Discussion and conclusion

This chapter discusses and reflects on the accomplished theoretical (see Chapter 2 and Chapter 3), methodological (see Chapter 4), and the empirical research (see Chapter 5). The present work is part of Phase C of the transdisciplinary research agenda in sustainability science (see Section 2.3.4; e.g. Lang et al., 2012). It draws on previous studies and problem framings from research and practice (Phase A), makes use of prior disclosures from the scientific and the practitioner community (Phase B), and finally provides new results that are relevant for both research and practice (Phase C).

2001) and thereby updates existing frameworks (see Chapter 2; e.g. Chofreh & Goni, 2017). The perspective gap has been closed theoretically, and further contributions result. First, this work is the first to review sustainable development assessment methods by a method's level of applicability (i.e. by the aggregational size of an object of investigation; see Figure 3.1). This organisation is advantageous in further aspects that are outlined in Section 6.2. Second, resulting from this review and based on the sustainable development assessment principles, this work is the first to identify the most suitable multilevel assessment method for comprehensive sustainable development measurement. Indicator sets that include a composite measure have been revealed as such a method. Third, this work contributes an advanced multilevel indicator set that includes a composite measure and can be applied to meso and macro objects for comparative analyses and benchmarking. The intersection of the meso GRI and the macro SDG frameworks at target level as outlined in GRI and UNGC (2018a) has been refined to indicator level and adjusted to current data availabilities for the German economy by official statistics. On the other hand, decisions for sustainable development should be made at operational, strategic, and normative tiers (see Section 2.3.2; e.g. Ulrich, 2001). An operational-to-normative gap is present because decision makers mostly address the operational tier only (see Section 2.3.2; e.g. Baumgartner & Rauter, 2017). Including the St. Gallen management model in the conceptual framework also points towards indicator sets that include a composite measure as the most successful tool in comprehensive multilevel measurement of sustainable development performances: Indicators and indices address the operational and the strategic tiers (see Section 3.2; e.g. Baumgartner, 2014) while being inherently normative (see Section 3.2; e.g. Waas et al., 2014).
The third identified research gap is the knowledge gap (see Section 2.3.3; e.g. Weitz et al., 2018). By tackling this gap, this work contributes insights about the interconnections of individual sustainable development elements. In doing so, this work is the first to apply an entropy-based information-theoretic algorithm to compute a sustainable development index. Indices in the field of environmental sustainable development that apply methods of information theory include, e.g. Fath and Cabezas (2004); P. E. Meyer, Kontos, Lafitte and Bontempi (2007); and Pawlowski, Fath, Mayer and Cabezas (2005). These are based on the parametric Fisher information, but the non-parametric entropy should be preferred (see Section 4.3.7.4). Entropy-based index approaches include, e.g. Rajsekhar, Singh and Mishra (2015); Ulanowicz, Goerner, Lietaer and Gomez (2009); and Y. Zhang, Yang and Li (2006). Furthermore, Nie, Lv and Gao (2017) Hall et al., 2017). The present work contributes to this bottleneck by providing detailed information about its methodological approach and data sources, such that the MLSDI can be re-built by interested change agents. Furthermore, this work is the first to publish data on 44 sustainable development key indicators, three subindices, and an overall sustainable development index for 62 twodigit industries as well as five aggregated branches, including the cross-sectional health economy, in the German economy from 2008 to 2016. Providing detailed information about the methodological approach, data sources, and objective, macro-economic benchmarks entails two advantages: First, it enhances decision usefulness across the decisional tiers by identifying and improving relevant sustainable development key indicators; and second, it encourages corporations and further objects of investigation to compare their performances to the provided macro-economic benchmarks, preventing greenwashing.
Fifth and last, previous sustainable development indices do not only lack compliance with the conceptual framework (see Section 3.3 and above), but especially the assessment principle methodological soundness is violated (see Section 4.2). Insufficient data cleaning, weighting, aggregation, and a lack of sensitivity analyses are frequent shortcomings. This work has overcome these deficits and contributes a methodologically sound sustainable development index: The MLSDI imputes missing values and treats outliers, establishing credibility, validity, and reliability of measurement; it applies a sophisticated information-theoretic algorithm to objectively determine relevances and interconnections of individual sustainable development elements; it obeys mathematical aggregation rules for credibility, validity, and reliability; and it conducts sensitivity analyses, proving the measurement's robustness and confirming its previously claimed credibility, validity, and reliability. Compared to the reviewed sustainable development indices, the MLSDI is the only index that can be deployed at multiple levels (see Table 4.5). Hence, it features a wider scope than the previous indices. Because the reviewed indices are distinct in their indicator bases and regional scopes, data results are not comparable, and the MLSDI is only related to the previous indices in respect of its methodology. The MLSDI may serve management decisions, national industry policy, and international affairs, whereas single level indices only address one level of decision making. For example, the DJSI support corporate decision making, and the SSI assists international policy making by comparing country performances. In comparison with indices of single domains (e.g. the EPI; Esty & Emerson, 2018), the MLSDI supports decision making with regard to all three contentual domains of sustainable development. The MLSDI is based on 44 key indicators and exceeds the number of indicators of five of the nine reviewed indices. Previous indices with a narrower indicator base include the ICSD (Krajnc & Glavič, 2005), FEEM SI (e.g. Pinar et al., 2014), HSDI (e.g. Bravo, 2018), SDI (Bolcárová & Kološta, 2015), and the SSI (e.g. van de Kerk et al., 2014). Their number of indicators range from four to 38 (HSDI vs. ICSD, respectively). In conclusion, the MLSDI assists a broader range of essential topics in sustainable development performance measurement. Moreover, decision making based on the MLSDI will be more accurate in general because of its overall methodological soundness. Only one of the nine reviewed indices -the MISD (e.g. Shaker, 2018) -eliminates statistical biases by sound missing value imputation. Statistical biases that originate in outlying observations remain for all nine previous indices. With regard to scaling, three of the nine reviewed indicesthe SDGI (e.g. Schmidt-Traub et al., 2017a), SSI, and the WI (Prescott-Allen, 2001)apply a scaling method that correctly interplays with the deployed aggregation method. However, of these three indices, the SSI is the only index that implements geometric aggregation, which is essential to map the desired weak sustainability with minimised substitutability (see Section 2.2.4 and Table 4.1). Only one of the reviewed indices -the SDI -deploys the required bottom-up statistical weighting. The SDI determines weights by a PCA, a powerful tool that is used in further sustainable development indices (e.g. Barrios & Komoto, 2006;T. Li, Zhang, Yuan, Liu & Fan, 2012) and adjacent fields of quantitative investigations of sustainable development (e.g. Fernandez-Feijoo, Romero & Ruiz, 2014;Hansmann, Mieg & Frischknecht, 2012;Wallis, 2006). Nonetheless, the methodological and empirical analyses have shown that the information-theoretic algorithm outperforms this multivariate statistical technique because both linear and higher order correlations are detected. Among the reviewed indices, the MLSDI is the only index that implements an information-theoretic algorithm (see above) and hence contributes a major methodological advancement to the index literature in general. Last, only three of the reviewed indices -the FEEM SI, SDGI, and the SSI -investigate sensitivities. The MLSDI improves their sensitivity analyses by intending to investigate three calculation steps instead of one or two steps only. However, testing sensitivities of missing value imputation becomes superfluous, given the Amelia II's failure (see Section 5.2.2).

Implications for practice
The present work provides several implications for corporate and political practices on sustainable development. This work encourages practitioners to always view sustainable development as one integrated crisis of environmental protection, social development, and economic prosperity (see Section 2.2.4; WSSD, 2002). The economic domain is hallmarked by the misconception that economic growth or profits are part of sustainable development. This work reminds practitioners to eliminate this misconception (see Section 2.2.3; e.g. Jackson, 2009;Vermeulen, 2018). The present study advises corporate practitioners to follow societal instrumental finality (see Section 2.3.2; e.g. T. Hahn & Figge, 2011) because not the long-term survival of the company (i.e. profits) is part of corporate sustainability, but corporations should contribute to the society level concept of sustainable development. In fact, their contributions are inevitable for achieving the SDGs (see Section 2.3.1; e.g. Dahl, 2012;Griggs et al., 2014). Furthermore, this work recommends politicians to abandon GDP (i.e. economic growth) as a measure of societal wellbeing (see Section 3.3.3; Costanza, Fioramonti & Kubiszewski, 2016) and replace it by the MLSDI, which alludes to progress comprehensively and soundly. However, political will might be lacking to let up on GDP (Jesinghaus, 2018).
This work further provides practitioners with an updated compilation of sustainable development assessment principles, which should be considered in any sustainable development assessment. The present study also delivers an updated overview of sustainable development methods. For practitioners, the provided overview by aggregational size might be easier to follow than, for example, overviews that are structured by the methodological approach (see Section 3.2; e.g. Sala et al., 2015). Practitioners might be unaware of the methods required for their problem setting, but they most likely know if they want to appraise, among others, a product, corporation, or a policy. The evaluation of sustainable development assessment methods by means of the assessment principles (see Section 3.2) entails two implications for practice. First, this work delivers an understanding of each method, and second, the present study encourages practitioners to implement sustainable development indicator sets that include a composite measure if they aim to comprehensively measure sustainable development performances by multilevel objects. Moreover, the evaluations of assessment principle compliances (see Section 3.3) and methodological approaches (see Section 4.2) of previous sustainable development indices result in two implications for practice. First, this work informs practitioners about existing alternatives of sustainable development indices. Second, the present study serves practitioners information about "do's" and "don'ts" in sustainable development index construction with regard to both the conceptual and the methodological phase. Concerning the methodology, this work discloses profound knowledge, such that the MLSDI can be re-built (see Section 6.1). The probably most important methodological aspect for corporations provided in this work might be the utilisation of GVA instead of revenues, sales, or profits (see Section 4.3.4). By means of the derived effectiveness and efficiency indicators, the present study supports practitioners to manage absolute and relative decoupling of sustainable development influences and economic activity, respectively. This is a major challenge for decision makers (see Section 3.2; Holden et al., 2014). Furthermore, this work promotes the implementation of paradox teleological integration to practitioners. All indicators should be followed at the same time, even if they are conflicting (see Section 2.3.2; e.g. T. Hahn & Figge, 2011). Moreover, this study delivers an advanced alignment of the GRI and the SDG frameworks at indicator level for the geographical region Germany. The indicator base is expected to be valid in further European countries. It further invites corporations that seek to report their performances on the macro SDGs to rely on this alignment. The provided alignment might be especially useful for corporations that are not able to allocate sufficient resources to report on the comprehensive option of the GRI framework but are not satisfied with the sparse core option. This study suggests collecting 36 key figures, a number that balances comprehensiveness and resources in practice. Further, this work encourages practitioners who are interested in data beyond the selected branches or Germany to take advantage of the benchmarking opportunities the MLSDI provides by enclosing detailed empirical analyses and data sources to re-produce the sample. Last, this work may support the action plan for financing green growth in the EU. First, the present study contributes to Action 1 of this plan, which encompasses the establishment of a unified classification system for sustainable activities, also termed "EU taxonomy" (EC, 2018). On the one hand, the derived conceptual framework (see Figure 2.11) may guide the establishment of the "shared understanding of what 'sustainable' means" (EC, 2018).
On the other hand, the elaborated indicator set that is applicable to both the meso and the macro levels may support determining the environmental and the social objectives investors should aim for. Second and foremost, this work contributes to Action 5: developing sustainability benchmarks. More transparent and sounder methodologies of sustainable development indices are demanded in order to halt greenwashing (EC, 2018). The MLSDI and its well-researched and transparently exposed methodology (see Chapter 4) is capable to serve exactly this purpose. The consideration of multiple levels sacrifices detailed analysis within one level.

Limitations and future outlook
In contrast to footprints, indicator sets typically report sustainable development performances of one object of investigation while disregarding upstream or downstream sustainable development performances. To deliver a holistic picture of the supply chain, the MLSDI should be combined with footprint analyses: A multilevel sustainable development footprint should be derived in future research. A combination of the multilevel index with single level life cycle assessment, a powerful tool to quantify a product's sustainable development performance, for example, from "cradle to grave" (see Section 3.2; Finnveden et al., 2009), might also spread interesting insights but could be methodologically challenging. Topics such as economic proximity (e.g. Torre & Zuindeau, 2009) are only reflected in the performance scores, and benefits that economic objects may experience through proximity cannot be analysed in detail. The literature review is limited by the definition of sustainable development indices, but indices that are not included in the review might provide valuable methodological insights. Further indices that apply information-theoretic weighting have been outlined in Section 6.1. Moreover, the MLSDI's methodology is subject to several limitations. Adjustments of current prices of key figures reported in monetary units would increase methodological soundness (see Section 4.3.1) because nine years of calculation are covered, and efficiency indicators rely on both monetary and non-monetary units. An iterative algorithm on the single missing value imputation that matches the aggregated branches would refine the imputation results (see Section 4.3.3.2) and also enhance methodological soundness. The multiple missing value imputation by the Amelia II algorithm might not only fail because of the violation of the normality assumption, but because outliers are still present (see Section 4.3.3.3 and Section 5.2.2). An iterative algorithm over the calculation steps missing value imputation and outlier treatment could be tested. Only one micro index -the BLI (see Section 3.3.3; OECD, 2017) -has been identified in the literature, and the MLSDI's key indicator base is currently limited to the alignment of the meso GRI and the macro SDG frameworks (see Section 4.3.4). Further micro indices and a micro framework should be developed. Literature to verify the GRI and the SDG frameworks might unfold gaps and weaknesses in these reporting schemes. Conflicts might be present (Spaiser et al., 2017), and the frameworks' reflections of the planetary and the social boundaries (i.e. the safe and just operating space) could be investigated. Despite theoretical justifications, more sophisticated outlier detection and treatment methods could be explored in future studies because the conducted sensitivity analyses have revealed the importance of this calculation step. As the information-theoretic algorithm outperformed established multivariate statistical methods for weighting, information-theoretic outlier detection and treatment might be of interest. Further information can be found in, e.g. Aggarwal (2017).
Probably the major limitation of the MLSDI is the applied internal scaling (see Section 4.3.6.2). Targets and boundaries are excluded due to unavailable data. Results depend on the distribution, and their significance is reduced. For example, there will still be well performing economic objects, if all objects feature a bad performance (Dahl, 2018). Therefore, the safe and just operating space must be converted into lower aggregational levels of corporations, industries, and nations expressed in terms of the SDGs (Dahl, 2018;Schmidt-Traub et al., 2017a;Steffen et al., 2015). Nonetheless, to the best of the author's knowledge, the safe and just operating space has neither been disassembled to corporate nor to industry level yet. Consequently, targets and boundaries could not be included in the German sample (nor in any other geographical region). Methods and precise data generation at corporate, industry, and national levels of the planetary and the social boundaries constitute a major future field of research. The MLSDI connects to this new stream: Once the boundaries are broken down, these data can be fed in the MLSDI to precisely quantify a meso object's contribution to the macro SDGs. Moreover, the boundaries' scientific relationship must be known and hence explored in future research for accurate weighting (see Section 4.3.7; e.g. Ebert & Welsch, 2004;Steffen et al., 2015), making statistical weighting obsolete.
Furthermore, the three applied weighting methods (see Section 4.3.7) will never assign zero weights because indicators that are not perfectly correlated always add variation to the data set. The indicator selection and derivation process (see Section 4.3.4) cannot be reverted. Weighting across the contentual domains currently fails, and the sum of weights of one domain reflects the number of included key indicators. Subsequent adjustment is accomplished (see Section 4.3.7), but the MLSDI remains biased towards efficiency. More ratio than growth indicators are comprised without subsequent adjustments. Further research is required to develop methods that implicitly account for unbalanced numbers of indicators. The equal temporal weighting of the MRMRB algorithm is justified by the PTA's temporal weights (see Section 4.3.7.4 and Section 5.4.3). This procedure might be inaccurate as the PC family is generally outperformed. Structures of the temporal dimension could be investigated by information-theoretic applications in future studies.
To strengthen the MRMRB algorithm's empirical results, sensitivities of discretisation methods could be tested. Despite successful punishment of bad performances by the geometric aggregation, the MLSDI is not capable of indicating urgency. This judgement remains with decision makers and is hence subjective. Sensitivity analyses could be advanced as OAT is generally criticised in the literature. More sophisticated methods are available (Saltelli & Annoni, 2010;Saltelli et al., 2008).
The current sample is limited to meso-level and macro-level applications because micro-level frameworks are not available. For a complete micro-to-macro connection, micro frameworks must be developed, and macro boundaries must be downscaled to lower aggregational levels (see above). To demonstrate the MLSDI's capability of implementing the multilevel perspective and highlighting the benchmarking opportunities across aggregational levels, an empirical application to meso objects (i.e. corporations) should be prospectively performed. Data sources are attached in the supplementary material to facilitate future applications. Generally, the change agent group society is underrepresented in the present sample. Business is involved by constituting the objects of investigation, policy is reflected by the SDG framework, and science is included by the investigation itself. Incorporating micro objects of investigation (i.e. individuals) would solve these two limitations simultaneously. Moreover, the present indicator selection exhibits several limitations. First, the inclusion of more indicators in the MLSDI is desirable to cover all multilevel aspects of the SDGs, but further data are missing for the German sample. Second, interpretability of existing indicators may be limited. For example, the environmental tax intensity, which is the ratio of environmental taxes and the GVA, rises if more environmental taxes are paid. On the one hand, the increase affects sustainable development positively because pollution is paid up for. On the other hand, more taxes are paid because more pollution is generated, harming sustainable development. Effectiveness as well as efficiency of a taxation system remains subject to further investigations (see Section 5.3.1.1). Regarding the social domain, the VAT's effective direction may also be questionable as the VAT is a non-progressive tax on an economic object's created value added. Financially well-placed economic objects are equally burdened in nominal terms as economic objects in weaker financial positions. The latter might suffer from financing social development. The key indicators on apprentices might be limited in their explanatory power. The number of university students may complete the picture on education, and data on labour market demands by educational level is required to draw reliable conclusions on the effective directions key indicators on education should carry. Indicators on trade also feature ambiguities. First, trade's effect on sustainable development may be ambiguous in general. Further information on the contribution of trade to the SDGs can be found in, e.g. WTO (2018). Second, Germany's net import intensity might not indicate support for developing countries. Products are mainly imported from the People's Republic of China, the Netherlands, France, United States of America, and Italy (descending order; Destatis, 2019a). Only China is an economy in transition, while the other countries of origin are developed countries (UN, 2019c). The poor to medium performances of the capital indicators entail uncertain interpretations. Classically, a decrease in capital indicators is interpreted negatively. However, in the digital era of big data and digitalisation, economic prosperity might be possible to be achieved despite decapitalisation and deinvestments -the IT industry stands out as the best performer (see Section 5.5.2).
Forward-looking scenarios as approached by, e.g. Carraro et al. (2013;see Section 3.3.3) should be explored to develop future pathways for comprehensive multilevel solutions by means of the MLSDI (see Section 2.2.4 and Section 2.3.4; e.g. Lang et al., 2012;Leach et al., 2013). A forecast of six SDG indicators can be found in Joshi, Hughes and Sisk (2015), and a review that provides assistance for national SDG scenario modelling can be found in Allen, Metternicht and Wiedmann (2017)

Summary and conclusion
In this dissertation, a methodological sound sustainable development index that is applicable to the micro, meso, and the macro levels has been developed. Multilevel assessment is crucial because the society level concept sustainable development can only be achieved if micro and meso objects contribute. Moreover, methodological soundness is a prerequisite for serving as a credible, valid, and reliable basis for decision making. First, this work has elaborated a conceptual framework and assessment principles of sustainable development. Based on these, indicator sets that include a composite measure have been proven to be most successful in comprehensively quantifying multilevel sustainable development performances. A new index -the MLSDI -has been derived by linking the conceptual framework and the assessment principles to each index calculation step. The empirical analysis has confirmed the accuracy and robustness of the MLSDI's methodology. For improved sustainable development, environmental efficiency indicators on climate change and social effectiveness indicators on employment as well as the chemical industry's environmental performances and the agricultural industry's performances in all three contentual domains should be focused.
Manifold implications for research and practice follow from the conducted research. This work is the first to contribute a methodologically sound multilevel indicator set and a multilevel index (perspective gap) that address operational, strategic, and normative tiers (operational-to-normative gap). It is also the first to deploy an entropybased, information-theoretic algorithm to examine interactions of individual sustainable development elements (knowledge gap). This work provides unrestricted transparency for replicability (sustainability gap), and the MLSDI serves a wide scope of managerial and political decision-making purposes. An alignment of the meso GRI and the macro SDG frameworks at indicator level is delivered for corporate practice, and politicians are encouraged to replace GDP as a measure of wellbeing with the MLSDI.
In conclusion, the usefulness of the suggested approach for informed managerial and political decision making is expected to be high from both theoretical and methodological viewpoints but remains subject to further investigations at the micro, meso, and the macro levels to succeed in the long-term goal and vision of sustainability.
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