=Paper= {{Paper |id=Vol-2927/paper8 |storemode=property |title=Applying of Data Envelopment Analysis to Study Public Administration Effectiveness During a Pandemic |pdfUrl=https://ceur-ws.org/Vol-2927/paper8.pdf |volume=Vol-2927 |authors=Tamara Klebanova,Nataliya Poluektova,Olha Rudachenko }} ==Applying of Data Envelopment Analysis to Study Public Administration Effectiveness During a Pandemic== https://ceur-ws.org/Vol-2927/paper8.pdf
                                                                                           94


 Applying of Data Envelopment Analysis to study public
    administration effectiveness during a pandemic

      Tamara Klebanova1[0000-0002-0284-9839], Nataliya Poluektova2[0000-0001-5664-2131],
                       Olha Rudachenko3[0000-0001-9597-5748]

        1
            Simon Kuznets Kharkiv National University of Economics, Ukraine,
                                     t_kleb@ukr.net,
                 2
               V. I. Vernadsky Crimean Federal University, Ukraine,
                          npoluektova68@gmail.com,
    3
      O. M. Beketov National University of Urban Economy in Kharkiv, Ukraine,
                                polkin87@ukr.net

       Abstract. The article deals with the problem of assessing the effectiveness of
       the measures taken by the governments to overcome the crisis caused by the
       COVID19 pandemic. This problem is urgent since the governments and the
       international institutions have not defined common approaches and rules for
       state regulation during a pandemic. The varying degrees of restrictions and
       support measures applied by the governments of different countries have led to
       different results. The proposed model makes it possible to assess the
       effectiveness of government decisions by comparing the cost-benefit ratio with
       the maximum possible value reached in a group of similar countries. The
       mathematical apparatus used in this case is Data Envelopment Analysis, DEA.
       Several DEA-analysis models presented in this article allow us to assess the
       comparative efficiency for 20 European countries based on the ratio of inputs -
       the Government Stringency Index or individual policies of restrictions or
       support, and outputs - mortality rates and changes in the GDP. The study results
       show that this approach makes it possible to assess the effectiveness of state
       regulation and to suggest the directions of potential improvement.

       Keywords: Pandemic, Public Adminisrtation efficiency, Data Envelopment
       Analysis (DEA).


   1. Introduction
    The world's main problem in 2020 was the coronavirus pandemic, which has put
humanity before unexpected and complex challenges. Besides the main tragedy - the
death of more than 2.5 million people around the world, the epidemic has caused
unprecedented consequences in the political and socio-economic spheres: in most
countries the GDP level sank, millions of people lost their jobs, there were global
changes in the structure of employment and forms of labor activity. A crisis of non-
payments is accumulating, many businesses, especially those related to transport,
tourism, and recreation, are ruined.
    The pandemic led to a very complex crisis, which revealed the unpreparedness of
the international community for such tests, both at the level of individual states and
governments, and at the level of international organizations responsible for global


Copyright © 2021 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
95

security, such as the United Nations, the World Health Organization, etc. National
and international institutions still have not developed a unified approach to the
management of citizens' security systems under the new conditions. The health
systems of all countries without exception were not ready for the spread of the new
virus, regardless of their economic development and political system. Governments
were forced to find a balance between the actions to protect the population from the
infection and the actions to ensure economic stability. Some countries, Sweden, for
example, denied the necessity of quarantine measures, others, such as the UK,
decided not to introduce a quarantine for a long time or made it not strict enough.
    The coronavirus pandemic continues in the world - tens of thousands of new cases
of infection are being detected every day in different parts of the world, and many
epidemiologists are talking about the high probability of new pandemics. Under such
circumstances, we need to find methods that allow us to analyze the effectiveness of
the actions taken in individual countries and their communities so that we can identify
patterns, which lead to unfavorable outcomes.
    There are several aspects, which are important while assessing the effectiveness of
government regulation during a pandemic.
    First, it is necessary to take into account the ethical aspect. If we consider
efficiency from this point of view, then the preservation of life and health of people
should have the highest priority. Therefore, performance criteria that reflect the
reduction of cases of infection and death should be used.
    Second, the technical concept of cost efficiency as the ratio between costs and
benefits assumes that the data is comparable and represented in the same units.
However, the main metrics in assessing the effectiveness of management systems
during a pandemic are obviously mortality and economic development indicators, and
the main cost indicator is the degree of government efforts that contribute to the
improvement of the outcome metrics. Quantifying such efforts is a difficult task, and
ensuring comparability and uniformity of such diverse characteristics is even more
difficult.
    Considering these features, this paper proposes an approach that allows assessing
the technical efficiency of public administration systems in an epidemic situation
using the Data Envelopment Analysis (DEA) method. It is this approach, in our
opinion, that makes it possible to overcome the above problems. It proposes to assess
the effectiveness of governance in countries of very different size and level of
development based on identifying the leading countries by a defined performance
indicator, forming a shell or frontier of efficiency and the degree of deviation of other
countries from this frontier, which serves as an indicator of inefficiency.


     2. Literature Review
    Data Envelopment Analysis (DEA) is a technique that is successfully used to
assess the technical efficiency of complex systems. The method allows estimating the
ratio between the costs and the results of any object’s activity, which are compared
with the maximum possible ratio for a group of similar objects.
    For the first time M.Farrell suggested this model to assess the comparative
efficiency of the systems with one input and one output [1]. The works of A. Charns,
                                                                                     96

W. Cooper and E. Rhodes [2,3] and further studies offer multiplicative and additive
versions of models of this type.
    It is possible to present the interesting results of applying this approach to solve
many different problems of evaluating effectiveness. Most of the works are devoted to
the analysis of the production efficiency [4] and the efficiency of banking
technologies or services [5]. However, in recent years more and more often this
method is used to assess the effectiveness of different models for solving
environmental [6, 7], and political problems. So, in the work of J.-M. Huguenin [8],
the DEA method is used to analyze the comparative effectiveness of political
decision-making models. The work of Maragos, Elias K., at all [9] is closest to this
study. It is devoted to the study of the effectiveness of health policies in the EU
countries, based on DEA method.
     The main idea of the method for the problem considered in this paper can be
presented as follows. Suppose, we need to compare the degree of effectiveness of
public administration systems in 20 European countries during a pandemic. The
Government Stringency Index, which is an indicator for government regulation, is
used as an input. It is a composite indicator based on nine different response
indicators, including school closings, job closings, travel bans, etc. on a scale from 0
to 100. Here the average values for the period from March 2020 to February 2021 are
used. The inverse of the average death rate per million people, in the same countries,
for the same period is used as an output or result.




                     Fig. 1. Illustration of the efficiency frontier principle

    Figure 1 shows a set of points that correspond to the costs and the benefits for
each country. The figure shows that the two countries - Estonia and Russia form an
efficiency frontier - the maximum result for a given amount of effort. These
conclusions will not become final in further research and are used here only to
illustrate the essence of the approach. The points, which do not lie on the frontier,
correspond to the states whose activities can be considered ineffective. With the help
of the DEA, we can identify the sources and the extent of inefficiency.
    Below we will explain in more detail the essence of the method.
97

     3. Methodology and Data
    Let there be n objects, each of which has a certain amount (m) of resources, and t
different results. Comparative efficiency is assessed based on the fact, that with a
given amount of resources it is impossible to increase the performance indicators
without a simultaneous deterioration in the performance of other objects.
    To determine effectiveness, the DEA method considers a special ratio between the
weighted sum of the results and the weighted sum of the costs:

                              ∑
                                                                                  (1)
                              ∑

    where are the weights of the output parameters, are the values of the output
parameters for each of the objects j, are the weights of the input parameters, are
the values of the input parameters for each of the objects j.
    The effective object reaches the value of one in the ratio:

             ∑                      ∑                                    (2)
                                {                       ̅̅̅̅̅}
             ∑                      ∑

   The value of this ratio, which is less than one, suggests that the activity of other
objects proves the relative inefficiency of the activity of the object under study.
   The general formulation of the problem, in the formulation "to exit" (achieving the
maximum result at a given value of resource consumption), thus has the form:

                                    ∑                                          (3)
                                    ∑
                                                    ,
     with constraints:

                     ∑                                                      (4)
                                            ̅̅̅̅̅
                     ∑
                                    ̅̅̅̅̅       ̅̅̅̅.                       (5)

   Problem 3-5 can be transformed to linear form for practical reasons. The work of
Charns - Cooper [2] describes the principle of such transformation.
   Expressions 6-9 describe the corresponding linear programming problem.

                               ∑                                            (6)

     with constraints:

                         ∑                                                  (7)
                                                                                      98


              ∑             ∑                    ̅̅̅̅̅                        (8)

                                    ̅̅̅̅̅     ̅̅̅̅,                           (9)

   where ε is an infinitesimal constant, of the order of 10-5.

    This paper uses the model 6-9 as it makes it possible to solve the problems
mentioned in the introduction - the problem of comparability of compared objects by
determining the boundaries of comparative efficiency, which is defined for this set of
objects and the problem of using indicators in different units by introducing weight
coefficients.
    The baseline data for the study was obtained from the following sources.
    1. Data on mortality from COVID-19 by country, taken from the COVID-19 data
repository of the Center for Systems Science and Engineering (CSSE) at Johns
Hopkins University (JHU) [5].
    2. Data on excess mortality during the pandemic, taken from the Human Mortality
Database [6].
    3. Data on the decline in the level of gross domestic product (forecast for 2020)
obtained from the International Monetary Fund [7].
    4. Information about "Government Stringency Index" obtained from the studies of
the Oxford Coronavirus Government Response Tracker (OxCGRT) [8]. The
Government Stringency Index is calculated daily as the average of 9 indicators,
including school closures; the closure of jobs; cancellation of public events;
restrictions on public gatherings; the closure of public transport; requirements not to
leave the place of residence; public information campaigns; restrictions on internal
movement and international movement control. The method for calculating the index
can be found in [9].
    5. Information about the separate indicators forming the Government Stringency
Index and some additional metrics were obtained from OxCGRT too. These
indicators reflect the following policies:
    1) School closures (0 - no actions, 1 - recommendation to close; 2 - requirement to
close certain levels or categories; 3 - requirement to close all levels and categories of
educational institutions).
    2) Workplace closures (0 - no actions; 1 - recommendation to close (or work from
home); 2 - demand to close (or work from home) for some sectors or categories of
workers; 3 - demand to close (or work from home) for all jobs, except for the main
ones (for example, grocery stores, doctors).
    3) Cancellation of public events (0 - no actions; 1 - recommendation to cancel; 2 -
demand to cancel).
    4) Restrictions on public gatherings (0 - no restrictions; 1 - restrictions on
meetings of more than 1000 people; 2 - restrictions on meetings from 100 to 1000
people; 3 - restrictions on meetings from 10 to 100 people; 4 - restrictions on
meetings of less than 10 people ).
    5) Public transport (0 - no actions; 1 - recommendation to close or significantly
reduce the volumes / routes / available vehicles; 2 - requirement to close or prohibit
most citizens from using vehicles).
99

    6) Public information campaigns (0 - no public information campaign about
COVID-19; 1 -state officials urge caution in connection with COVID-19; 2 -
coordinated public information campaign in traditional and social networks).
    7) Stay at home requirements (0 - no actions; 1 - a recommendation not to leave
the house; 2 - a requirement not to leave the house, with the exception of daily
workouts, grocery shopping and "important" trips; 3 - a requirement not to leave the
house with minimal exceptions, for example, it is allowed to go out only once every
few days, or only one person can go out at a time, etc.).
    8) Internal movement (0 - no actions; 1 - recommendation to restrict internal
movements; 2 - requirement to restrict movement).
    9) International travel controls (0 - no actions; 1 - screening; 2 - quarantine
measures for those arriving from high-risk regions; 3 - a ban on travel to high-risk
regions; 4 - complete closure of the border).
    10) Testing policy (0 - no testing policy; 1 - only those who have symptoms and
who meet certain criteria are tested (key staff, hospitalized, contacted with a known
case, returned from overseas); 2 - testing any person with COVID symptoms -19; 3 -
open public testing (for example, "end-to-end" testing available to asymptomatic
people)).
    11) Contract tracking (0 - no contact tracing; 1 - limited contact tracing - not
performed for all cases; 2 - complex contact tracing - performed for all cases).
    12) Face covering (0 - no policy; 1 - recommended; 2 - required in some specific
public places outside the home where other people are present, or in some situations
where social distancing is not possible; 3 - required in all public places outside the
home where other people are present, or in all situations where social distancing is
impossible; 4 - always required outside the home, regardless of the location or
presence of other people).
    13) Vaccination policy (0 - not available; 1 - accessibility for one of the
categories: key workers / clinically vulnerable groups / elderly groups; 2 -
accessibility for several of the following categories: key workers / clinically
vulnerable groups / elderly groups; 3 - accessibility for the following three categories:
key workers / clinically vulnerable groups / elderly groups; 4 - accessibility for all
three plus partial additional accessibility for other categories or age groups; 5 -
universal accessibility).
    14). Income support (0 - no income support; government pays less than 50% of
lost average wages; 2 - government pays 50 percent or more of lost wages).
    15) Debt and contract relief (0 - no relief of debt obligations; 1 - relief, for one
type of obligation; 2 - relief of many types of obligations).
    All of the above data is collected and updated daily on the Our World in Data web
resource [10].
    The data is stored as daily metric values. In this study, we calculated the average
values for three seasons - spring, summer and autumn, conventionally corresponding
to the first wave of the pandemic, the weakening of the epidemic and the second
wave. We also calculated the average values for all indicators for the entire
observation period.
    Data for some countries was not comprehensive enough in the reviewed sources,
that’s why they were excluded from some models.
                                                                                                                                                                        100

4. Results and analysis

   During the study, several data envelope models were built.
   The first model evaluates the effectiveness of public administration actions in 20
European countries based on the average Government Stringency Index as an input
parameter and the average mortality rate in these countries, in the first version -
according to the mortality statistics from COVID 19, and in the second – according
to the excess mortality rate. The model includes 20 linear programming problems of
the following form (10-12).

                                                                                                                                           (10)
  with constraints:
                                                                                                                                           (11)
                                                                            ̅̅̅̅̅
                                                                                                                                           (12)



   where      - the mortality rate for the country under study (the inverse of), -
mortality for each country (the inverse of),     - the Government Stringency Index
for the country under study, - the Government Stringency Index for each country,
μ , ω are weight coefficients.
   The efficiency values for each country are presented in Fig. 2.

                                                         1
                         1    1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
                       0,9                               1

                       0,8                 0,68
                                                                                                                     0,72
                                                                                                                                                    0,68 0,66
                                                                                  0,65                        0,63
                       0,7
   efficiency values




                                                                                         0,62 0,62
                             0,56                 0,57
                       0,6                                   0,53 0,54 0,52
                                                                                                                            0,49 0,51
                                                                                                                                                                 0,46
                       0,5          0,41 0,58                                                          0,43                             0,42 0,58          0,6
                                                                    0,57                                                                      0,4   0,57
                             0,53                                                 0,53                               0,54 0,54
                       0,4                                   0,46                        0,45
                                                                                                              0,48
                       0,3                        0,41                                                 0,39
                                    0,34                                   0,36                                                  0,35
                       0,2                                                                      0,31                                                             0,29

                       0,1
                                                                                                                                        0,14
                         0




                                mortality statistics from COVID 19                                       the excess mortality
                                frontier efficiency


                        Fig. 2. Management efficiency based on average Government Stringency Index and
                       average COVID mortality and excess mortality over the entire observation period
101

    The presented results show that Estonia is at the maximum efficiency level not
only in terms of mortality from COVID, but also in terms of excess mortality.
Among other countries, the Baltic countries, Russia, Romania and Switzerland show
higher management efficiency. However, given the excess mortality, the level of
effectiveness falls in most countries, especially in Poland, Russia, Spain. This can be
explained by the fact, that in the pain of coronavirus, governments have weakened
overall health care efforts. In Sweden and Slovakia, these efforts have had a better
effect on the relative excess mortality rate than on the Covid 19 death rate.
    Next, the efficiency indicators were calculated using the same two outputs and
the 15 policies described above as inputs. The results are presented in Fig. 3.

1,2
                                1          1          1    1     1          1   1          0,98          1   1   1    1
                                                                     0,93
  1                 0,88 0,85
                                               0,84
                                    0,82                                                          0,83
      0,79
             0,73               1          1          1                                                  1   1   1
0,8                                                                                 0,67
                                                                           0,83
0,6 0,74 0,76                                             0,77
                                                                   0,720,69 0,75                                     0,74
                                    0,66                                        0,62
        0,59 0,59                              0,58            0,57
0,4

0,2
                                                                                                  0,24
  0




                       mortality statistics from COVID 19                           the excess mortality

      Fig. 3. Technical effectiveness of country management based on individual policies,
                  taking into account restrictive and supportive measures

    Based on the consideration of different regulatory policies, more countries are at
the upper limit of effectiveness in terms of preventing deaths from COVID. Estonia,
Germany, the Netherlands, Poland, Romania, Russia, Sweden, Switzerland, and
Ukraine acted most effectively in terms of the level of statistically proven mortality
from the virus. However, in terms of excess mortality, it turns out that Romania, the
Netherlands, Poland, Portugal, Russia, and Great Britain made insufficient efforts in
comparison to other countries. Perhaps, the reason is the imperfect methodology for
collecting the mortality statistics from COVID. Such countries as Germany,
Slovakia, Sweden, and Switzerland can serve as examples here.
    Furthermore, it is interesting to analyze how governments were adapting to the
changing situation by adjusting the measures taken. Fig. 4-8 represent some of the
considered policies, averaged over three seasons. The first season, conditionally
“spring”, considers the average daily scores of policies from the beginning of
observations until 01.06.2020. The second season, “summer”, considers these
indicators from 01.06.2020 until 01.10.2020, third season - "autumn" - data from
October 2020 until February 2021.
                                                                                               102


                             workplace_closures

   3
 2,5
   2
 1,5
   1
 0,5
   0




                                                 Slovenia
        Germany
          Austria
        Belgium




                                                Portugal



                                                Slovakia

                                                   Spain
                                                Romania
         Croatia

         Estonia




                                                 Sweden
            Italy
       Lithuania




                                                                                   Ukraine
        Czechia




                                                  Poland
          France




                                                  Russia
        Bulgaria




                            "spring"     "summer"       "autumn"

  Fig. 4. Change in the policy of restricting access to work according to the seasons of the
                                           pandemic


                                   cancel_public_events
 2,5
   2
 1,5
   1
 0,5
   0
          Austria




                                                  Slovenia
        Belgium




        Germany




                                                 Romania

                                                 Slovakia

                                                    Spain
                                                 Portugal
         Croatia

         Estonia



            Italy




                                                   Russia




                                                  Sweden

                                                                                   Ukraine
        Czechia




       Lithuania

                                                   Poland
          France
        Bulgaria




                             "spring"     "summer"        "autumn"

  Fig. 5. Change in the policy of restricting public events for the seasons of the pandemic




Fig. 6. Change of policy on the requirement of wearing masks according to the seasons of the
                                         pandemic
103




  Fig. 7. Change of policy on control of international travel according to pandemic seasons




 Fig. 8. Change in the policy on financial support of citizens according to the seasons of the
                                          pandemic

    The figures do not represent all indicators, but we can see that most governments
have stepped up their response over time, despite the weakening of the epidemic in
the summer months. We can assess how effective such a policy was by constructing
DEA analysis models for each of the seasons. The calculation results for these
models are shown in Fig. 9-11.
    As we can see, most countries in the first wave of the pandemic made little
effort, which, even with excess mortality, led to maximum efficiency indicators. The
exceptions are those countries that suffered the most in the first wave - Belgium,
France, Italy, Spain and Great Britain.
    In the summer period, which in most countries was characterized by a decrease
in morbidity and mortality, governments did not weaken but even tightened
restrictive actions, which was an overuse of resources.
    On the other hand, the delayed problems of the health care systems emerged,
which is shown by the values of the excess mortality factor. Namely, it can be seen
in fig. 10, that in Russia, Romania, Slovakia and some other countries, the efficiency
indicator for excess mortality is significantly lower than the indicator calculated
according to official data on mortality from COVID. At the same time, most of the
countries most affected by the first wave of the epidemic have improved
management effectiveness.
                                                                                                                          104



   1        1 1     111111         1 1          1 1          1 1       1 1     111111          1 1     1111        1
                                                                             0,95
 0,9
0,85
 0,8                                                           0,84
                                                                0,86

 0,7
 0,6
                                                  0,66
 0,5 0,54         0,5       0,53         0,52
                                     0,47             0,44                                                             0,41
 0,4                                                                                                 0,37
 0,3
 0,2
                                                                                        0,16                0,21
 0,1
   0




                        mortality statistics from COVID 19                          the excess mortality

       Fig. 9. Effectiveness of government management actions during the first wave of the
                                     coronavirus pandemic

     1          1              1                1               1
    0,93 0,9      0,93 0,95                       0,94
   0,9    1         1 1            1 0,91 0,92 1 1 0,891 0,9
                                                          1                  0,9             1
                                 0,81                                  0,84                     0,82
   0,8
             0,85           0,87      0,85                                  0,86 0,75 0,73      0,86 0,77 0,89
   0,7                                     0,78                   0,67                     0,69
   0,6
                                                                                 0,66                0,65
   0,5                                                                                0,59
   0,4
   0,3                                                       0,43 0,42
   0,2                                                                 0,29
   0,1
     0




                                                 mortality statistics from COVID 19
                                                 the excess mortality
                                                 "Frontier of efficiency"

   Fig. 10. The effectiveness of public administration actions in the summer period of the
                                   coronavirus pandemic

    The second wave of the epidemic was much more severe than the first, and
consequently the strengthening of restrictive actions in all countries led to an
increase in efficiency.
105


   1,2
                  0,99 1       1              1 0,99 1                     1                                                   1     1     1   1
                                                                                0,89                      0,91
       1
           0,77                               1     1     1     0,74 1                                            1                  1     1   1
                  0,97 0,99        0,99                                                            0,71                                            0,68
   0,8                                                                                 0,65 0,88                              0,91
                                                                                                                 0,6                               0,84
                              0,81 0,55                         0,81                   0,79 0,56                       0,51
   0,6     0,72                                                                 0,72                                   0,73
                                                                                                   0,67 0,67

   0,4

   0,2

       0




                                    mortality statistics from COVID 19                                     the excess mortality

       Fig. 11. Effectiveness of public administration actions during the second wave of the
                                       coronavirus pandemic

    Only in some countries, there was a significant deviation from the general level.
In Poland, Portugal, Czech Republic, and Slovenia, this is reflected in the death rate
from COVID, while the level of measures to reduce excess mortality is sufficient. In
Russia, the situation is opposite. This can be related to an insufficiently effective
system for collecting statistics.
    And, finally, the last model of DEA allows assessing the second result indicator -
the level of change in gross domestic product. In all the countries under
consideration, without exception, it decreased in relation to the previous year. In
contrast to all the previous models, here both the mortality rate and the GDP change
were used as output parameters. The outcome is shown in Fig. 12.

 1,2

   1
                  1                       1                            1               1
 0,8                                                                           0,95                                                      0,95
                                                        0,89                                                                                 0,87
                              0,84                             0,8                             0,84 0,8
                          0,76                                                                                                                   0,79
 0,6 0,72                                         0,7                                      0,73
                      0,67                                                                                       0,670,69
                                                                                                             0,57        0,59
 0,4

 0,2

   0




 Fig. 12. Relative efficiency of public administration, taking into account mortality
                      statistics from Covid and changes in GDP
                                                                                       106


   In terms of the impact on the economy, Belarus, Estonia, Lithuania and Poland
formed the efficiency frontier among the considered countries. The most ineffective
were government regulations in Slovakia and Sweden.

5. Conclusions

    Based on the results of the study, we can make a general conclusion that the
DEA can be used as a tool for assessing the performance of government bodies in
terms of the effectiveness of actions taken to achieve certain strategic goals. The
method makes it possible to reveal the relative efficiency in comparison with the
results of the activities of similar objects, taking into account the influence of factors
expressed in various metrics.
    In the context of this study, various indicators of the relative effectiveness of
governance in European countries during the coronavirus pandemic were identified.
For the countries outside of the efficiency frontier, the DEA efficiency indicator
shows to which degree the input measures can be reduced without decay in output
metrics.
    Other DEA models, extended by age categories of the population, cultural and
behavioral characteristics of countries and regions, can be built to identify the causes
of inefficiency more accurately and to determine effective actions.


References
    1. Farrell, M. J. (1957). The measurement of productive efficiency. Journal of
the Royal Statistical Society. Series A, 120, pp. 253–281.
    2. Charnes, A.,.Cooper, W.W, Seiford, L.M.and oth. (1982). Multiplicative
model for efficiency analysis. Socio–Economic Planning Sciences. 16(5), pp. 223-
224.
    3. Charnes, A., Cooper, W.W., Rhodes, E. (1978). Measuring the efficiency of
decision making units. European Journal of Operational Research. 2, pp. 429-444.
    4. Lie-Chien Lin, Lih-An Tseng (2005). Application of DEA and SFA on the
Measurement of Operating Efficiencies for 27 International Container Ports.
Proceedings of the Eastern Asia Society for Transportation Studies. Vol. 5, pp. 592
– 607.
    5. Tsolas, I. E., Charles, V., Gherman, T. (2020). Supporting better practice
benchmarking: A DEA-ANN approach to bank branch performance assessment
Expert Systems with Applications. V. 160. doi:10.1016/j.eswa.2020.113599.
    6. Yang M. et al. (2020). Assessment and optimization of provincial CO2
emission reduction scheme in China: an improved ZSG-DEA approach. Energy
Economics. Т. 91. doi:10.1016/j.eneco.2020.104931.
    7. Guo, J. et al. (2021). Study on the distribution of PM emission rights in
various provinces of China based on a new efficiency and equity two-objective DEA
model. Ecological Economics. V. 183. doi: 10.1016/j.ecolecon.2021.106956.
107

    8. Huguenin, J. M. (2015). Adjusting for the environment in DEA: A
comparison of alternative models based on empirical data. Socio-economic planning
sciences. V. 52, pp. 41-54 doi: 10.1016/j.seps.2015.10.004
    9. Maragos, E. K., Maravelakis, P. E., Linardis, A. I. (2020). A DEA
evaluation of the successful implementation of HEALTH2020 policies. Socio-
Economic Planning Sciences. doi:10.1016/j.seps.2020.100968.
    10. The Johns Hopkins University & The Johns Hopkins Health System. URL:
http://COVID-19 Data Repository by the Center for Systems Science and
Engineering (CSSE) at Johns Hopkins University
    11. The Human Mortality Database. URL: https://www.mortality.org
    12. International              Monetary              Found.             URL:
https://www.imf.org/en/Publications/WEO/weo-database/2020).
    13. COVID-19         GOVERNMENT           RESPONSE       TRACKER.       URL:
https://www.bsg.ox.ac.uk/research/research-projects/coronavirus-government-
response-tracker
    14. Oxford       Coronavirus     Government      Response     Tracker.   URL:
https://github.com/OxCGRT/covid-policy-
tracker/blob/master/documentation/index_methodology.md
    15. Research and data to make progress against the world’s largest problems.
URL: https://ourworldindata.org/