Non-Parametric Computational Measures for the Analysis of Resource Productivity

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.


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.

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 CO 2 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, CO 2 emissions, biomass and recycled municipal waste data, the Eurostat resource was used [44].

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: 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: The EC index can be further decomposed into pure technical efficiency change (PEC) and scale efficiency change (SEC) as follows: Therefore, the M index can be decomposed into the three components: 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.

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 (CO 2 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: 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. The ML index may be decomposed into technical efficiency (ECL) and technological progress (TCL) as follows: The ECL index can be further decomposed into pure technical efficiency (PECL) and scale efficiency (SECL) as follows: Therefore, the ML index can be decomposed into the three components:

Results
The Malmquist and the Malmquist-Luenberger productivity scores of the 28 European countries for the period 2000 to 2018 are given in Tables 4 and 5, respectively. As shown in Tables 4 and 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 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 CO 2 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 CO 2 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 (Tables 4-6, Tables A1 and A2 (Appendix A).         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:

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 CO 2 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.