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Article

Non-Parametric Computational Measures for the Analysis of Resource Productivity

1
Department of Regional Development, Faculty of Economic Sciences, Ionian University, Filosofon & Tzeveleki, 31100 Lefkada, Greece
2
Laboratory of Operations Research, Department of Economics, University of Thessaly, 78 October 28th Street, 38333 Volos, Greece
*
Author to whom correspondence should be addressed.
Energies 2021, 14(11), 3114; https://doi.org/10.3390/en14113114
Received: 17 March 2021 / Revised: 1 May 2021 / Accepted: 23 May 2021 / Published: 26 May 2021

Abstract

:
In this study, we assumed that 28 European countries (Decision Making Units (DMUs)) aimed to accomplish higher economic outputs, using fewer resources and producing fewer emissions in the form of environmental degradation. In this context, we studied the drivers of total factor productivity change (TFPCH) in DMUs, associated with either managerial capabilities (efficiency change (EC)) or innovations (technical change (TC)) in resource-saving production methods, before and after the integration of CO2 (carbon dioxide) emissions as an additional variable (undesirable output) in the initial model of one output (gross domestic product (GDP)) and five inputs (labor, capital, energy, domestic material consumption and recycled municipal waste). The primary focus of this study is to identify best practices that policymakers can adopt as they attempt to reduce productivity loss. Our results highlight the weak areas of individual countries and seem to indicate the action that should be taken to improve their productivity by taking into consideration the main driving force behind productivity and technical efficiency change. Our findings reveal that an effective use of technological developments is determined as important strategic information for ensuring managerial performance.

1. Introduction

Resource productivity related to material and energy flow analysis is an important analytical challenge of international environmental economics and policy. Among dynamic approximations with the objective of quantifying the evolution of productivity over a period of time, there is an extensive body of methodological innovations to characterize network data envelopment analysis (DEA) models [1,2] and dynamic changes in productivity when the data of the evaluated DMUs are panel data of multiple periods [3,4,5,6,7,8,9,10,11]. Such methodological innovations are addressed through the prism of the window analysis framework which is based on the moving average principle [12,13,14], and the Malmquist index that evaluates the dynamic changes of productivity in two periods [15,16].
In this study, we applied non-parametric computational measures for the analysis of resource productivity based on Malmquist and Malmquist–Luenberger models. It is noteworthy here that some non-parametric applications to estimate the performance of different DMUs in the presence of undesirable outputs or material and energy flows is one of the most notable advancements which has attracted considerable attention. Table 1 contains representative literature on the specific research topics.
The main contribution of this paper lies in the fact that new parameters (i.e., recycled municipal waste) are taken into account in DEA-based models to provide valuable managerial insights into resource productivity, and thus, sustainable development. In terms of resource productivity, tied with the prevention of waste creation and loss, there is a need for a more accurate approach to planning sustainable development paths. This study mainly aims to enrich the existing literature on the nonparametric productivity indices by providing additional evidence that deals with material and energy flow management in European countries. Furthermore, the study points out the delineation of the objectives to be achieved by individual countries and indicates the pathways for inefficient countries to help them improve their efficiency.
In this context, we illustrate the application of Malmquist DEA methods to panel data to examine the drivers of total factor productivity change for DMUs under consideration over different time periods. This allows us to decompose the total factor productivity index into its components of technological change (TC—shift on the frontier); technical efficiency change (EC—catching up with their own frontier); pure efficiency change (PEC); and scale efficiency change (SEC) [41,42].
After a brief review of the existing relative literature in Section 1, the structure of the paper is as follows. Section 2 presents the data, the empirical methodology and the formulation of the proposed models. Section 3 provides the empirical findings of the analysis. The final section concludes the paper.

2. Materials and Methods

2.1. Data Analysis: Determining the Total Factor Productivity Change

In our analysis, we determined the index of total factor productivity change and its components by using DEA-based Malmquist (M) and Malmquist–Luenberger (ML) productivity index models (see Table 2) in the case of the 28 European countries (our sample of 28 European countries includes the EU 27 countries as well as the United Kingdom, which officially left the European Union on 31 January 2020), for a period spanning from 2000 to 2018.
As inputs, capital (capital stock at constant 2011 national prices, in million USD, 2011), labor (number of persons engaged, in millions), energy (energy use, in kilograms of oil equivalent per capita), domestic material consumption (biomass, in tons per capita) and recycled municipal waste (tons per capita) were used, while we utilized GDP (GDP per capita, in current USD value) and CO2 emissions (metric tons per capita) as desirable and undesirable outputs, respectively (see Table 3).
The source for capital, labor, GDP and population data was the Penn World Table, version 9.0 [43], and for the energy use, CO2 emissions, biomass and recycled municipal waste data, the Eurostat resource was used [44].

2.2. The Model for the Determination of Malmquist Productivity Index

The Malmquist Index was first proposed by Malmquist [45] and was further extended by Caves et al. [46] and Färe et al. [16]. In simple terms, this index represents the total factor productivity change between the most recent production point relative to the earlier production point by calculating the ratio of the distances of each data point relatively with a specific regular technology.
Relying on Färe et al. [16], the output-oriented Malmquist productivity index is defined as follows:
M = [ D 0 ( x 1 , y 1 ) D 0 ( x 0 , y 0 ) × D 1 ( x 1 , y 1 ) D 1 ( x 0 , y 0 ) ] 0.5
where M represents the productivity of the most recent production point ( x 1 , y 1 ) relative to the earlier production point ( x 0 , y 0 ), in relation to a specific common technology. ( x 0 , y 0 ) and ( x 1 , y 1 ) indicate the previous and the most recent production points, respectively. x denotes the input vector, y denotes the output vector, and D denotes the output distance function. D 0 ( x 0 , y 0 ) represents the output distance function evaluated at the earlier production point under period 0 technology. D 1 ( x 1 , y 1 ) represents the output distance function evaluated at the most recent production point under period 1 technology. D 1 ( x 0 , y 0 ) represents the output distance function evaluated at the earlier production point under period 1 technology. D 0 ( x 1 , y 1 ) represents the output distance function evaluated at the most recent production point under the period 0 technology.
The M index may be decomposed into technical efficiency (EC) and technological progress (TC) as follows:
M = E C × T C
or
M = D 1 ( x 1 , y 1 ) D 0 ( x 0 , y 0 ) E C [ D 0 ( x 1 , y 1 ) D 1 ( x 1 , y 1 ) × D 0 ( x 0 , y 0 ) D 1 ( x 0 , y 0 ) ] T C 0.5
The EC index can be further decomposed into pure technical efficiency change (PEC) and scale efficiency change (SEC) as follows:
E C = P E C × S E C
Therefore, the M index can be decomposed into the three components:
M = P E C × S E C × T C
or
M = D v , 1 ( x 1 , y 1 ) D v , 0 ( x 0 , y 0 ) P E C × D c , 1 ( x 1 , y 1 ) D v , 1 ( x 1 , y 1 ) D c , 0 ( x 0 , y 0 ) D v , 0 ( x 0 , y 0 ) S E C × ( D c , 0 ( x 1 , y 1 ) D c , 1 ( x 1 , y 1 ) × D c , 0 ( x 0 , y 0 ) D c , 1 ( x 0 , y 0 ) ) T C 0.5
The first two components determine the performance of a DMU under both CRS and VRS technologies, while the third component (TC) is calculated relative to the CRS technology. The values of the M index and its components (PEC, SEC and TC) can be greater, equal to, or smaller than 1. When the M index is greater (less) than unity, there is an improvement (decline) in productivity. If the M index and its components are equal to 1, the total factor productivity remains unchanged.

2.3. The Model for the Determination of Malmquist–Luenberger Productivity Index

The ML productivity index is employed to measure productivity growth by introducing both desirable (GDP) and undesirable (CO2 emissions) outputs in the production model. The ML productivity index is constructed and decomposed in a similar way to the abovementioned productivity index of Malmquist. According to Chung et al. [47], the output-oriented ML productivity index based on the two periods (from 0 to 1) directional distance function (DDF) is identified as:
M L = { [ 1 + D 1 ( x 0 , y 0 , b 0 ; y 0 , b 0 ) ] [ 1 + D 1 ( x 1 , y 1 , b 1 ; y 1 , b 1 ) ] × [ 1 + D 0 ( x 0 , y 0 , b 0 ; y 0 , b 0 ) ] [ 1 + D 0 ( x 1 , y 1 , b 1 ; y 1 , b 1 ) ] } 0.5
where ML represents the productivity of the most recent production point ( x 1 , y 1 , b 1 ) relative to the earlier production point ( x 0 , y 0 , b 0 ), in relation to a specific common technology. ( x 0 , y 0 , b 0 ) and ( x 1 , y 1 , b 1 ) indicate the previous and the most recent production points, respectively. x denotes the input vector, y denotes the desirable output, b represents the undesirable (bad) output, and D denotes the output distance function. D 1 ( x 0 , y 0 , b 0 ; y 0 , b 0 ) represents the output distance function evaluated at the earlier production point under period 1 technology. D 1 ( x 1 , y 1 , b 1 ; y 1 , b 1 ) represents the output distance function evaluated at the most recent production point under period 1 technology. D 0 ( x 0 , y 0 , b 0 ; y 0 , b 0 ) represents the output distance function evaluated at the earlier production point under period 0 technology. D 0 ( x 1 , y 1 , b 1 ; y 1 , b 1 ) represents the output distance function evaluated at the most recent production point under period 0 technology.
The ML index may be decomposed into technical efficiency (ECL) and technological progress (TCL) as follows:
M L = E C L × T C L
or
M L = [ 1 + D 0 ( x 0 , y 0 , b 0 ; y 0 , b 0 ) ] [ 1 + D 1 ( x 1 , y 1 , b 1 ; y 1 , b 1 ) ] E C L { [ 1 + D 1 ( x 0 , y 0 , b 0 ; y 0 , b 0 ) ] [ 1 + D 0 ( x 0 , y 0 , b 0 ; y 0 , b 0 ) ] × [ 1 + D 1 ( x 1 , y 1 , b 1 ; y 1 , b 1 ) ] [ 1 + D 0 ( x 1 , y 1 , b 1 ; y 1 , b 1 ) ] } T L 0.5
The ECL index can be further decomposed into pure technical efficiency (PECL) and scale efficiency (SECL) as follows:
E C L = P E C L × S E C L
Therefore, the ML index can be decomposed into the three components:
M L = P E C L × S E C L × T C L
or
M L = 1 + D v , 0 ( x 0 , y 0 , b 0 ; y 0 , b 0 ) 1 + D v , 1 ( x 1 , y 1 , b 1 ; y 1 , b 1 ) P E C L × 1 + D c , 0 ( x 0 , y 0 , b 0 ; y 0 , b 0 ) 1 + D v , 0 ( x 0 , y 0 , b 0 ; y 0 , b 0 ) 1 + D c , 1 ( x 1 , y 1 , b 1 ; y 1 , b 1 ) 1 + D v , 1 ( x 1 , y 1 , b 1 ; y 1 , b 1 ) S E C L × ( [ 1 + D c , 1 ( x 0 , y 0 , b 0 ; y 0 , b 0 ) ] [ 1 + D c , 0 ( x 0 , y 0 , b 0 ; y 0 , b 0 ) ] × [ 1 + D c , 1 ( x 1 , y 1 , b 1 ; y 1 , b 1 ) ] [ 1 + D c , 0 ( x 1 , y 1 , b 1 ; y 1 , b 1 ) ] ) T C L 0.5
where D c , 0 , D v , 0 , D c , 1 , and D v , 1 , represent the directional distance functions under constant and variable returns to scale, in relation to a specific common technology.
The first two components determine the performance of a DMU under both CRS and VRS technologies. Specifically, the PECL component in each period is defined with respect to the VRS technology, as the ratio of the own-period distance functions, whereas the SECL component in each time period is constructed as the ratio of the distance function from both CRS and VRS frontiers. The third component (TCL) is calculated relative to the CRS technology.
Similar to the M index, the ML index and its components (PECL, SECL and TCL) also show productivity advances if their values are greater than one, and reductions in productivity if the values are less than unity.

3. Results

The Malmquist and the Malmquist–Luenberger productivity scores of the 28 European countries for the period 2000 to 2018 are given in Table 4 and Table 5, respectively. As shown in Table 4 and Table 5, the productivity scores of the Malmquist index range between 0.359 and 3.856, while the productivity scores of the Malmquist–Luenberger index range between 0.587 and 2.51. According to the annual means of the specific indices, the countries can be divided into two categories based on their productivity growth. The first category includes countries whose mean productivity scores is less than unity. In this case, the slowdown in productivity is linked to the loss in productive performance.
The first category includes Bulgaria, Ireland, Denmark, Luxembourg, Belgium, Spain, the Netherlands, France, Italy, Austria, Germany, Finland, Portugal, Sweden, Greece, the United Kingdom, Cyprus, Malta, and Slovenia, based upon the Malmquist model, and Ireland, Denmark, Luxembourg, Belgium, Netherlands, Austria, Finland, Italy, France, Spain, Sweden, Greece, Germany, the United Kingdom, Cyprus, and Portugal, based upon the Malmquist–Luenberger model.
The second category where the mean productivity scores are greater than unity is directly linked to productivity gains and includes Hungary, Poland, Estonia, Slovakia, Latvia, Czechia, Lithuania, Croatia, and Romania, based upon the Malmquist model, and Malta, Slovenia, Hungary, Poland, Bulgaria, Latvia, Slovakia, Croatia, Czechia, Lithuania, Estonia, and Romania, based upon the Malmquist–Luenberger model.
In the cases of Bulgaria (11.65%), Ireland (0.20%), Belgium (0.17%), Spain (1.24%), Netherlands (0.20%), Italy (0.45%), France (0.63%), Germany (0.59%), Austria (0.07%), Portugal (2.28%), Greece (0.06%), the United Kingdom (0.04%), Cyprus (1.10%), Malta (3.03%), Slovenia (1.19%), Hungary (0.77%), Estonia (5.86%) and Slovakia (1.83%), there is an increase in the TFPCH index after the integration of CO2 emissions as an additional variable in the initial model.
In the cases of Denmark (−0.12%), Sweden (−0.01%), Poland (−1.49%), Latvia (−2.19%), Czechia (−1.58%), Lithuania (−1.94%), Croatia (−2.86%) and Romania (−8.67%), there is a decrease in the TFPCH index after the integration of CO2 emissions as an additional variable in the initial model.
In many cases, the differences are due to the advanced use of emission abatement technology indicated by the Malmquist–Luenberger models and serve as a benchmarking target among DMUs. Additionally, the level of industrialization has a significant impact on energy consumption and CO2 emissions, and therefore on productivity change, which varies among countries with different levels of development and transition to clean energy.
Comparing the productivity scores before (Malmquist model) and after (Malmquist–Luenberger model) the integration of CO2 emissions as an additional variable, we found that in the cases of Luxembourg (0.00%) and Finland (0.00%), the TFPCH index remained unchanged.
The productivity analysis and the identification of the best practice DMUs with different production mixes to the efficient frontier indicated the flexibility of an inefficient DMU to choose an improvement direction that optimizes energy and material flow management, and thus its productivity.
The decomposition analysis of the TFPCH index on its driving forces was determined as an important strategic information tool for increasing the competitive power of inefficient DMUs, guaranteeing their comparative advantage in the long run (Table 4, Table 5 and Table 6, Table A1 and Table A2 (Appendix A).
In Table 6, the profile of each country in terms of energy and material flow management is mapped. From Table 6, we can conclude the following points:
  • In the Malmquist model, the primary driving force of productivity change in the whole sample arises as a result of an improvement in technical efficiency;
  • In the Malmquist–Luenberger model, the primary driving force of productivity change arises either as a result of an improvement in technical efficiency (Bulgaria, Ireland, Denmark, Luxembourg, Belgium, Spain, the Netherlands, Italy, France, Germany, Austria, Portugal, Finland, Sweden, Greece, United Kingdom, Cyprus, Slovenia, Poland and Estonia) or due to technological progress (Malta, Hungary, Slovakia, Latvia, Czechia, Lithuania, Croatia and Romania);
  • In the Malmquist model, the primary driving force of efficiency change is related either to an improvement in pure technical efficiency (Denmark, Belgium, Spain, the Netherlands, Italy, France, Germany, Austria, Portugal, Sweden, Greece, United Kingdom, Slovenia, Hungary, Poland, Estonia, Slovakia, Latvia, Czechia, Lithuania, Croatia and Romania) or to an improvement in scale efficiency (Bulgaria, Ireland, Finland, Cyprus, Malta). In the case of Luxembourg, the driving forces of pure and scale efficiency change are of equal importance;
  • In the Malmquist–Luenberger model, the primary driving force of efficiency change is related either to an improvement in pure technical efficiency (Bulgaria, the Netherlands, Estonia, Czechia and Romania) or to an improvement in scale efficiency (Ireland, Denmark, Belgium, Spain, Italy, France, Germany, Austria, Portugal, Finland, Sweden, Greece, United Kingdom, Slovenia, Hungary, Poland, Slovakia, Latvia, Lithuania and Croatia). However, in the cases of Luxembourg, Cyprus and Malta, the driving forces of pure and scale efficiency change are of equal importance.

4. Discussion

In the cases of Austria, Belgium, Denmark, France, Germany, Greece, Italy, the Netherlands, Portugal, Slovenia, Spain, Sweden and the United Kingdom, although improvement in both management and technology factors reflects the achievement of optimal allocation of resources in the production process of DMUs and therefore the improvement in technical efficiency, the overall productivity has remained poor due to the adverse shift in the production frontier that can negatively impact resource conservation and recovery. This implies that resource allocation and resource saving production methods must be based on the perspective of technological progress and innovation to encourage increased throughput of raw materials and energy.
In the cases of Bulgaria, Cyprus, Finland, Ireland and Malta, DMUs’ improvement in technical efficiency which results from the improvement in scale efficiency and thus the largest, most productive scale size is expressed by the convergence between their optimal production scale and the actual production scale. However, in contrast to the technical efficiency improvement, the overall productivity has remained poor, which indicates that there is considerable room for targeted knowledge that advanced technologies can create for the production activities of companies and countries. This will help policymakers to develop accurate business investments in order to build a successful strategic business plan of high value-adding technologies and the utilization of local resources.
By contrast, Croatia, Czechia, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia, which performed the best in terms of overall productivity (productivity gains), experienced a strong efficiency progress due to the achievement of the optimal allocation of resources in the production process. To maintain such significant gains and further boost productivity, the specific DMUs need to enhance the introduction of advanced technologies in key areas (i.e., energy storage) and determine their future impact, by capturing current technical readiness and adoption levels across processes, industries, and geographies.
It is worth noting that after the integration of CO2 emissions as an additional variable in the initial model, a dispute arose in the majority of the countries analyzed (Denmark, Belgium, Spain, Italy, France, Germany, Austria, Portugal, Sweden, Greece, United Kingdom, Slovenia, Hungary, Poland, Slovakia, Latvia, Lithuania and Croatia), relating to the fundamental driving force (SECL) of technical efficiency, through which the specific countries could manage to reduce the long-term average cost as production increases.

Author Contributions

Conceptualization, C.B. and G.H.; methodology, C.B. and G.H.; software, C.B.; validation, C.B. and G.H.; formal analysis, C.B. and G.H.; investigation, C.B. and G.H.; resources, C.B.; data curation, C.B. and G.H.; writing—original draft preparation, C.B.; writing—review and editing, G.H.; visualization, C.B.; supervision, G.H. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Table A1. Annual means, for the entire period, of Malmquist productivity index components by country.
Table A1. Annual means, for the entire period, of Malmquist productivity index components by country.
CountriesECTCPECSEC
Austria1.02600.94111.02531.0009
Belgium1.01020.94181.00851.0018
Bulgaria0.97980.93890.98721.0089
Croatia1.06291.04571.05741.0084
Cyprus1.00910.96371.00001.0102
Czechia1.05401.04201.06470.9713
Denmark1.00660.94201.00551.0010
Estonia1.10310.97701.23031.0150
Finland1.02160.95191.01151.0152
France1.01510.94791.01451.0004
Germany1.02250.94481.02171.0015
Greece1.02690.94441.02671.0012
Hungary1.03920.96661.04400.9950
Ireland1.00000.93921.00001.0000
Italy1.01220.95021.00971.0037
Latvia1.09451.01741.09161.0653
Lithuania1.11231.00311.13601.0271
Luxembourg1.00000.94961.00001.0000
Malta1.00150.97181.00001.0015
The Netherlands1.01760.94061.01321.0056
Poland1.05900.99851.06451.0006
Portugal1.02350.94411.02251.0024
Romania1.09251.08121.00000.9351
Slovakia1.05051.01601.05221.0002
Slovenia1.05010.95261.05001.0130
Spain1.01080.94581.00961.0022
Sweden1.02420.94551.01231.0121
United Kingdom1.01710.95461.01331.0038
Table A2. Annual means, for the entire period, of Malmquist–Luenberger productivity index components by country.
Table A2. Annual means, for the entire period, of Malmquist–Luenberger productivity index components by country.
CountriesECLTCLPECLSECL
Austria1.02290.94561.00471.0178
Belgium1.00920.94510.99801.0115
Bulgaria1.02541.01621.01231.0114
Croatia1.00011.08291.00001.0002
Cyprus1.00000.98331.00001.0000
Czechia1.03871.04651.02771.0143
Denmark1.00180.94551.00001.0018
Estonia1.13090.99751.08291.0268
Finland1.02160.95180.99931.0221
France1.01180.95850.99991.0119
Germany1.02020.95271.00841.0111
Greece1.00080.97160.99171.0086
Hungary1.00351.00500.99431.0091
Ireland1.00000.94121.00001.0000
Italy1.00660.96110.99741.0090
Latvia1.01561.05331.00001.0156
Lithuania1.03521.04301.00691.0316
Luxembourg1.00000.94961.00001.0000
Malta1.00001.00501.00001.0000
The Netherlands1.01190.94871.00861.0029
Poland1.01871.01281.00351.0141
Portugal1.00530.98670.99641.0080
Romania1.00031.14521.00000.9987
Slovakia1.02641.05390.99681.0275
Slovenia1.03390.99140.99731.0305
Spain1.00580.96530.99301.0123
Sweden1.02460.94581.00001.0246
United Kingdom1.01130.96041.00251.0085

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Table 1. Methodology and input/output factors used in the previous studies.
Table 1. Methodology and input/output factors used in the previous studies.
AuthorData Sample/Time IntervalMethodVariables (Inputs–Outputs)
Mirmozaffari et al. [17]Cement companies/2015–2019Machine learning algorithms, DEA modelsInput: energy consumption
Intermediate products: cement production, pollution control investment
Outputs: waste material removed, waste gas removed, solid waste removed
Wang and Wang [18] Chinese industry/2011–2016DEAInputs: capital, labor, energy
Outputs: industrial output value, CO2 emission
Shen et al. [19] 15 provinces in the tropics and subtropics of China/2005–2016DEAInputs: ecological footprint, capital stock, labor force
Output: Human Development Index
Wang et al. [20]37 industrial sub-sectors in Liaoning province/2003–2012DEA, Malmquist–Luenberger Productivity IndexInputs: fixed assets, labor force, energy consumption
Desirable output: added value
Undesirable output: CO2 emissions
Savović and Mimović [21] Acquired companies in the cement industry/2000–2018 DEA Window analysis, Malmquist Productivity IndexInputs: material, capital, labor
Output: operating revenues
Piao et al. [22]30 provinces in China/2005–2014 DEA, Malmquist–Luenberger Productivity IndexInputs: employment, annual water consumption, capital stock, energy consumption
Desirable output: GDP
Undesirable output: CO2, SO2, waste water produced, solid wastes produced
Gao et al. [23] 21 major industrial sectors in China’s 30 provinces/2004–2014 DEA, Malmquist Productivity IndexInputs: capital, labor, energy
Desirable output: gross industrial output value
Undesirable output: CO2 emissions
Le et al. [24]9 East Asian countries/2002–2010DEA, Malmquist Productivity Index, slacks-based measure (SBM)Inputs: labor, capital stock, agricultural land, agricultural consumption of fertilizers
Desirable output: gross agricultural production value
Undesirable output: GHG emissions
Xian et al. [25]China’s power industry/2016–2020DEA, Luenberger Productivity IndexInputs: employee, fuel consumption, installed capacity
Intended output: gross electricity generation
Unintended output: CO2 emissions
Wang et al. [26] China’s thermal power industry/2006–2014DEAInputs: energy consumption, installed capacity, employee
Desirable output: electricity generation
Undesirable outputs: CO2 emission, SO2 emission, NOx emission, Soot emission
Undesirable output abatements: absorbed SO2, absorbed NOx, absorbed soot
Li and Zhang [27]18 EU countries/1995–2006DEAInputs: capital stock, labor, intermediates (energy, materials and services)
Desirable output: gross output
Undesirable outputs: CO2 emissions
Lee [28] 30 provinces in China power sector/2010DEAInputs: Nameplate capacity, labor force, energy consumption
Desirable output: electricity
Undesirable outputs: CO2, SO2, NOx
Song et al. [29]30 provinces in China/2006–2013DEA, Luenberger Productivity IndexInputs: employees, installed capacity, coal consumption
Desirable output: electricity generation
Undesirable outputs: CO2 emissions, SO2 emissions, NOx emissions, dust emissions
Bampatsou et al. [30]EU 15 countries/1995–2011DEA, Malmquist Productivity IndexInput: total primary energy consumption
Desirable output: GDP
Undesirable output: CO2 emissions
Li et al. [31]17 EU member states/1995–2006DEA, Sequential Malmquist Productivity IndexInputs: capital stock, labor, intermediates (energy, materials and services)
Desirable output: gross output
Undesirable outputs: CO2 emissions
Nielsen [32]Iron and steel sector in 14 market economies and 7 planned economies /1973, 1980, 1990 and 2000 DEAInputs: coke, iron ore, energy, scrap
Outputs: pig iron, crude steel
Rácz and Vestergaard [33]Danish centralized biogas power plants/1992–2005DEA, Malmquist Productivity IndexInputs: animal manure, other organic waste
Output: biogas product
Pardo Martínez and Alfonso Piña [34]Colombian departments in the manufacturing industries/2005 and 2013 DEA, Malmquist Productivity IndexInputs: energy, labor, capital, materials
Desirable output: gross production
Undesirable output: CO2 emissions
Zhou et al. [35]29 OECD countries/2000–2011DEA, Malmquist Productivity IndexInputs: capital stock, labor force
Desirable output: gross production
Undesirable output: CO2 emissions, CH4 emissions, N2O emissions
Xue et al. [36]30 provinces in China/2004–2009DEA, Malmquist Productivity IndexInputs: coal consumption, electricity consumption
Output: industrial value added
Kapelko et al. [37]Spanish (5706) and Portuguese (965) construction firms/2002–2011DEA, Luenberger Productivity IndexInputs: capital, labor, materials
Output: operating revenues
Anser et al. [38]8 world regions/2010–2016DEAInputs: primary energy consumption, total labor force
Desirable output: GDP
Undesirable output: CO2, NO2
Chen et al. [39]56 Belt and Road Initiative countries/2005–2015DEA, Malmquist Productivity IndexInputs: energy consumption, total capital formation, labor
Desirable output: GDP
Undesirable output: carbon emissions
Mavi and Mavi [40]OECD countries/2012–2015DEA, Malmquist Productivity IndexInputs: labor force, energy use
Outputs: GDP, renewable energy, GHG, municipal waste
Notes: OECD: Organization for Economic Cooperation and Development, EU: European Union, GHG: greenhouse gas, CH4: methane, SO2: sulfur dioxide, NO2: nitrogen dioxide, NOx: nitrogen oxides, N2O: nitrous oxide.
Table 2. Variables of DEA-based Malmquist and Malmquist–Luenberger productivity index models.
Table 2. Variables of DEA-based Malmquist and Malmquist–Luenberger productivity index models.
MML
OutputsGDP (gdppc)GDP (gdppc)
CO2 emissions (nCO2pc)
InputsCapital (ck)Capital (ck)
Labor (emp)Labor (emp)
Energy (eupc)Energy (eupc)
Biomass (mf2pc)Biomass (mf2pc)
Recycled Municipal Waste (rwastepc)Recycled Municipal Waste (rwastepc)
Table 3. Descriptive statistics of variables used in our analysis.
Table 3. Descriptive statistics of variables used in our analysis.
VariableObsMeanStd. Dev.MinMax
gdppc53229,026.0920,606.091609.882118,823.6
nCO2pc5327.59023.517852.6826224.8246
ck5322,812,4134,021,60125,376.4515,800,000.00
emp5328.01489610.368550.148066443.62769
eupc5323423.7551451.4351494.759428.812
mf2pc5323.7687911.7183021.27310.286
rwastepc532145.9269110.14520.0000000001424.743
Table 4. Malmquist productivity indices.
Table 4. Malmquist productivity indices.
Country2000–20012001–20022002–20032003–20042004–20052005–20062006–20072007–20082008–20092009–20102010–20112011–20122012–20132013–20142014–20152015–20162016–20172017–2018Mean
Austria1.0430.9330.8360.9210.9700.9510.8520.9221.0151.0770.9001.0330.9680.9551.1600.9800.9290.9320.965
Belgium0.9890.9030.8240.8710.9550.9420.8850.9101.0511.0590.8711.0010.9770.9331.1450.9540.9440.9120.952
Bulgaria1.0010.8540.7640.8820.8090.8850.7060.8680.9331.0790.9251.0050.9220.9811.1710.9460.9500.8940.921
Croatia1.2671.0590.8331.0911.0981.1090.8950.8590.9631.4611.6421.7550.9880.9971.1540.9900.9270.9211.112
Cyprus0.9900.9170.8180.8431.0260.9700.9621.0461.0741.0040.9781.0760.9121.0351.1320.9230.9040.8910.972
Czechia0.9420.7750.7532.4590.9711.0261.0510.8361.2751.0931.0041.3811.0411.1011.1861.1170.8940.8951.100
Denmark1.0170.9080.8550.8480.9300.9650.8780.9141.0611.0320.8811.0200.9560.9151.1400.9470.9420.8680.949
Estonia1.4210.5461.9250.8730.8600.7470.9230.7611.2530.8781.0250.7730.8981.9921.0590.9211.0320.9071.044
Finland0.9940.9660.8490.8770.9630.9430.8670.8781.0511.0500.9681.0270.9120.9861.2150.9810.9250.9410.966
France1.0000.9380.7770.9500.9500.9470.8780.9231.0531.0290.8981.0750.9590.9581.1720.9510.9540.9070.962
Germany0.9730.9150.7791.0140.9470.9300.9520.9261.0431.0340.8901.0660.9490.9481.1570.9700.9520.9280.965
Greece0.9830.8960.7780.8590.9910.8580.8680.8851.0701.0581.0171.1130.9120.9991.2270.9980.9940.9450.969
Hungary0.8950.9800.9801.2210.9530.9780.8010.9331.1151.0730.9501.2120.9111.0101.1661.0160.8810.9291.000
Ireland0.9610.9020.8010.8920.9310.9340.8820.9711.1231.0680.8741.0470.9390.9210.9240.9680.8980.8740.939
Italy0.9810.9250.8280.9460.9890.9420.8980.8991.0411.0510.9061.0440.9420.9581.1880.9210.9290.9200.962
Latvia1.2640.9191.5461.3960.7370.9510.8490.9131.4661.0150.9061.3451.4140.9821.2050.9440.9130.8751.091
Lithuania0.9970.9040.806.0.8830.8892.4620.9201.1490.6662.2741.1210.9170.9741.1770.9510.8920.8791.110
Luxembourg0.9320.9410.8150.9450.8930.9670.8510.8461.1030.9900.8641.1110.8351.0391.0660.9741.0160.9060.950
Malta1.0180.7820.9880.9611.1051.0770.6160.8581.1651.0101.2511.1130.8430.8721.0730.9720.9500.8920.975
The Netherlands0.9730.9090.8190.8950.9140.9300.9460.9211.0701.0840.8781.0870.9510.9371.1430.9690.9390.8560.957
Poland1.1700.8060.8561.2011.0851.0540.8650.9651.2771.0180.7371.0861.0961.3861.2401.0650.8980.9191.040
Portugal0.9870.9060.8120.9080.9600.9050.8820.9111.1000.9900.9521.1180.9501.0081.1990.9590.9330.9120.966
Romania2.3851.0420.3592.2381.1240.4270.6171.3311.2573.8560.7791.2550.8080.9291.1160.9990.9670.6971.233
Slovakia1.0390.8730.8170.8860.4541.4011.2261.0181.1261.0971.0361.2220.7840.9741.7031.4441.0030.9611.059
Slovenia0.8031.5560.8410.9930.9250.8840.8650.8310.9811.1551.0621.0410.9530.9621.1371.0350.8611.0120.994
Spain0.9600.9230.7990.8830.9280.9240.8730.8841.0041.0370.9441.1060.9430.9591.1860.9950.9120.9420.956
Sweden1.1260.9410.7880.9001.0320.8080.9040.9331.1290.9590.8601.0470.9450.9901.1750.9750.9550.9630.968
United Kingdom1.0220.9520.8930.8910.9660.9330.8571.0531.1480.9990.8781.0030.9700.8661.0441.0671.0100.9140.970
Table 5. Malmquist–Luenberger productivity indices.
Table 5. Malmquist–Luenberger productivity indices.
Country200–20012001–20022002–20032003–20042004–20052005–20062006–20072007–20082008–20092009–20102010–20112011–20122012–20132013–20142014–20152015–20162016–20172017–2018Mean
Austria1.0420.9330.8380.9210.9700.9510.8520.9301.0121.0710.9011.0320.9700.9611.1470.9930.9270.9370.966
Belgium0.9880.9020.8260.8700.9550.9450.8950.9131.0711.0570.8710.9980.9770.9401.1370.9430.9650.9050.953
Bulgaria1.0740.9320.9590.9220.9861.0861.0061.1860.8961.0421.1690.9831.0331.1751.1201.1051.0140.9851.037
Croatia1.2651.0560.8611.0581.1061.1071.0180.9520.9511.2991.5061.2451.0771.0331.0311.0480.9440.9351.083
Cyprus0.9740.9170.8970.8321.0321.0170.9871.0461.0630.9610.9771.0580.9251.0751.0870.9950.9410.9170.983
Czechia0.9420.7750.7532.1940.9611.0471.0830.8371.2751.0391.0041.3811.0791.1431.0641.1650.8750.9011.084
Denmark1.0170.9070.8650.8420.9290.9650.8780.9201.0571.0280.8811.0180.9670.9201.1170.9510.9070.8870.948
Estonia1.1190.7152.5100.8520.9410.8901.2560.7651.2450.9491.0250.7730.8981.9921.0590.9211.0320.9071.103
Finland0.9950.9660.8490.8770.9630.9430.8670.8781.0511.0500.9681.0270.9120.9861.2150.9810.9250.9410.966
France1.0010.9310.7950.9870.9200.9630.9320.9371.0491.0120.9171.0760.9590.9651.1510.9650.9620.9110.968
Germany0.9600.9100.7681.0430.9350.9381.0140.9481.0451.0230.9081.0660.9510.9571.1510.9790.9540.9300.971
Greece0.9750.9050.8470.8500.9880.8910.9360.9131.0470.9870.9981.0940.9341.0651.0661.0310.9550.9820.970
Hungary1.0400.8750.9000.9701.0381.0220.9731.0111.0040.9910.9840.9731.0961.1061.1021.1120.9451.0001.008
Ireland0.9610.9020.8010.8880.9310.9340.8970.9731.1161.0620.8741.0470.9420.9270.9420.9730.8990.8760.941
Italy0.9730.9280.8510.9370.9830.9470.9080.9171.0681.0190.9330.9900.9830.9971.1530.9390.9290.9360.966
Latvia1.1480.9651.1301.0690.9641.0961.1400.9771.1260.8451.0801.2671.2131.0921.0851.0770.9890.9831.069
Lithuania1.0070.9510.907.0.9931.0231.8571.0590.9710.7721.5391.0901.0481.1071.1311.1060.9890.9801.090
Luxembourg0.9320.9410.8150.9450.8930.9680.8520.8471.1030.9900.8651.1110.8361.0391.0650.9741.0140.9050.950
Malta1.0290.7391.0770.9591.0411.1600.7700.9221.2170.9011.2431.1430.9240.9561.0781.0320.9680.9291.005
The Netherlands0.9710.8870.8060.8900.9020.9460.9500.9451.0731.0380.9061.0960.9780.9481.1390.9760.9790.8280.959
Poland0.9420.9040.9480.9190.9801.1001.0091.0071.0611.0480.8621.0821.1741.2981.1441.0910.9480.9401.025
Portugal0.9620.9600.8420.8980.9960.9501.0150.9501.0670.9280.9851.0081.0891.0481.1331.0450.9650.9590.989
Romania1.2680.9910.8962.0271.2770.6060.7771.5021.1331.8561.0381.1331.0051.0491.0731.1001.0300.8621.146
Slovakia1.1300.8970.8601.0330.5871.3561.2241.0471.1181.0751.0641.2130.8691.0351.4841.4800.9460.9761.077
Slovenia0.9151.4190.9200.9380.9360.9360.9510.8560.8101.1211.0280.9241.1121.2351.0281.0930.8261.0651.006
Spain0.9610.9290.8520.8840.9200.9540.9310.8920.9880.9980.9881.0610.9890.9841.1501.0440.9230.9810.968
Sweden1.1220.9420.7900.9001.0320.8080.9040.9361.0990.9720.8601.0470.9560.9921.1760.9750.9550.9630.968
United Kingdom1.0180.9490.8920.8900.9670.9370.8681.0561.1200.9860.9081.0040.9720.8741.0471.0621.0070.9150.971
Table 6. Determinants of TFPCH index before and after the inclusion of undesirable output in the initial model.
Table 6. Determinants of TFPCH index before and after the inclusion of undesirable output in the initial model.
TFPCHThe Main Determinants of TFPCH: EC-TCThe Main Determinants of
EC: PEC-SEC
CountriesMMLMMLMML
Austria, Belgium, Denmark, France, Germany, Greece, Italy, Portugal, Spain, Sweden, United-KingdomPerformance worseningCatch-up effectIncreasing
trend in PEC
Increasing
trend in SEC
Finland, IrelandIncreasing trend in SEC
LuxembourgPEC and SEC are of equal importance
The NetherlandsIncreasing trend in PEC
CyprusIncreasing trend in SECPEC and SEC are of equal importance
BulgariaPerformance worseningPerformance improvingCatch-up effectCatch-up effectIncreasing trend in PEC
MaltaFrontier shift effectPEC and SEC are of equal importance
SloveniaCatch-up effectIncreasing
trend in PEC
Increasing
trend in SEC
Hungary, Latvia, Lithuania, SlovakiaPerformance improvingCatch-up effectFrontier shift effect
Croatia
Czechia, RomaniaIncreasing
trend in PEC
PolandCatch-up effectIncreasing
trend in SEC
EstoniaCatch-up effectIncreasing trend in PEC
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Bampatsou, C.; Halkos, G. Non-Parametric Computational Measures for the Analysis of Resource Productivity. Energies 2021, 14, 3114. https://doi.org/10.3390/en14113114

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