |
82.91 |
2 |
6.03 |
18 |
420 |
11 |
Odisha |
25163 |
15 |
73.45 |
10 |
10.37 |
5 |
405 |
13 |
Punjab |
47854 |
7 |
76.68 |
7 |
7.03 |
13 |
401 |
14 |
Rajasthan |
30839 |
11 |
67.06 |
18 |
6.65 |
16 |
457 |
10 |
Tamil Nadu |
58360 |
4 |
80.33 |
3 |
6.88 |
15 |
579 |
5 |
Uttar Pradesh |
18635 |
18 |
69.72 |
14 |
13.45 |
3 |
372 |
16 |
Uttarakhand |
55375 |
6 |
79.63 |
4 |
8.01 |
11 |
625 |
3 |
West Bengal |
34177 |
10 |
77.08 |
6 |
8.44 |
10 |
410 |
12 |
All India |
38856 |
|
74.04 |
|
64.83 |
|
|
|
| Source: Different publications and estimated values of ranks. * The highest in value is denoted as 1. |
Table 2: Infant Mortality Rate (IMR) in Indian States, 2013 |
| India/States/ Union Territories |
Infant mortality rate 2013 |
Total |
Rank* |
Rural |
Rank |
Urban |
Rank |
Andhra Pradesh |
39 |
11 |
44 |
12 |
29 |
11 |
Assam |
54 |
18 |
56 |
18 |
32 |
13 |
Bihar |
42 |
13 |
42 |
10 |
33 |
15 |
Chhattisgarh |
46 |
14 |
47 |
14 |
38 |
17 |
Gujarat |
36 |
8 |
43 |
11 |
22 |
4 |
Haryana |
41 |
12 |
44 |
12 |
32 |
13 |
Jammu & Kashmir |
37 |
9 |
39 |
9 |
28 |
10 |
Jharkhand |
37 |
9 |
38 |
8 |
27 |
9 |
Karnataka |
31 |
5 |
34 |
6 |
24 |
7 |
Kerala |
12 |
1 |
13 |
1 |
9 |
1 |
Madhya Pradesh |
54 |
18 |
57 |
19 |
37 |
16 |
Maharashtra |
24 |
3 |
29 |
4 |
16 |
2 |
Odisha |
51 |
17 |
53 |
16 |
38 |
17 |
Punjab |
26 |
4 |
28 |
3 |
23 |
6 |
Rajasthan |
47 |
15 |
51 |
15 |
30 |
12 |
Tamil Nadu |
21 |
2 |
24 |
2 |
17 |
3 |
Uttar Pradesh |
50 |
16 |
53 |
16 |
38 |
17 |
Uttarakhand |
32 |
7 |
34 |
6 |
22 |
4 |
West Bengal |
31 |
5 |
32 |
5 |
26 |
8 |
India |
40 |
|
44 |
|
27 |
|
| Source: Ref.17;* The lowest IMR (in value) is denoted as 1 (or top rank). |
In this paper, we make an attempt to find out technical efficiency using a non-parametric approach known as Data Envelopment analysis (DEA).[11,12]
The DEA methodology, originating from Farrell’s (1957) and further by Charnes, Cooper and Rhodes (1978), assumes the existence of a convex production frontier. The production frontier in the DEA approach is constructed using linear programming methods. The term “envelopment” stems from the fact that the production frontier envelops the set of observations.[11,12]
The general relationship that we consider is given by the following function for each district i:
Yi = f (Xi), i=1...n (1)
Where Yi –our output measure; Xi – the relevant inputs
If Yi< f (Xi), it is said that unit i exhibits inefficiency. For the observed input levels, the actual output is smaller than the best attainable one and inefficiency can then be measured by computing the distance to the theoretical efficiency frontier.
The variable-returns to scale hypothesis, which we use here for an output-oriented specification, is described as below. Suppose there are k inputs and m outputs for n Decision Management Units (DMUs). For the i-th DMU, we can define X as the (k x n) input matrix and Y as the (m x n) output matrix. The DEA model is then specified with the following mathematical programming problem, for a given i-th DMU:
Max δ,λ δ
Subject to –δyi + Yλ≥0
xi- Xλ≥ 0 (2)
n1’λ’= 1
λ≥0
In problem (2), δ is a scalar (that satisfies 1/δ≥1), more specifically it is the efficiency score that measures technical efficiency. It measures the distance between a unit and the efficiency frontier, defined as a linear combination of the best practice observations. With 1/δ<1, the unit is inside the frontier (i.e. it is inefficient), while δ= 1 implies that the unit is on the frontier (i.e. it is efficient).
The vector λ is a (n x 1) vector of constants that measures the weights used to compute the location of an inefficient DMU if it were to become efficient, and n1 is an n-dimensional vector of ones. The inefficient DMU would be projected on the production frontier as a linear combination of those weights, related to the peers of the inefficient DMU. The peers are other DMUs that are more efficient and are therefore used as references for the inefficient DMU. The restriction n 1 'λ'=1 imposes convexity of the frontier, accounting for variable returns to scale. Dropping this restriction would amount to admit that returns to scale were constant. Problem (2) has to be solved for each of the n DMUs in order to obtain the n efficiency scores.
Figure 1 presents the DEA production possibility frontier in the simple one input-one output case. States A, B and C are efficient States. Their output scores are equal to 1. State D is not efficient. Its score [d2/(d1+d2)] is smaller than 1.
 |
Figure 1: DEA production possibility frontier in one input-one output case |
Results
We used the IMR as an output variable. Using a Principal component analysis 18,19 we tried a sub-set of variables which had low correlations (Table 3). These included Total beds in ESI (Employees state Insurance scheme) hospitals, Population per doctor of PHPM (Public Health and Preventive Medicine), Full Vaccination, Full ANC (ante natal care) and Total Doctors in ESI hospitals and dispensaries.
Table 3: Correlation Matrix |
| Total beds ESI |
1 |
|
|
|
|
Population per doctor of PHPM |
-0.1283 |
1 |
|
|
|
Full Vaccination |
-0.1637 |
-0.2368 |
1 |
|
|
Full ANC |
-0.1663 |
0.1029 |
0.293 |
1 |
|
Total Doctors ESI |
0.7256 |
0.0437 |
-0.1285 |
0.1304 |
1 |
| Source: estimated |
Using principal component analysis (PCA) we identified thus three components with an Eigen value greater than one. These related to Total beds in ESI (Employees state Insurance scheme) hospitals, Population per doctor of PHPM (Public Health and Preventive Medicine,) and Full Vaccination (Table 4).
Table 4: Principal Component |
| Component |
Eigenvalue |
Difference |
Proportion |
Cumulative |
Comp1 |
1.7953 |
0.5027 |
0.3591 |
0.3591 |
Comp2 |
1.2927 |
0.1401 |
0.2585 |
0.6176 |
Comp3 |
1.1526 |
0.5999 |
0.2305 |
0.8481 |
Comp 4 |
0.5527 |
0.3459 |
0.1105 |
0.9586 |
Comp 5 |
0.2068 |
- |
0.0414 |
1 |
| Source: Estimated |
The factor scores for these three components were used as input variables with inverse of IMR at the aggregate level as output variable in the Data Envelopment analysis (DEA). All the variables were used in natural log. The resulting efficiency estimates for the districts of Tamil Nadu retaining two components, namely, Total beds ESI and Full Vaccination are presented in Table 5.
Table 5: DEA results using Total beds ESI and Full Vaccination as inputs and inverse lnimr2008 as output |
|
IMR2008 |
Scale efficiencies |
Returns-
to-scale |
Efficiency scores |
CCR score |
Ranks |
Deviations from Average |
Chennai |
2.22 |
1 |
constant |
1.0000 |
1.0000 |
1 |
0.6307 |
Coimbatore |
9.73 |
0.90541 |
decreasing |
0.2485 |
0.2250 |
22 |
-0.1444 |
Cuddalore |
17.97 |
0.63117 |
increasing |
0.4471 |
0.2822 |
13 |
-0.0872 |
Dharmapuri |
3.26 |
0.85997 |
decreasing |
0.4784 |
0.4114 |
7 |
0.0421 |
Dindigul |
18.76 |
0.80922 |
decreasing |
0.1928 |
0.1560 |
28 |
-0.2133 |
Erode |
10.62 |
0.75423 |
decreasing |
0.2393 |
0.1805 |
26 |
-0.1889 |
Kancheepuram |
14.3 |
0.67302 |
decreasing |
0.2125 |
0.1430 |
29 |
-0.2263 |
Kanyakumari |
14.77 |
0.98841 |
increasing |
0.2663 |
0.2632 |
14 |
-0.1061 |
Karur |
8.18 |
0.84142 |
decreasing |
0.2690 |
0.2263 |
21 |
-0.1430 |
Madurai |
3.51 |
0.7672 |
decreasing |
0.4502 |
0.3454 |
9 |
-0.0239 |
Nagapattinam |
9.11 |
0.81911 |
decreasing |
0.2559 |
0.2096 |
23 |
-0.1597 |
Namakkal |
6.6 |
0.83778 |
decreasing |
0.3015 |
0.2526 |
16 |
-0.1167 |
Perambalur |
8.32 |
0.91251 |
increasing |
0.3843 |
0.3507 |
8 |
-0.0186 |
Pudukottai |
4.31 |
0.93521 |
increasing |
1.0000 |
0.9352 |
3 |
0.5659 |
Ramanathapuram |
1.94 |
0.99413 |
increasing |
0.9276 |
0.9221 |
4 |
0.5528 |
Salem |
10.12 |
0.94963 |
decreasing |
0.2442 |
0.2319 |
19 |
-0.1374 |
Sivagangai |
3.28 |
0.9757 |
increasing |
0.5331 |
0.5201 |
6 |
0.1508 |
Thanjavur |
8.12 |
0.9105 |
increasing |
0.3528 |
0.3212 |
11 |
-0.0481 |
the Nilgris |
17.28 |
0.8618 |
decreasing |
0.2019 |
0.1740 |
27 |
-0.1953 |
Theni |
10.52 |
0.97716 |
decreasing |
0.2659 |
0.2599 |
15 |
-0.1095 |
Thiruvallur |
5.58 |
0.7142 |
decreasing |
0.3288 |
0.2348 |
18 |
-0.1345 |
Thiruvarur |
10.06 |
0.85166 |
increasing |
0.3475 |
0.2960 |
12 |
-0.0734 |
Thoothukudi |
12.41 |
0.89976 |
decreasing |
0.2285 |
0.2056 |
24 |
-0.1637 |
Tiruchirappalli |
8.21 |
0.92042 |
decreasing |
0.2709 |
0.2493 |
17 |
-0.1200 |
Tirunelveli |
11.52 |
0.97385 |
decreasing |
0.2331 |
0.2270 |
20 |
-0.1423 |
Thiruvannamalai |
6.32 |
0.97942 |
increasing |
0.3441 |
0.3371 |
10 |
-0.0323 |
Vellore |
11.87 |
0.85145 |
decreasing |
0.2287 |
0.1947 |
25 |
-0.1746 |
Villupuram |
3.08 |
0.91398 |
increasing |
0.6079 |
0.5556 |
5 |
0.1863 |
Virudhunagar |
1.76 |
1 |
constant |
1.0000 |
1.0000 |
1 |
0.6307 |
Minimum |
1.76 |
|
Average |
0.4090 |
0.3693 |
|
|
Maximum |
18.76 |
|
|
|
|
|
|
| Source: Estimated |
Table 6: Districts according to population covered by medical personnel and facilities per ten thousand populations |
|
Pop per bed ESI |
Pop per doc ESI |
Pop per bed PHPM |
Pop per doc PHPM |
Pop beds ratio MRHS |
Pop per doc MRHS |
Chennai |
1732 |
13126 |
362 |
2780 |
na |
na |
Coimbatore |
1269 |
5248 |
5519 |
20141 |
6280 |
26307 |
Cuddalore |
29213 |
5843 |
3037 |
13038 |
2032 |
11931 |
Dharmapuri |
1512 |
10581 |
2473 |
15306 |
7260 |
21168 |
Dindigul |
4903 |
12772 |
3142 |
13876 |
2423 |
12351 |
Erode |
0 |
4364 |
4762 |
22928 |
1984 |
14035 |
Kancheepuram |
0 |
19755 |
4963 |
19348 |
4520 |
24187 |
Kanniyakumari |
4168 |
12259 |
4197 |
20936 |
4104 |
16062 |
Karur |
15596 |
23395 |
3860 |
13510 |
2024 |
11702 |
Krishnagiri |
8298 |
21838 |
3391 |
14966 |
3265 |
16100 |
Madurai |
986 |
4462 |
3997 |
13686 |
6181 |
21568 |
Nagapattinam |
1199 |
1799 |
3288 |
16399 |
1404 |
10481 |
Namakkal |
0 |
4445 |
2856 |
10296 |
2387 |
11552 |
Perambalur |
0 |
7819 |
6874 |
3954 |
2498 |
10856 |
Pudukkottai |
618 |
2882 |
2850 |
13848 |
1378 |
9751 |
Ramanathapuram |
0 |
0 |
2646 |
12422 |
1252 |
8519 |
Salem |
2146 |
2555 |
3575 |
11488 |
4813 |
23674 |
Sivaganga |
0 |
4817 |
2749 |
11371 |
1900 |
7578 |
Thanjavur |
5025 |
7538 |
4639 |
15008 |
2171 |
14475 |
The Nilgiris |
0 |
8352 |
3072 |
11475 |
909 |
5976 |
Theni |
7997 |
13328 |
2669 |
10545 |
2122 |
10910 |
Thiruvallur |
0 |
27362 |
4631 |
19517 |
6068 |
17999 |
Thiruvarur |
0 |
0 |
2767 |
11343 |
2297 |
10310 |
Thoothukkudi |
2288 |
9855 |
3097 |
13145 |
3231 |
13372 |
Tiruchirappalli |
2143 |
7201 |
3429 |
11490 |
4531 |
19385 |
Tirunelveli |
9627 |
9627 |
3743 |
15321 |
3142 |
16884 |
Tiruppur |
0 |
21656 |
9343 |
18911 |
2728 |
17652 |
Tiruvannamalai |
0 |
3826 |
2825 |
11269 |
2607 |
15055 |
Vellore |
5398 |
8807 |
3583 |
17916 |
3944 |
17153 |
Viluppuram |
0 |
16653 |
4199 |
17469 |
5454 |
19790 |
Virudhunagar |
4903 |
12772 |
3173 |
16223 |
1617 |
10504 |
minimum |
0 |
0 |
362 |
2780 |
909 |
5976 |
maximum |
29213 |
27362 |
9343 |
22928 |
7260 |
26307 |
minimum excluding zero values |
618 |
1799 |
362 |
2780 |
1378 |
9751 |
| Source: Ref. 20 |
Table 7: Second Stage Regression Results |
| Number of obs= 29; F(3,25)= 8.14; Prob > F=0.0006; R-squared= 0.4941; Adj R-squared=0.4334; Root MSE= 0.19613 |
Deviations from average |
Coeff. |
S.E |
t values |
P>|t| |
Hh improved source of drinking water |
-0.06104 |
0.017806 |
5 -3.43 |
0.002 |
Hh puccahouse |
0.012699 |
0.004089 |
9 3.10 |
0.005 |
Hh bpl cardholder |
0.012235 |
0.00451 |
1 2.71 |
0.012 |
constant |
5.073867 |
1.76063 |
8 2.88 |
0.008 |
| Source: Estimated using data from Ref. 20 |
The efficiency scores and CCR (Constant returns to scale) are presented in Table 5 for 31 districts of Tamil Nadu. The results indicate that two of the three districts, namely, Chennai, Pudukottai and Virudhnagar have an efficiency score of one. However, if we focus on CCR scores, we find that only two of them, namely, Chennai and Virudhnagar, are the top performers. By contrast, Kancheepuram has appeared as lowest performer with its CCR score rank 29 (Table 5). In order to explore the reason for these differentials in efficiency, we look into various parameters of availability of health services. These include population covered per bed and doctors for ESI hospitals, PHPM hospitals and MRH (ministry of rural health services) (Table 6). It is observed from the Table 6 that population per bed and doctors in all the three types namely, ESI, PHPM and MRHS, is the lowest for Chennai (Row 1). Further comparison with Virudhnagar with the lowest performer namely, Kancheepuram, indicates that the latter has higher population covered across all the three systems of provider (Table 6, rows 7th and last one). It could be easily inferred from these parameters that the low performance of Kancheepuram is mainly owing to low availability of these health inputs. By contrast, we could also observe that lowest population burden for hospitals and a doctor is not for either Chennai or Virudhnagar. In fact, the lowest population coverage per hospital for all the three types excluding zero values happens to be for the districts of Nagapattinam (618 for ESI), Chennai (362 for PHPM) and Pudukottai (1378 for MRHS).
In terms of burden of population per doctor in all the three systems, the lowest remains in each case (after ignoring zero values and non-available figures) as Nagapattinam (1799 for ESI), Chennai (2780 for PHPM) and Pudukottai (9751). It could be inferred that higher efficiency of Chennai is due to better availability of hospital beds and doctors per population. However, this is not true with respect to Vrudhnagar which does not belong to either maximum or minimum population coverage in either of the hospital beds and doctors. If we focus on the lowest efficient district of Kancheepuram, we notice that the highest population burden for all the three types happens to be for Cuddalore (29213), Tiruppur (9343) and Dharmapuri (72607). Likewise in terms of the burden of population on doctors in the respective three systems happens to be maximum for Thiruvallur (27362) and Coimbatore (26307). It is thus not so much the higher burden on facilities or doctors but rather less efficient utilisation of inputs in Kancheepuram which may partly explain lowest efficiency of this district.
Besides the variation in inputs availability and usage efficiency, there may be reasons which are external to health system. In order to explore these reasons we further carried out second stage regressions using the deviations of CCR scores from the average score of all the districts as dependent variable. Among the set of explanatory variables we tried a number of variables including households with: electricity, improved source of drinking water, improved access to sanitation, use of LPG (Liquefied petroleum gas), living in pucca house and having BPL (below poverty line) card. Out of these variables only three variables emerged as statistically significant. These are, improved source of drinking water, living in pucca house and having BPL (below poverty line) card. The negative sign of improved source of drinking water indicates that supportive input of better potable water supply helps to improve in general health status and thus reduce inter-district disparities in health system efficiency. However, there are other inputs like owning of pucca houses (relative to those living in Kuccha house) and holding a BPL card-thus providing many of the items of food consumption at a subsidised rate and a free state owned health insurance, might have added to some extent in increasing inter-district disparities. Since the districts where either the better housing exists more or where the proportion of BPL are relatively more must have an edge over other non-similar districts.
Conclusion
Our analyses for district level data of Tamil Nadu state indicates that there are significant inter district disparities in the state. These relate both to availability of beds and doctors per capita across three systems of health service provision within the state, known as Employees state insurance scheme (ESI), public health and preventive medicines (PHPM) and rural health services. Some of the districts like state capital Chennai have a better availability of some of these health inputs making it an efficient unit. There are other districts like Virudhnagar which is also an efficient unit but it is more due to its better utilisation of inputs rather than better input availability. However, there are lower performing districts like Kancheepuram, which owe its inefficiency partly due to its low availability of inputs and partly due to less than efficient utilisation of health inputs. In addition to it, there are certain supportive factors which are as such external to existing health system. These include statistically significant variables like improved source of water supply, better housing and BPL card ownership. In order to overcome or minimise disparities in the district level health systems; our analysis indicates that there is a need for higher public budgetary expenditure on health in some of the very low performing districts. At the same time an attempt to improve efficient utilisation of health inputs could be attempted by government or other agencies by better training of manpower at different levels in the district health systems. Besides these, it is suggested by our analysis that the publicly funded health insurance meant for below poverty line population in the state should also be extended to other areas or districts where currently the supportive inputs of improved potable water supply are inadequate. This step might help to enhance efficiency in certain districts where supportive input of improved water supply is inadequate leading to more morbidity and where BPL privilege of free health insurance is not available to a large section of district population.
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