The  five  steps  in  this  thesis

Each of the five steps identified above will be discussed in one of the sections 3.2 through 3.6.

This section gives an overview of their content, their influence on the results, and their rela-tionship to each other. The five steps are presented in table 2 along with their lead questions and an illustrative example for an SR. The example describes an environmental phenomenon because it can be presented without multilevel characteristics.

First, the theoretical framework describes the basis for all subsequent steps. It consists of the composite indicator’s primary objective, the objects of analysis, and the phenomenon. These preliminary fixings are the basis for further decision-making in the construction of the compo-site indicator. Any compocompo-site indicator is based on the assumption that measuring the phe-nomenon for each object of analysis contributes to achieving the primary objective. For example in table 2, measuring the environmental performance of companies is assumed to predict financial performance. The phenomenon needs to be defined. A spelled-out definition can be complemented by a list of dimensions that may be relevant in theory. The primary ob-jective, object of analysis, and phenomenon affect the results due to their influences on subse-quent decisions. Metaphorically speaking, they span the room of the composite indicator construction.

Second, the data selection describes how to identify relevant dimensions and how to select corresponding variables. Relevant dimensions are the ones that are actually considered by the composite indicator. They are chosen based on a selection criterion that spells out the primary objective. Choosing variables operationalizes the phenomenon and determines which varia-bles will eventually enter the calculation. To account for differences between the objects of analysis, a scaling variable is also chosen for some of the variables. As variables and scaled

Table 2: Five steps of the construction of a composite indicator as discussed by this thesis.

Name and Description Lead questions Illustrative example Theoretical Framework (3.2)

Defining the primary objective. - What is the primary objective of

the SR? Primary objective: Predicting

financial performance.

Defining the objects of analysis. - Which objects of analysis are

rated? Set of objects of analysis 𝐴

in-cludes 𝑁 companies 𝑎_!. Defining the phenomenon. - What is the definition of the

phenomenon?

Deriving relevant dimensions. - Which criterion is the basis for the derivation of relevant

Dimension m_! is climate impact.

Selecting variables for each

- Which weight is attributed to each dimension?

Equal weights for all dimensions.

Weighting coefficient is 𝑤_! =1/𝑀′.

Normalization (3.5)

Normalizing variables. - Which normalization method should be used?

Own presentation. Numbers in brackets refer to the section in this thesis. The example is illustrative.

variables are the origin of what is part of the aggregation rule, the data selection affects the results.

Third, the derivation of weights describes how to obtain the set of weights 𝐻. Weights repre-sent a degree of significance with respect to the phenomenon. There are a variety of different methods leading to different weights. Weights influence the results because they are part of the aggregation rule.

Fourth, the normalization prepares the variables for aggregation. Different normalization methods exist and they lead to different indicator values. Normalization is sometimes referred to as standardization, although this is only one possible method of normalization according to the OECD handbook (2008). The indicator values influence the results, because they are part of the aggregation rule.

Finally, the aggregation of indicators and weights is based on an aggregation rule. Various aggregation rules exist and they imply different compensability among the indicators. Thus, the aggregation influences the results.

Figure 2 illustrates the relationship of the elements to each other. It shows the primary objec-tive above all other elements, as it influences everything else. The phenomenon is defined by the global set of dimensions 𝐺. Most of these dimensions will have sub-dimensions. This mul-tilevel aspect is illustrated by 𝑚_! and 𝑚_!, which are both assigned to the non-numbered di-mension 𝑚. The set of relevant dimensions 𝐺′ does not necessarily include all dimensions from the theoretical definition, as illustrated by 𝑚_!. Consequently the number of dimensions decreases, i.e. 𝑀 > 𝑀′.

All the relevant dimensions are assigned to a variable  𝑥_!,!. Some of the variables are also di-vided by a scaling variable, as illustrated by 𝑥_!,𝑗 and 𝑥_!,𝑗. Variables that already represent rati-os (e.g. share of female top management) or that are on the ordinal level (e.g. other ranking results) remain non-scaled. This is illustrated by 𝑥_!,!, 𝑥_!,!, and 𝑥_!!,!. The resulting set of vari-ables for the composite indicator consists of scaled varivari-ables and non-scaled varivari-ables.

The dimensions’ index number 𝑘 counts all dimensions at the lowest level, i.e. the level that is used for the calculation of the composite indicator. For each relevant dimension, a weight  𝑤_! needs to be derived. Normalization transforms the variables into indicators 𝐼_!. Subsequently, there are 𝑀′ relevant dimensions, variables, weights, and indicators.

This section identified five steps in the construction of a composite indicator that have a direct influence on the results. Because of the framework’s applicability for constructing an SR, I can now use insights from the composite indicator literature about these steps to find out which methods are used and which decisions are made during the construction of an SR. To this end, I follow the five-step structure, beginning with the theoretical framework.

Figure 2: Schematic presentation of a composite indicator.

Sources: (Hsu et al., 2013; Munda, 2008; OECD, 2008). Own presentation.

Phenomenon 𝑚_!

Global set of dimensions 𝐺

𝑚 𝑚_! 𝑚_! 𝑚_!  

𝑥_!,!

Variables and scaling variables

𝑥_!!,!  

𝑥_!,!

𝑥_!,! 𝑥_!,!

𝑦_!   𝑦_!

𝑥_!,!

Variables for

for company 𝑗 𝑥!_!,𝑗 𝑥!_!,𝑗 𝑥_!,! 𝑥_!^!_,!

𝑚_! Set of relevant

dimensions 𝐺′ 𝑚_! 𝑚_! 𝑚_! 𝑚_!!  

Primary Objective

𝑚_! 𝑚_!

𝑤_!

Weights 𝑤_! 𝑤_! 𝑤_! 𝑤_!!

𝐼_!

Indicators 𝐼_! 𝐼_! 𝐼_! 𝐼_!!