Research Article
Data Envelopment Analysis and Malmquist Index Application: Efficiency of Primary
Health Care in Morocco and Covid-19
Youssef Er Rays
a, Hamid Ait Lemqeddem
baLaboratory of Organizational Management Sciences, National School of Business and Management, Ibn Tofail University, Kenitra, Morocco. E-mail: raysyoussef@gmail.com
bLaboratory of Organizational Management Sciences, National School of Business and Management, Ibn Tofail University, Kenitra, Morocco. E-mail: glemqeddem@gmail.com
Article History: Received: 11 January 2021; Accepted: 27 February 2021; Published online: 5 April 2021 Abstract: The Primary Health Care in Morocco plays a very strategic role in the prevention against various diseases, in particular the current pandemic COVID 19. The efficiency of these centers has a direct impact on the reduction of this pandemic. First, this is why will try to research the literature review about the technical efficiency of primary health care. In the second step, the non-parametric: Data Envelopment Analysis method will be used to apply the empiric phase during the period 2012-2015, to estimate the relative technical efficiency, this method will be calculated by using two models: the theory of the return to scale constant with a middle equal to 0.437 and the theory of the variable return to scale with an average of 0.537. It’s necessary to combine the DEA approach with the Malmquist index to evaluate the factors of production. Finally, to compare the results of the proposed method which are generally very poor, and discuss his policy implications for health care.
Keywords: Data Envelopment Analysis (DEA), Malmquist Index, Efficiency, COVID-19 and Primary Health Care.
1. Introduction
The health system is a difficult institution by their feature, the relationship between various stakeholders namely patients, medical, nursing, and administrative staff, primary health care, hospitals, health insurance, and regional authorities. “These stakeholders linked through a series of relationships based on responsibility for one another” (Smith et al., 2008). This duty begins with efficiency, equity (Ait-Lemqeddem, 2020) and responsiveness to the health resources exploited: financial, human, and material (Ait Lemqeddem, 2009).
To do this, it’s necessary to try verifying the thesis that if the framework of the law 34-09 promulgated in 2011 improves the performance of basic health care institutions, helps to check equity in primary health care. In this vision, this problem is interested in knowing the score of the efficiency the primary health care in front of current constraints and particularly the COVID-19 health crisis in Morocco?
The objective is to calculate the technical efficiency of the primary health care in Morocco (doctors, nurses), the epistemology is part of a constructive proposition, the method to use the non-parametric method: Data Envelopment Data (DEA), it's interesting to combine it with the Malmquist Index (MI), the aim of which is to benchmark the productivity factors of the Primary Health Care.
This work plan focuses on three areas to answer our question. First, it's important to discuss the literature review of the nonparametric method. Second, apply the nonparametric method to the empirical study. Thirdly, compared the results of the proposed method with other recent studies. Finally, try to conclude and give the contribution of this paper.
2. Journal Literature
WHO (World Health Organization) gives a greater significance on Primary Health Care (PHC) as an easy-to-access first contact (Organization, 2008), comprehensiveness, continuity, coordination and centering on the person (Liu et al., 2013a), WHO considered PHC to be a combination of promotion, prevention, treatment and rehabilitation (WHO, 2010), PHC is also the linchpin of the effective health care delivery (Kringos et al., 2010), coordinates care at all levels of the health care system and provides comprehensive health services on an ongoing basis to the majority of the population (Starfield, 1992).
Several publications define the efficiency as an ambiguous concept (Vu, 2008), it can take on a dimension according to Bouquin and Kuszla (2013) as “maximizing the amount of products and services obtained from a given amount of the resources” (cited by (Er Rays & Ait Lemqeddem, Sep. 2020)).
This last idea can be calculated by using two methods: parametric (stochastic) and non-parametric (Data Envelopment). In this paper, the second DEA will be selected to calculate efficiency, to check this approach, the DEA method will be focused on two models that are the most used during these recent years. The first is the CRS ratio model introduced in 1978 (Charnes et al., 1978) based on the assumption of constant returns to scale. This model proposes, on a vision, an assessment of overall efficiency and on the other vision identifies the sources and estimates the amounts of inefficiencies thus identified. The second is the VRS model proposed by Banker and colleagues (Banker et al., 1984). They shall address the difference between technical inefficiencies and scale inefficiencies by estimating, on the side, pure technical efficiency to the given scale of operations and, on the other side, by identifying whether the possibilities for increasing, decreasing or constant value of the scale efficiencies are present for wider exploitation.
Various publications evaluated with this proposition, 3203 types of research-tested during the years 1987-2002 (Tavares, 1987-2002), of which 2152 studies covered by the DEA method, 4500 topics are looked at until 2009, including 700 works (ISI Web of Science concerning the DEA method). This approach has not seen a faint sign since the time of Charnes and his colleagues (1978) (Liu et al., 2013a). Hollingsworth and colleagues examine 91 DEA methods about health care, noticed that the most DEA applications published up to 1997 were hospital-based. Only five of these 91 types of research based on primary care (Hollingsworth et al., 1999). Hollingsworth and colleagues examine 91 DEA methods about health care, noticed that the most DEA applications published up to 1997 were hospital-based. Only five of these 91 types of research based on primary care (Pelone et al., 2015) against kohl and his colleagues who processed 262 articles on the DEA methods concerning hospitals between 2005 and 2016 (Kohl et al., 2019).
3. Research Methodology
At this stage of this research, first of all, the aim is to analyze the literature review on the notion of the efficiency of the primary health care centers and the calculating of the efficiency will be do it by using the non-parametric DEA method. Then, it is important to evaluate the importance of the performance as a tool of good management of non-profit organizations that are characterized by their complexity of its nature, and finally, to meet the increased expectations of the primary health care and the COVID19.
In this framework, we selected the seventy-five PHCP/P networks that permit us to release three inputs and three outputs that we want to analyze.
3.1. Problem Formulation
In this case, the application of the DEA method, which is a non-parametric approach based on linear programming, is used to assess the relative efficiency of the several organizations operating in the same, taking into account several dimensions simultaneously.
The feature of this method does not require applying an optional model to the productive equation which needs the boundaries of production processes. In order to accept this assumption only if PHC plants are categorized on their optimal scale of production. However, constraints such as the structure of PHC, financial, and organizational problems have made PHC stand out from this optimal scale.
One criticism of the DEA methodology is that the efficiency scores obtained are sensitive to the prior selection of the outputs and the inputs. Analysis of the panel data when it comes to efficiency measures, the question of how their values change over time. Simple quantification of the PHC efficiency only provides a snapshot in time, and the outliers can skew the results. Panel data analysis gives a means of revealing temporal trends.
In this study, it’s interesting to consider that there is a total network of Primary Health Care for each Province or Prefecture (PHCP/P), each PHC uses the combination U inputs produce U’ outputs.
𝐼𝑝𝑐ℎ=(𝑖1𝑝𝑐ℎ, 𝑖2𝑝𝑐ℎ, … , 𝑖𝑈𝑝𝑐ℎ): is the Input vectors observed from the second PHCP/P.
𝑂ℎ=(𝑜1𝑝𝑐ℎ, 𝑜2𝑝𝑐ℎ, … , 𝑜𝑈′𝑝𝑐ℎ): are the Observed output vectors of the second PHCP/P.
Farrell’s work focused on the results of a non-parametric boundary for the measurement of the technical efficiency (TE) (Farrell, 1957):
𝐸𝑇𝑃𝐻𝐶= 𝑚𝑖𝑛𝜆 (1) Under constraints: ∑ 𝜐𝑖𝑜𝑢′𝑖≥ 𝑖 𝑜𝑢′𝑝ℎ𝑐 (𝑚 = 1, … , 𝑁𝑃) (2) ∑ 𝜐𝑖𝑖𝑢𝑖≤ 𝜆𝑝ℎ𝑐𝑖𝑢𝑝ℎ𝑐 𝑖 (𝑛 = 1, … , 𝑀𝑃) (3) ∑ 𝜐𝑖 𝑖 = 1. (𝜐𝑖≥ 0) (4)
The method determined the efficiency score be assigned to each entity by the linear program resolution, under the assumption based on the variable scale inputs and returns.
There are:
i = 3 input and o = 3 outputs;
phc = 75 Decision Making Unit (DMU = from a province or a prefecture); I: as an input of matrix (mp phc) and O as an output of matrix (np phc).
z: is a vector of constants (n*1) which measures the weights used to measure the location of a DMU In the above problem, is a lambda between 1 and ∞.
To analyze the total production efficiency of several periods, the Malmquist index (IM) is used, which complements the DEA method to measure productivity (Ray, 2004) factors (Malmquist, 1953).
The MI always compares two adjacent periods (Ray, 2004) 𝑇𝑜𝑡(𝑢𝑡, 𝑎𝑡) et 𝑇𝑜𝑡+1(𝑢𝑡+1, 𝑎𝑡+1) are intra-period
distance functions.
TFP = CTFP = CE* CT = (CP* CS) *CT (5)
MI is composed of the total productivity change (Coelli & Prasada Rao, 2001) (CTFP) EC: Change in Technical Effectiveness (Lovell, 2003);
CT: Change in technical efficiency; can be subdivided into: PI: Pure efficiency
CS: Scale efficiency. 𝑀𝑃𝐼 = 𝑇𝐹𝑃 = 𝑇𝑜𝑣𝑡+1(ut+1,at+1) 𝑇𝑜𝑣𝑡+1(𝑢𝑡,𝑎𝑡) [ 𝑇(ut+1,at+1) 𝑇 𝑜𝑐𝑡+1(ut+1,at+1) ⁄ 𝑇𝑜𝑣𝑡+1(𝑢𝑡,𝑎𝑡) 𝑇 𝑜𝑐𝑡+1(𝑢𝑡,𝑎𝑡) ⁄ × 𝑇𝑜𝑣𝑡 (ut+1,at+1) 𝑇⁄𝑜𝑐𝑡(ut+1,at+1) 𝑇𝑜𝑣𝑡(𝑢𝑡,𝑎𝑡) 𝑇⁄𝑜𝑐𝑡(𝑢𝑡,𝑎𝑡) ]1/2 (6) With 𝑀𝑜𝑡= 𝑇𝑜𝑡+1(𝑢𝑡+1, 𝑎𝑡+1) 𝑇𝑜𝑡(𝑢𝑡, 𝑎𝑡) (7) 𝑀𝑜𝑡+1= 𝑇𝑜𝑡+1(𝑢𝑡+1, 𝑎𝑡+1) 𝑇𝑜𝑡+1(𝑢𝑡, 𝑎𝑡) (8)
3.2. Data and Variables
3.2.1. Data
It is the only African country with coastal exposure to both the Atlantic Ocean and the Mediterranean Sea. It contains about 34 million populations (annex 1), it is divided into twelve administrative regions. In turn, segmented to several provinces or prefectures, each of them includes a set of PHC.
In this paper, the aim to choose the statistical data of the Ministry of Health of Morocco (2012-2015), whose objective is to clarify the polemic of the health care institution performance of each province or prefecture (PHCP/P). The primary health care supply consists of 2,448 PHC (2015), spread over seventy-five provinces or prefectures (PP). The selection of the seventy-five primary health carenetworks for each province or prefecture, whose data allows us to analyze the inputs and the outputs. It’s difficult to find recent data in the absence of statistics.
3.2.2 Input and Output Statistical Variables and Descriptive
Inputs: the public PHC network in each province or prefecture uses various resources:
Figure 1. Type of Primary Health Care X1: the number of PHC of each province or prefecture.
X2: the total number of physicians in the PHC network in each province or prefecture. X3: the total number of paramedics in each province or prefecture
Outputs: The specification of the production function is based not only on inputs but also on outputs: Y1: the average number of the medical consultations per capita.
Y2: the average number of the consultations Paramedical per capita. Y3: number of the births in PHC.
4. Outcome and Discussion
4.1. Result
In this study, the DEAP software developed by (Coelli, 1996) is opted to measure efficiency scores.
4.1.1. The Efficiency Score
Table 1 and annex 2 show the result of the mean of efficiency scores obtained by using the provision of the PHCP/P in Morocco. The results show that the average technical efficiency score is 0.414, which equals 41% efficiency. Under an input orientation, this result shows that the supply of the primary care of provinces or prefectures can improve their level of input obtained to 59%, by considering of the resources given above. Average scores fell overall in the study period from 0.416 in 2012 to 0.451 in 2015.
Efficiency scores for each PHCP/P are presented in annex 2 of the 75 PHCP/P, under constant scale returns (CRS) efficiency is generally very low but this number is clearly stable over the four periods, so that 6 PHCP/P represent 8 % of total PHCP/P, 8 (11 %), 6 (8 %) and 11 ( 15%) are technically efficient 100 %, respectively in 2012, 2013, 2014 and in 2015 while 67 PHCP/P represent 89 % of total PHCP/P, 66 (88%), 64 (85%), and 62 (83%) are technically inefficient because this value is lesser than 0.849, respectively in 2012, 2013, 2014 andin 2015 (view annex 2).
Table 1. Mean of Efficiency Scores CRS VRS Scale 2012 0.416 0.499 0.833 2013 0.380 0.471 0.802 2014 0.408 0.471 0.852 2015 0.451 0.503 0.885 Mean total 0.414 0.486 0.843
Under the variable scale returns (VRS) 10 PHCP/P (13%), 12 (16%), 9 (12%) and 13 (17%) are technically efficient 100%, respectively in 2012, 2013, 2014 and in 2015 while 63 ESSBP/P (84%), 62 (83%), 62 (8%) and 64 (85%) are technically inefficient below the 0.849 score, 2012, 2013, 2014 and in 2015, respectively.
4.1.2. Malmquist Index
In table 2 and annex 4, the average Malmquist index (Total Factors of Production) in 2013 was 1.150 which explains why the PHCP/P experienced an average increase of 15 % in total productivity of their resources. In 2014, this index is equal to 1.080, there was a 8 % increase in the total productivity of their resources. In 2015, this index is equal to 0.793. The difference is equal to 0.207. This means that PHCP/P experienced gives a 20.7% decrease in the total productivity of its resources. These three developments results in an average Malmquist index are 0.995 (figure 2 and annex 3). Thus, in the period 2012-2015, the PHCP/P improved the total productivity of their factor of production by 0.05%. The sixteen out of the 75 PHCP/P achieved on average an improvement in the total productivity of their factors in the period 2012-2015.
Table 2. Malmquist Index Summary of Annual Means Year effch techch pech sech tfpch 2013 1.049 1.095 1.043 1.006 1.150 2014 1.020 1.059 1.050 0.971 1.080 2015 1.051 0.755 1.039 1.012 0.793 Mean 1.040 0.957 1.044 0.996 0.995
Figure 2. Average Malmquist Index of PHC Supply 2012-2015 With :
effch : CE : Change in Technical Effectiveness ; techch : CT : Change in technical efficiency ; Pech : CP : Pure efficiency;
Sech : CS : Scale efficiency ;
4.2. Discussion
4.2.1. Technical Efficiency
It’s clear that the technical efficiency of PHCP/P is generally very low under an input-oriented approach during the period 2012-2015. The analysis shows that the average technical efficiency score obtained is 0.414 under the constant scale performance (CRS), which explains that the score is 41.4%. In contrast, the average efficiency score under the variable scale return (VRS) has posted 80.44%. The PHCP/P system can increase its efficiency level taking into account the input equal to 59% under the CRS hypothesis and 19.56% under the VRS hypothesis while considering the outputs obtained.
These results are similar to those of the other studies do it in a few African countries of 135 health clinics in Kwazulu-Natal province, South Africa, showing that 30% of them are (Kirigia et al., 2001). In Kenya, 44% of the 32 health centers are efficient in the study conducted by (Kirigia et al., 2004). Osei and his colleagues concluded that out of 31 health centers in Ghana, 82% are satisfactory (Osei et al., September 2005).
1.04
0.957
1.044
0.996 0.995
4.2.2. Malmquist Index
The analysis of the components of Total Factors Production shows that the weakness in the variation of the total productivity resources is explained by the contrary evolution of pure technical efficiency and efficiency due to the technological progress. Pure technical efficiency increased by an average of 4% over the period, while gains due to technical progress decreased by 4.3%. 81% of PHCP/Ps, improved their pure technical efficiency compared to 10% for technological progress. The average increase in gains from pure technical efficiency improvements is the result of the two improvements achieved in 2013, 2014, and 2015 of 4.9%, 2%, and 5.4% respectively.
5. Conclusion
The activities of the PHCP/P have a preventive role that curative the efficiency of this network does not allow to act effectively to contain the health problems for years independence, during the study period 2012-2015, we can project this situation during the COVID 19 health crisis and the next years. To this end, despite the improvement in the supply of Primary Health Care since the 2012-2015 study period, notably through the increase in infrastructure, financial and material resources, and medical, paramedical, and administrative staff, it is generally found that the performance of Primary Health Care is very low. The main issue is not the number of substructures, the funding, or the number of employees, but the management select, the lack of management control, the pressure exerted by political and union lobbies in the administration which is not destined in the supreme interest of the health of a citizen, so that the leaders which work under union or political pressure, their main interesting is to satisfy the orientations of the union or political, consequently, they indirectly neglect the managerial aspect of an order of general interesting.
The efficiency of primary health care based on equity and the quality of management in both urban and rural areas is a difficult objective to achieve due to the complexity of the sector and the numerous constraints weighing on the health system in the area his outfit. To overcome these difficulties gradually and effectively, it is necessary to carry out an in-depth reform of the system, served by a strong political system, and to gradually extend medical coverage. Indeed, the efficiency of the Primary Health Care Network is based on management principles that will allow answering the increased needs of the population in terms of preventive and curative care, through the provision of preventive benefits, curative, promotional, and rehabilitation. This analysis is relative, hence the need to open up several lines of scientific research on the management of public health organizations.
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Annex
Annex 1. The Population of Each Province or Prefecture
DMU * Provinces and Prefectures Populati on in 2014 DM U Provinces and Prefecture s Population in 2014 DM U Provinces and Prefectures Populat ion in 2014 25 Chichaoua 369 955 51 El Jadida 786 716 1
Oued-Eddahab 142 955 26 El Kelaa 537 488 52 Safi 691 983
2 Baoujdour
Laayoune 288 662 27 Essaouira 450 527 53
Sidi
Bennour 452 448
3 Assa-Zag 44 124 28 Marrakech 1330 468 54 Youssou
fia 251 943
4 Es-Semara 66 014 29 Rhamna 315 077 55 Azilal 554 001
5 Guelmim 187 808 30 Berkane 289 137 56 Beni
Mellal 550 678 6 Tan-Tan 86 134 31 Figuig 138 325 57 Fqih Ben Salah 502 827 7 Tata 117 841 32 Jrada 108 727 58 El Hajeb 247 016
8 Agadir 600 599 33 Nador 565 426 59 Errachid
ia 418 451
9 Chtouka- 371 102 34
Oujda-Angads 551 767 60 Ifrane 155 221
10 Inzeggane 541 118 35 Taourirt 233 188 61 Khenifr
a 371 145
11 Ouarzazate 297 502 36 Ain Chock
3359 818 62 Meknes 835 695 12 Sidi Ifni 115 691 37 Ain-Sebaa Hay-Mohamma d 63 Midelt 289 337
13 Taroudante 838 820 38 Al Fida 64 Boulem
ane 197 596
14 Tinghir 207 367 39 Ben Msik 65 Fes 1 324 210
15 Tiznit 322 412 40 Casa-Anfa 66 Sefrou 286 489
16 Zagora 307 306 41 Hay Hassani 67 Al Hoceim a 399 654
17 Kenitra 1 061 435 42 Mediouna 172 680 68 Guercif 216 717
18 Sidi Kacem 522 270 43 Mohamma
dia 404 648 69
Taounat
e 662 246
19 Sidi Slimane 320 407 44
Moulay-Rachid 70 Taza 528 419
20 Ben Slimane 233 123 45 Nouaceur 333 604 71 Chefcha
ouen 457 432
21 Berrechid 484 518 46 Sidi
Bernoussi 72 Larache 496 687
22 Khouribga 542 125 47 Khemisset 542 221 73
Mdiq-Fnideq 209 897
23 Settat 634 184 48 Rabat 577 827 74 Ouazzan
e 300 637
24 Al Haouz 573 128 49 Salé 982 163 75
Tanger-Assilah 1 065 601
50
Annex 2. Evolution of PHCP/P (DMU) Efficiency Scores 2012/2015
2012 2013 2014 2015
DMUa CRSb VRSc Scaled CRS VRS Scale CRS VRS Scale CRS VRS Scale
1 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 2 0.277 0.492 0.563 irs 0.277 0.492 0.563 irs 0.393 0.544 0.722 irs 0.555 0.697 0.796 irs 3 0.204 0.516 0.396 irs 0.204 0.516 0.396 irs 0.335 0.555 0.604 irs 0.421 0.643 0.656 irs 4 0.275 0.401 0.688 irs 0.275 0.401 0.688 irs 0.328 0.408 0.804 irs 0.324 0.394 0.823 irs 5 0.411 0.914 0.450 irs 0.411 0.914 0.450 irs 0.446 0.876 0.509 irs 0.387 0.791 0.489 irs 6 0.204 0.742 0.275 irs 0.204 0.742 0.275 irs 0.233 0.698 0.334 irs 0.323 0.755 0.428 irs 7 0.203 0.575 0.354 irs 0.203 0.575 0.354 irs 0.247 0.546 0.452 irs 0.353 0.578 0.611 irs 8 0.251 0.291 0.864 irs 0.251 0.291 0.864 irs 0.320 0.337 0.951 irs 0.361 0.394 0.914 irs 9 0.240 0.499 0.481 irs 0.240 0.499 0.481 irs 0.289 0.487 0.594 irs 0.366 0.542 0.676 irs 10 0.434 0.589 0.737 irs 0.434 0.589 0.737 irs 0.598 0.676 0.885 irs 0.747 0.820 0.911 irs 11 0.317 0.327 0.969 irs 0.317 0.327 0.969 irs 0.315 0.317 0.995 irs 0.322 0.327 0.985 irs 12 0.325 0.366 0.888 irs 0.325 0.366 0.888 irs 0.411 0.438 0.938 irs 0.443 0.448 0.987 irs 13 0.755 0.779 0.969 irs 0.755 0.779 0.969 irs 0.953 0.953 1.000 - 0.825 0.838 0.984 drs 14 0.278 0.293 0.949 irs 0.278 0.293 0.949 irs 0.293 0.328 0.893 irs 0.396 0.424 0.933 irs 15 0.246 0.316 0.779 irs 0.246 0.316 0.779 irs 0.282 0.357 0.789 irs 0.382 0.441 0.867 irs 16 0.235 0.268 0.876 drs 0.235 0.268 0.876 drs 0.266 0.383 0.693 drs 0.348 0.440 0.791 drs 17 0.210 0.247 0.850 irs 0.210 0.247 0.850 irs 0.224 0.268 0.835 irs 0.270 0.315 0.859 irs 18 0.069 0.136 0.508 irs 0.069 0.136 0.508 irs 0.070 0.126 0.555 irs 0.112 0.158 0.707 irs 19 0.216 0.272 0.796 irs 0.216 0.272 0.796 irs 0.209 0.275 0.760 irs 0.251 0.293 0.855 irs 20 0.385 0.557 0.690 drs 0.385 0.557 0.690 drs 0.433 0.464 0.932 drs 0.389 0.557 0.698 drs 21 0.128 0.172 0.743 irs 0.128 0.172 0.743 irs 0.169 0.211 0.802 irs 0.201 0.227 0.885 irs 22 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 23 0.317 0.411 0.772 irs 0.317 0.411 0.772 irs 0.354 0.414 0.855 irs 0.281 0.303 0.927 irs 24 0.366 0.376 0.972 drs 0.366 0.376 0.972 drs 0.348 0.353 0.986 irs 0.297 0.299 0.994 drs 25 0.252 0.256 0.984 irs 0.252 0.256 0.984 irs 0.268 0.276 0.971 irs 0.269 0.270 0.997 irs 26 0.169 0.182 0.932 irs 0.169 0.182 0.932 irs 0.231 0.232 0.996 irs 0.303 0.304 0.996 irs 27 0.184 0.184 0.999 - 0.184 0.184 0.999 - 0.194 0.204 0.953 irs 0.255 0.263 0.970 irs 28 0.248 0.273 0.910 irs 0.248 0.273 0.910 irs 0.377 0.387 0.973 irs 0.429 0.435 0.987 irs 29 0.365 0.402 0.908 drs 0.365 0.402 0.908 drs 0.361 0.361 1.000 - 0.510 0.518 0.985 drs 30 0.101 0.120 0.845 irs 0.101 0.120 0.845 irs 0.106 0.127 0.830 irs 0.157 0.175 0.898 irs 31 0.175 0.186 0.945 irs 0.175 0.186 0.945 irs 0.193 0.196 0.987 irs 0.198 0.198 1.000 - 32 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 33 0.326 0.415 0.785 irs 0.326 0.415 0.785 irs 0.373 0.431 0.866 irs 0.327 0.373 0.877 irs 34 0.163 0.251 0.649 irs 0.163 0.251 0.649 irs 0.208 0.286 0.729 irs 0.209 0.274 0.764 irs 35 0.160 0.246 0.651 irs 0.160 0.246 0.651 irs 0.241 0.315 0.765 irs 0.300 0.353 0.850 irs 36 0.466 0.482 0.966 irs 0.466 0.482 0.966 irs 0.499 0.559 0.893 irs 0.616 0.618 0.996 drs 37 0.092 0.184 0.500 irs 0.092 0.184 0.500 irs 0.139 0.197 0.707 irs 0.177 0.222 0.797 irs 38 0.469 0.485 0.967 irs 0.469 0.485 0.967 irs 0.515 0.515 0.999 - 0.382 0.458 0.833 drs 39 0.196 0.329 0.594 irs 0.196 0.329 0.594 irs 0.262 0.358 0.733 irs 0.294 0.361 0.814 irs 40 0.696 1.000 0.696 drs 0.696 1.000 0.696 drs 0.902 1.000 0.902 drs 1.000 1.000 1.000 - 41 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 42 0.730 0.910 0.802 irs 0.730 0.910 0.802 irs 0.348 0.430 0.809 irs 0.405 0.451 0.898 irs
43 1.000 1.000 1.000 - 1.000 1.000 1.000 - 0.937 0.953 0.983 irs 0.919 1.000 0.919 drs 44 0.250 0.271 0.921 irs 0.250 0.271 0.921 irs 0.274 0.281 0.976 irs 0.346 0.350 0.989 drs 45 0.602 1.000 0.602 drs 0.602 1.000 0.602 drs 0.551 0.633 0.870 drs 1.000 1.000 1.000 - 46 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 47 0.585 0.616 0.949 drs 0.585 0.616 0.949 drs 0.580 0.610 0.950 drs 0.671 0.715 0.939 drs 48 0.422 0.470 0.898 drs 0.422 0.470 0.898 drs 0.400 0.402 0.995 irs 0.380 0.408 0.933 drs 49 0.147 0.161 0.914 irs 0.147 0.161 0.914 irs 0.124 0.158 0.784 irs 0.158 0.171 0.924 irs 50 0.727 0.804 0.904 drs 0.727 0.804 0.904 drs 0.714 0.724 0.985 drs 1.000 1.000 1.000 - 51 0.316 0.431 0.734 irs 0.316 0.431 0.734 irs 0.374 0.479 0.782 irs 0.560 0.642 0.873 irs 52 0.144 0.154 0.938 irs 0.144 0.154 0.938 irs 0.198 0.209 0.946 irs 0.196 0.202 0.970 irs 53 0.567 0.892 0.636 drs 0.567 0.892 0.636 drs 0.543 0.631 0.860 drs 0.480 0.497 0.966 drs 54 0.337 0.339 0.994 drs 0.337 0.339 0.994 drs 0.414 0.415 1.000 - 0.544 0.548 0.993 drs 55 0.290 0.359 0.809 irs 0.290 0.359 0.809 irs 0.335 0.362 0.926 irs 0.270 0.300 0.899 irs 56 0.303 0.315 0.961 drs 0.303 0.315 0.961 drs 0.296 0.297 0.996 drs 0.357 0.365 0.978 drs 57 0.227 0.318 0.712 irs 0.227 0.318 0.712 irs 0.215 0.272 0.791 irs 0.260 0.295 0.881 irs 58 0.222 0.233 0.954 irs 0.222 0.233 0.954 irs 0.225 0.243 0.925 irs 0.241 0.258 0.936 irs 59 0.088 0.117 0.754 irs 0.088 0.117 0.754 irs 0.110 0.123 0.893 irs 0.099 0.104 0.951 irs 60 0.721 1.000 0.721 drs 0.721 1.000 0.721 drs 0.870 1.000 0.870 drs 0.939 1.000 0.939 drs 61 0.105 0.150 0.698 irs 0.105 0.150 0.698 irs 0.136 0.182 0.748 irs 0.150 0.182 0.822 irs 62 0.950 1.000 0.950 drs 0.950 1.000 0.950 drs 0.840 1.000 0.840 drs 1.000 1.000 1.000 - 63 0.289 0.379 0.762 irs 0.289 0.379 0.762 irs 0.376 0.421 0.893 irs 0.437 0.463 0.944 irs 64 0.105 0.173 0.609 irs 0.105 0.173 0.609 irs 0.159 0.206 0.771 irs 0.159 0.196 0.808 irs 65 0.188 0.190 0.988 irs 0.188 0.190 0.988 irs 0.167 0.184 0.908 irs 0.286 0.302 0.948 irs 66 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 67 0.314 0.357 0.879 drs 0.314 0.357 0.879 drs 0.338 0.389 0.869 drs 0.385 0.425 0.908 drs 68 0.066 0.091 0.727 irs 0.066 0.091 0.727 irs 0.083 0.102 0.815 irs 0.093 0.113 0.823 irs 69 0.216 0.228 0.947 irs 0.216 0.228 0.947 irs 0.222 0.251 0.885 irs 0.307 0.326 0.941 irs 70 0.158 0.607 0.261 irs 0.158 0.607 0.261 irs 0.181 0.619 0.293 irs 0.181 0.524 0.345 irs 71 0.309 0.312 0.993 drs 0.309 0.312 0.993 drs 0.324 0.346 0.938 irs 0.369 0.392 0.940 irs 72 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 1.000 1.000 1.000 - 73 0.475 0.486 0.978 drs 0.475 0.486 0.978 drs 0.574 0.575 0.998 drs 0.534 0.557 0.958 irs 74 0.211 0.265 0.798 irs 0.211 0.265 0.798 irs 0.227 0.264 0.860 irs 0.274 0.286 0.959 irs 75 0.057 0.130 0.437 irs 0.057 0.130 0.437 irs 0.070 0.133 0.523 irs 0.068 0.162 0.420 irs Mean 0.416 0.499 0.833 0.380 0.471 0.802 0.408 0.471 0.852 0.451 0.503 0.885
With:
a. Decision Making Unit b. Technical efficiency from CRS c. Technical efficiency from VRS d. Scale efficiency = crste/vrste e. Efficiency of crescent scale f. Efficiency of decreasing scale
Annex 3. Malmquist Index Summary of Firm Means
DMU Effcha Techchb Pechc Sechd Tfpche DMU Effch Techchb Pechc Sech Tfpche
1 0.980 0.907 1.000 0.980 0.888 40 1.004 0.964 1.000 1.004 0.967 2 0.926 0.901 0.868 1.067 0.835 41 1.486 2.649 1.385 1.073 3.936 3 1.038 0.925 0.956 1.086 0.960 42 1.258 2.348 1.246 1.010 2.954 4 1.019 0.894 0.967 1.053 0.911 43 1.494 2.386 1.422 1.051 3.565 5 1.000 1.111 1.000 1.000 1.111 44 1.042 0.902 1.039 1.003 0.939 6 1.000 1.056 1.000 1.000 1.056 45 1.076 0.958 1.000 1.076 1.031 7 1.137 0.909 1.081 1.052 1.034 46 0.927 1.074 1.087 0.853 0.996 8 1.045 0.909 1.021 1.024 0.950 47 0.833 1.132 1.000 0.833 0.943 9 1.062 0.887 0.939 1.131 0.942 48 1.097 0.878 1.090 1.006 0.964 10 0.862 0.906 0.918 0.939 0.781 49 1.072 0.823 1.066 1.006 0.883 11 1.147 0.882 1.115 1.029 1.012 50 1.050 0.919 1.057 0.994 0.965 12 0.885 0.993 0.890 0.994 0.879 51 0.894 0.879 0.844 1.060 0.785 13 1.127 0.864 1.006 1.121 0.974 52 1.007 0.915 1.093 0.921 0.921 14 1.001 0.908 0.962 1.041 0.909 53 1.119 0.899 1.116 1.002 1.005 15 0.984 0.928 1.002 0.982 0.913 54 1.043 0.930 1.043 1.000 0.970 16 1.079 0.899 1.000 1.079 0.970 55 1.006 0.974 1.012 0.994 0.979 17 1.042 0.893 1.026 1.015 0.931 56 1.103 0.894 1.111 0.993 0.985 18 1.000 0.921 1.000 1.000 0.921 57 1.018 0.931 1.023 0.995 0.947 19 1.156 0.880 1.093 1.058 1.018 58 1.107 0.901 1.107 1.000 0.997 20 1.070 0.898 1.185 0.903 0.960 59 1.000 0.877 1.000 1.000 0.877 21 1.032 0.830 1.002 1.031 0.857 60 1.064 0.942 1.053 1.010 1.002 22 1.024 0.904 1.018 1.006 0.926 61 1.013 0.908 1.021 0.992 0.919 23 0.912 1.053 0.910 1.003 0.961 62 0.988 0.943 0.963 1.027 0.932 24 1.340 0.883 1.276 1.050 1.183 63 1.005 0.904 1.002 1.003 0.909 25 1.171 0.865 1.230 0.953 1.013 64 0.958 0.813 0.960 0.998 0.778 26 0.894 0.991 1.000 0.894 0.886 65 1.027 0.916 1.034 0.993 0.941 27 1.052 0.924 1.275 0.825 0.972 66 1.020 0.925 1.110 0.919 0.943 28 0.911 0.922 0.992 0.919 0.840 67 1.034 0.945 1.150 0.899 0.978 29 1.102 0.877 1.244 0.886 0.966 68 1.000 0.886 1.000 1.000 0.886 30 1.015 0.900 1.162 0.873 0.914 69 1.059 0.888 1.060 1.000 0.940 31 1.079 0.900 1.090 0.990 0.971 70 1.072 0.948 1.000 1.072 1.016 32 1.117 0.889 1.115 1.002 0.993 71 1.074 0.890 1.060 1.014 0.956 33 1.088 0.926 1.071 1.016 1.008 72 1.021 0.918 0.993 1.028 0.937 34 1.010 0.963 1.056 0.957 0.972 73 1.128 0.907 1.094 1.031 1.024 35 0.839 0.987 0.866 0.968 0.828 74 1.033 0.951 1.033 1.000 0.983 36 1.022 0.883 0.974 1.049 0.902 75 1.000 0.905 1.000 1.000 0.905 37 0.984 0.918 1.000 0.984 0.904 38 1.061 0.924 1.056 1.004 0.981 mean 1.040 0.957 1.044 0.996 0.995 39 1.074 0.889 1.033 1.040 0.955 With:
a. Change in total productivity b. Change in Technical Effectiveness c. Change in technical effectiveness d. Pure efficiency
Annex 4. Malmquist Index Summary
Year = 2013 Year = 2014 Year = 2015
firm effch techch pech sech tfpch firm effch techch pech sech tfpch firm effch techch pech sech tfpch
1 1.342 0.773 1.000 1.342 1.037 2 1.031 0.908 0.918 1.122 0.936 3 1.167 1.014 1.071 1.089 1.183 4 1.113 0.833 0.984 1.131 0.927 5 1.000 1.669 1.000 1.000 1.669 6 1.000 1.150 1.000 1.000 1.150 7 1.311 0.935 1.411 0.929 1.227 8 0.953 0.963 0.957 0.997 0.918 9 1.296 0.835 0.923 1.404 1.083 10 1.000 0.828 1.000 1.000 0.828 11 1.263 0.863 1.212 1.042 1.090 12 0.894 1.149 0.895 0.999 1.028 13 1.210 0.813 0.985 1.229 0.984 14 1.006 0.888 0.924 1.089 0.893 15 0.938 0.996 1.028 0.912 0.934 16 1.111 0.846 1.000 1.111 0.940 17 1.006 0.810 0.935 1.076 0.815 18 1.000 0.978 1.000 1.000 0.978 19 1.088 0.895 1.020 1.067 0.974 20 1.049 0.904 0.998 1.052 0.949 21 1.192 0.836 1.094 1.089 0.997 22 0.663 1.051 0.627 1.057 0.696 23 0.679 1.474 0.691 0.984 1.002 24 1.176 0.849 1.058 1.111 0.998 25 1.156 0.889 1.158 0.999 1.028 26 0.659 1.226 1.000 0.659 0.807 27 0.997 0.944 1.102 0.905 0.942 28 0.713 1.409 0.835 0.855 1.005 29 1.367 0.833 1.302 1.050 1.139 30 1.044 0.972 1.030 1.013 1.014 31 1.062 0.953 1.202 0.884 1.013 32 1.310 0.771 1.236 1.060 1.010 33 1.013 0.980 1.028 0.985 0.992 34 0.962 1.145 1.067 0.902 1.102 35 0.726 1.164 0.809 0.897 0.845 36 1.167 0.844 1.014 1.152 0.985 37 0.939 1.214 0.943 0.995 1.140 38 0.982 1.002 0.980 1.002 0.984 39 1.191 0.882 1.119 1.064 1.050 40 0.934 1.043 1.000 0.934 0.974 41 3.280 18.474 2.655 1.235 60.592 42 1.990 12.625 1.934 1.029 25.118 43 3.337 15.298 2.878 1.159 51.045 44 0.972 1.085 0.947 1.026 1.055 45 1.273 0.847 1.000 1.273 1.078 46 0.736 1.387 1.101 0.668 1.021 47 0.596 1.762 1.000 0.596 1.050 48 1.175 0.867 1.186 0.990 1.019 49 1.189 0.813 1.166 1.020 0.967 50 1.084 0.983 1.105 0.981 1.066 51 0.893 0.919 0.702 1.272 0.821 52 0.858 1.165 1.121 0.766 1.000 53 0.803 0.929 0.795 1.010 0.747 54 0.958 0.995 0.994 0.964 0.954 55 0.837 1.262 0.852 0.983 1.057 56 1.132 0.872 1.156 0.979 0.987 57 0.893 1.141 0.898 0.995 1.020 58 1.085 0.896 1.077 1.007 0.972 59 1.000 0.836 1.000 1.000 0.836 1 0.570 1.185 1.000 0.570 0.676 2 0.809 0.965 0.815 0.993 0.781 3 0.858 0.903 0.749 1.145 0.775 4 1.017 0.885 0.961 1.058 0.900 5 0.588 1.104 1.000 0.588 0.650 6 1.000 1.026 1.000 1.000 1.026 7 1.017 0.881 1.012 1.005 0.896 8 0.927 0.977 0.872 1.063 0.906 9 1.064 0.915 1.016 1.047 0.973 10 0.558 0.997 0.570 0.979 0.556 11 1.196 0.896 1.192 1.003 1.072 12 1.165 1.191 1.185 0.983 1.388 13 1.081 0.920 1.018 1.062 0.995 14 0.958 1.168 0.935 1.025 1.119 15 0.793 1.286 0.876 0.905 1.019 16 1.106 1.169 1.000 1.106 1.293 17 1.083 1.094 1.066 1.017 1.185 18 1.000 1.318 1.000 1.000 1.318 19 0.970 1.170 0.997 0.973 1.135 20 1.207 1.017 1.134 1.065 1.228 21 0.865 1.030 0.901 0.960 0.891 22 1.437 1.111 1.519 0.946 1.596 23 1.067 1.100 1.073 0.994 1.174 24 1.116 0.961 1.125 0.992 1.073 25 1.260 0.987 1.248 1.010 1.244 26 0.881 1.345 0.861 1.023 1.185 27 1.011 1.078 1.554 0.651 1.090 28 1.199 1.110 1.928 0.622 1.331 29 1.173 1.118 1.427 0.822 1.312 30 0.963 1.124 1.337 0.720 1.083 31 1.832 1.024 1.077 1.700 1.875 32 0.903 1.111 0.995 0.907 1.003 33 1.028 1.021 1.059 0.971 1.050 34 0.876 1.116 0.911 0.962 0.978 35 0.796 1.113 0.817 0.974 0.886 36 1.022 0.979 1.009 1.012 1.000 37 0.599 1.270 0.645 0.928 0.760 38 0.943 1.033 0.946 0.997 0.974 39 0.959 0.931 0.973 0.986 0.893 40 0.886 1.043 1.000 0.886 0.924 41 1.000 0.972 1.000 1.000 0.972 42 1.000 0.939 1.000 1.000 0.939 43 1.000 0.895 1.000 1.000 0.895 44 0.981 1.126 1.006 0.975 1.104 45 1.000 1.026 1.000 1.000 1.026 46 0.902 1.153 0.563 1.602 1.040 47 0.978 0.978 0.785 1.246 0.956 48 1.407 0.996 1.437 0.979 1.402 49 1.476 0.994 1.467 1.006 1.468 50 1.023 1.172 1.103 0.928 1.199 51 1.085 1.093 1.180 0.920 1.186 52 1.133 1.100 1.164 0.973 1.246 53 1.352 1.123 1.368 0.988 1.517 54 1.109 1.111 1.076 1.031 1.232 55 0.981 1.144 1.041 0.942 1.122 56 1.219 0.970 1.210 1.008 1.182 57 0.894 1.196 0.997 0.897 1.069 58 1.184 1.005 1.162 1.019 1.190 59 1.000 1.121 1.000 1.000 1.121 1 1.228 0.814 1.000 1.228 1.000 2 0.952 0.835 0.873 1.091 0.795 3 1.118 0.865 1.089 1.027 0.967 4 0.934 0.969 0.958 0.975 0.905 5 1.699 0.744 1.000 1.699 1.264 6 1.000 0.997 1.000 1.000 0.997 7 1.103 0.912 0.885 1.246 1.007 8 1.291 0.798 1.275 1.012 1.031 9 0.870 0.912 0.884 0.984 0.793 10 1.149 0.900 1.357 0.847 1.034 11 1.000 0.887 0.961 1.041 0.887 12 0.666 0.716 0.665 1.001 0.477 13 1.094 0.862 1.014 1.079 0.943 14 1.039 0.722 1.029 1.010 0.750 15 1.281 0.624 1.115 1.148 0.799 16 1.021 0.735 1.000 1.021 0.750 17 1.038 0.804 1.085 0.957 0.834 18 1.000 0.606 1.000 1.000 0.606 19 1.465 0.651 1.285 1.140 0.954 20 0.967 0.787 1.470 0.658 0.760 21 1.067 0.663 1.018 1.048 0.707 22 1.127 0.634 1.108 1.017 0.714 23 1.048 0.720 1.016 1.032 0.755 24 1.833 0.844 1.747 1.050 1.548 25 1.103 0.737 1.287 0.857 0.813 26 1.231 0.591 1.161 1.060 0.727 27 1.154 0.774 1.209 0.955 0.893 28 0.885 0.501 0.606 1.459 0.443 29 0.834 0.723 1.035 0.806 0.603 30 1.040 0.668 1.139 0.913 0.695 31 0.645 0.748 1.000 0.645 0.482 32 1.180 0.820 1.126 1.048 0.967 33 1.237 0.794 1.128 1.097 0.982 34 1.220 0.700 1.210 1.009 0.854 35 1.022 0.742 0.983 1.039 0.759 36 0.894 0.833 0.903 0.990 0.744 37 1.695 0.502 1.644 1.031 0.851 38 1.289 0.763 1.272 1.014 0.984 39 1.086 0.856 1.012 1.073 0.929 40 1.223 0.823 1.000 1.223 1.006 41 1.000 1.035 1.000 1.000 1.035 42 1.000 1.093 1.000 1.000 1.093 43 1.000 0.992 1.000 1.000 0.992 44 1.185 0.600 1.177 1.007 0.711 45 0.978 1.013 1.000 0.978 0.991 46 1.200 0.775 2.071 0.579 0.930 47 0.992 0.843 1.274 0.779 0.836 48 0.799 0.784 0.760 1.051 0.627 49 0.701 0.690 0.707 0.992 0.484 50 1.043 0.673 0.968 1.078 0.702 51 0.737 0.675 0.725 1.017 0.498 52 1.049 0.598 1.000 1.049 0.627 53 1.289 0.696 1.279 1.008 0.897 54 1.068 0.727 1.060 1.007 0.776 55 1.238 0.640 1.167 1.061 0.792 56 0.971 0.844 0.981 0.991 0.820 57 1.321 0.591 1.198 1.103 0.781 58 1.058 0.811 1.085 0.975 0.858 59 1.000 0.721 1.000 1.000 0.721
60 1.075 1.044 1.046 1.028 1.123 61 1.081 0.957 1.096 0.986 1.034 62 0.864 0.960 0.863 1.001 0.829 63 0.922 1.060 0.948 0.973 0.977 64 1.000 1.096 1.000 1.000 1.096 65 1.064 0.968 1.079 0.987 1.030 66 0.876 1.123 1.061 0.826 0.984 67 0.908 1.043 1.038 0.875 0.947 68 1.000 0.842 1.000 1.000 0.842 69 1.006 0.996 1.004 1.003 1.002 70 0.945 1.148 1.000 0.945 1.084 71 1.120 0.866 1.070 1.047 0.969 72 1.171 0.794 0.951 1.232 0.931 73 1.433 0.831 1.261 1.136 1.190 74 0.995 0.991 0.997 0.998 0.985 75 1.000 0.818 1.000 1.000 0.818 mean 1.049 1.095 1.043 1.006 1.150 60 1.038 1.067 1.026 1.012 1.107 61 0.895 1.114 0.926 0.966 0.997 62 1.063 1.037 0.793 1.340 1.102 63 0.964 1.112 1.038 0.929 1.072 64 1.000 1.104 1.000 1.000 1.104 65 1.144 1.094 1.156 0.989 1.251 66 1.601 1.061 1.444 1.109 1.699 67 1.080 1.181 1.480 0.730 1.275 68 1.000 1.014 1.000 1.000 1.014 69 1.776 1.086 2.157 0.823 1.929 70 0.874 1.107 1.000 0.874 0.968 71 1.042 0.967 1.073 0.971 1.008 72 1.002 0.943 1.038 0.965 0.944 73 0.891 1.097 0.944 0.943 0.978 74 1.379 1.069 1.361 1.013 1.474 75 1.000 0.939 1.000 1.000 0.939 mean 1.020 1.059 1.050 0.971 1.080 60 1.080 0.750 1.088 0.992 0.810 61 1.073 0.702 1.048 1.024 0.753 62 1.052 0.842 1.304 0.807 0.886 63 1.143 0.627 1.024 1.116 0.717 64 0.878 0.443 0.884 0.994 0.389 65 0.890 0.725 0.888 1.003 0.645 66 0.756 0.664 0.892 0.848 0.502 67 1.128 0.686 0.991 1.139 0.774 68 1.000 0.815 1.000 1.000 0.815 69 0.665 0.647 0.550 1.210 0.430 70 1.493 0.670 1.000 1.493 1.001 71 1.062 0.841 1.036 1.025 0.894 72 0.907 1.033 0.993 0.914 0.937 73 1.125 0.820 1.101 1.022 0.922 74 0.803 0.813 0.812 0.989 0.653 75 1.000 0.965 1.000 1.000 0.965 mean 1.051 0.755 1.039 1.012 0.793
