3.1. The Rationale of Fuzzy-Set Analysis
The Fuzzy-Set Analysis (methodology) is a special form of case study method known as Qualitative Comparative Analysis (QCA), suggested by Zadeh from the University of Berkeley in 1965, and it has been used in diverse ways by scholars, such as Ragin and Kvist, in application to Social Sciences [51
]. The fuzzy-set analysis is an improved version of the method from Qualitative Comparative Analysis [53
] previously used in Social Sciences. Going beyond the permission of the existing traditional two membership scores, 1 or 0, by using crisp set/set theory, utilization of fuzzy set with various membership scores between 0 and 1 can present not only the partial memberships but also the difference of the degree.
Specifically, the fuzzy-set analysis has some major advantages. First, through exercising the fuzzy-set methodology, disadvantages of case-oriented study and variable-oriented study can be overcome. The fuzzy-set analysis categorizes cases by a combined method of two strategies that variable-oriented quantitative methodology and qualitative case study take, and it distinguishes itself from the existing analysis/methodology by examining social diversity through comparative study [51
]. Second, due to this property, the fuzzy-set analysis enables dealing of the middle-case studies (15-25cases) that comparative case analysis and regression analysis could not address despite being substantial subjects to analysis and makes middle-class comparative analysis possible [51
]. Moreover, it is also used in analyzing joint causal relations by paying due consideration to interactive effects between each quality in a given case [51
Third, it can explain diverse social phenomenon. The fuzzy-set analysis overcomes this dichotomy method of 0 and 1 that have been used in many previous studies by enabling representation of various degrees between the 0 and 1, which minimizes the loss of information in the analysis [51
]. Fourth, it enables a more theoretical approach to the categorization of types. Many researchers have been using quantitative statistic methods such as cluster analysis to categorize types [56
]. While these types are confronted by criticism to be categorized by arbitrary interpretation of the researchers, however, the fuzzy-set analysis determines the number of memberships by categorization standards that consist the ideal type extracted under theoretical background [51
]. Accordingly, many recent studies are applying fuzzy-set analysis to categorizing types [59
3.2. Fuzzy-Set Multiple Conjunctural Analysis and Ideal Type Analysis
In the causal relationship between cause and effect (outcome) conducted in the existing quantitative analysis, the results did not perfectly correspond according to whether there was a cause or not. That is, there was the point during which it was difficult to distinguish correlation and cause and effect (outcome). However, the Fuzzy-Set Multiple Conjunctural Analysis, which defines the relationship between cause and effect as a necessary condition or a sufficient condition, has the advantage of overcoming such a problem. Other than that, as mentioned previously, it can be a powerful tool when it comes to analyzing the causal complexities in intermediate level case studies.
Contrary to the existing multiple regressions, the methodologies by the Fuzzy-Set Multiple Conjunctural Analysis are mainly divided into the following three. First, the problems of a degree of freedom and multi-collinearity that may occur due to a small number of cases in the existing regression analyses can be overcome. In order to secure the necessary statistical significance for researching the causality of dependent variables and independent variables in regression analysis, there has to be a sample of thirty or more. In addition, the statistical degree of freedom problem and the multi-collinearity problem due to the correlation between independent variables and the linear model assumption may occur. However, the Fuzzy-Set Multiple Analysis is able to analyze the combination of the reason variable conditions by targeting small number of cases. In other words, it has the advantage of being able to analyze the combination of causal conditions without having to use the assumption of the independence between variables and the linear relationship.
Second, Fuzzy-Set/QCA is the analysis, which combined quantitative analysis and qualitative analysis. It sets causal conditions and outcome conditions by qualitatively considering cases and variables and derives logical effects (outcomes) by going through the process of conversion into quantitative data. Third, it has the strength of identifying causal relationship by variously integrating not only the unilineal effects by certain variables but also multiple causal conditions [54
On the other hand, this research also categorizes twenty-four OECD countries through comparative analysis by utilizing Fuzzy-Set Ideal Type Analysis. Fuzzy-Set Ideal Type Analysis represented by fuzzy membership scores demonstrates by applying Fuzzy-Set Theory how close the subject of analysis is that is converted into fuzzy sets [62
]. Through this process it analyzes the degree of memberships of each category, translating the existing original data results into fuzzy-set membership scores. As the number of the sets is decided by the ideal type, different from the existing cluster analysis, through Fuzzy-Set Ideal Type Analysis that this research conveys, more systematic categorization and interpretation become available [59
The criteria for interpretation of membership scores of Fuzzy-Set Ideal Type Analysis drawn from this research is based on the one suggested by Ragin [54
]. In particular, after this study converted the scores into the fuzzy-set score system through the calibrate function of STATA 12.0, it measured them according to 3 qualitative anchors: ‘fully in’, ‘fully out’, and ‘crossover point’ as in the degree of the two. In other words, any score that is higher than the crossover point (0.5) is given strong membership (in the case the degree of full membership the given value possesses (FI: fully in or full membership) is higher than 95% (0.95)), and any score below is given low membership score (in the case the degree of full membership is not present (FO: fully out or full non membership) is lower than 5% (0.05)). The formula for calculating Degree of Membership Score in Fuzzy-Set Idea Type Analysis is as follows:
Degree of Membership = exp(log odds)/(1 + exp(log odds))
3.3. Measurement Frameworks
As described in below, this study presumes that the UN Global Goals for Sustainable Development (SDGs) with seventeen agendas are the universal framework for which all 193 UN member states have signed and can be symbolized as the goals of the green state. Therefore, it regards the Sustainable Development Goal (SDG) Index [65
] as the outcome set of the fuzzy-set multiple conjunctural analysis. SDG Index—produced by the Sustainable Development Solutions Network (SDSN—a global initiative for the UN) and the Bertelsmann Stiftung—shows how 193 UN member states are performing the UN Global Goals for Sustainable Development (SDGs) and how the Agenda 2030 can be implemented. SDG Index was built on a set of 232 indicators for each of the 17 SDGs using the most recently published data.
Table 2. The Variable Framework of Outcome and Causal Sets.
For the causal sets, as described in , the seven detailed variables of four variable categories (‘Ecological Authoritarianism’ (A), ‘Ecological Modernization’ (M), ‘Ecological Democracy’ (D), ‘Ecological Welfare’ (W)) were selected respectively. In the first A category, the detailed variable of ‘Environment-related Taxation’ refers to environmentally related taxes, proportion (%) of total government tax revenue. It can be regarded as a key element in relation to enforcing strict environmental restrictions for the sake of environmental policy in ‘Ecological Authoritarianism’. The second M category consists of the both detailed variables. ‘Environment-related Innovation’ is characterized by the patents (counts) in environment-related technologies and innovation, and ‘GDP per capita’—GDP per head of population, USD, constant prices. Both of the detailed variables are in line with the context of combining economic growth and environmental protection, particularly emphasizing a socio-technical and economic reform in ‘Ecological Modernization’.
In the third D category, the detailed variable of ‘Democracy Index’ produced by the Economist, based on five categories: electoral process and pluralism, civil liberties, the functioning of government, political participation; and political culture, was included. Also ‘Environmental Governance’ of ESI (Environment Sustainability Index), focusing on including environmental policy and regulations, civil and political liberties, and government effectiveness, was selected. Both of the detailed variables are included in light of democracy focusing on the reciprocal relationship among human, nature, and non-human, and of alternative democracy. The fourth W category consists of ‘Social Expenditure’, social welfare expenditure of public and mandatory private (% of GDP), and ‘Environmental Health’ of EPI (Environment Performance Index), integrating six indicators in the areas of air quality, water and sanitation, and heavy metals. Two of the detailed variables are in line with the context of collaboration of environmental and welfare issues in order to realize common good in ‘Ecological Welfare’.
This study takes the cases of twenty-four OECD countries out of all thirty-five member countries, in which the data of each variable in the four categories above are available. It attempted to collect the most recent data that may best show the characteristics of the seven detailed variables (from Y2005 to Y2018).
In addition, regarding conducting the fuzzy-set ideal type analysis, we first weighted and standardized the seven detailed variables and placed them in each of the four type variables (see ). Second, we converted (calibrated) the four type variables into fuzzy scores by utilizing the three anchors (minimum, median (p50), and maximum) respectively, to identify the types of green state in OECD countries.
Table 3. The Variable Framework of the Ideal Type Analysis.
The degree of membership in this research is calculated and interpreted by the ‘principle of negation’, the ‘minimum principle’, and the ‘maximum principle’. This research sets the four category variables ‘Ecological Authoritarianism’ (A), ‘Ecological Modernization’ (M), ‘Ecological Democracy’ (D), ‘Ecological Welfare’ (W) that has been reviewed previously. In this case, the principle of negation enables setting up negative categories of ‘a’, ‘m’, ‘d’, and ‘w’ through ‘1-fuzzy-set membership score of the applicable category’. Accordingly, the ideal type is determined by applying a number of cases that each category variable can take, and this research postulates sixteen ideal type sets (high or low) based on the four category variables (see ).
Table 4. The 16 Ideal Type Sets.
In addition, these sixteen ideal type sets are yielded and interpreted by the ‘Minimum Principle’ and the ‘Maximum Principle’ [55
]. The ‘Minimum Principle’ states that it is the minimum value among the fuzzy-set scores drawn from the principle of the sixteen types of ideal type categorization that will be the fuzzy-set membership score of the respective categories; in other words, among the fuzzy scores of the four variables (A, M, D, W) that consist of the corresponding category sets, the minimum value will be selected. For example, if the fuzzy score of A in Category ‘A*M*D*W’ appears to be the minimum value, the fuzzy-set membership score of Category ‘A*M*D*W’ will be denoted as the fuzzy score of ‘A’ itself. Moreover, the ‘Maximum Principle’ postulates that while the fuzzy-set membership score of twenty-four OECD countries can conclusively be presented by sixteen types of categories, one with the maximum value of the membership score will be the category for the corresponding area.