B.2 Empirical Steps

The Green Growth Index was constructed through aggregation of
the normalized indicators (metrics), indicator categories (pillars),
and dimensions (goals) (Figure C). Prior to the aggregation, several
steps were necessary to select, prepare, and validate the indicators
included in constructing the Index:

1. Indicator selection: Several criteria were applied in the
selection of indicators, including the relevance of the data
to the green growth dimensions based on conceptual and
empirical evidence, coverage of more than 140 countries
(including most GGGI member and partner countries);
availability of time-series data to allow updates of the Index
on a regular interval; accessibility of the data to ensure
replication of methods and credibility of their sources; and
acceptable level of association with other indicators in the
same dimension. In a few cases, however, the criteria for
country coverage and time-series data were waived due to
a significant lack of data. All data were collected from online
sources, mainly published in the UNSTATS SDG database
and databases from other international organizations (e.g.
FAO, World Bank, WIPO, UN COMTRADE, etc.).
2. Data preparation: Scaling and imputation are the most
important methods to prepare the data and improve the
comparability of the indicators. Scaling the data with an
appropriate denominator (e.g., GDP, land area, etc.) allows
an objective comparison across small and large countries.
Available data for all the indicators were scaled except
for the GHG emissions, export of environmental goods,
and patents of environmental technology. Imputing data
based on the available time-series data helps improve the
country coverage of the indicators. To minimize the effects
of imputation on data uncertainty, the simple method of
imputing data from the closest years was applied.
3. Data validation: The most important method to validate
the statistical appropriateness of the indicator data is
to check for outliers and correlation. Since outliers can
distort statistical properties and normalized values of the
indicators,5 their values were capped using lower or upper
fences based on the interquartile range from 75th and
25th percentiles. The aims of the correlation analysis are to
identify redundant indicators with very strong correlation to
improve the explanatory power of the indicators and verify
whether indicators have acceptable levels of association
in their respective dimensions. Indicators with very strong
correlation were excluded from the framework and replaced
with ones having acceptable levels of association.
4. Indicator weights: The indicators have implicitly equal
weights (i.e., no weights are attached to them). The explicit
weights of the indicators are not equal because the number
of indicators in each indicator category (or pillar) is not
equal. The results from Principal Component Analysis
validated the level of inequality in the explicit weights of
the indicators. The results from Analytic Hierarchy Process
revealed that there is low consensus among experts on the
weights to be assigned to the indicators.
5. Indicator normalization: To translate the indicators with
different units into a common scale, it is necessary to
apply a normalization method. Through normalization, the
indicator values measured in different units can be adjusted
to a single scale to make the data comparable across the
indicators. The re-scaling method (min-max transformation)
for normalization was applied for the following reasons: it is
the simplest and most widely used method that will facilitate
ease of comprehensibility and replication; the use of upper
and lower bounds will reduce issues related to outliers;
and the integration of the targets will allow benchmarking
against sustainability targets.

The normalized indicators were used as inputs to the aggregation
model (i.e., level 1) as presented. The two most common and simple
methods of aggregation include linear aggregation using arithmetic
mean and geometric aggregation using geometric mean. These two
methods have different underlying assumptions. Linear aggregation
allows full and constant compensability, i.e. low values in one
indicator can be traded off (substituted) by high values in another.
On the other hand, geometric aggregation allows only partial
compensability, limiting the ability of the indicators with very low
scores to be fully compensated by indicators with high scores. The
two methods were applied in the different aggregation models so
that, as the level of aggregation increases, the level of substitutability
decreases:

1. Level 1: Arithmetic mean was applied to linearly aggregate
the normalized indicators, allowing compensability of the
individual indicators in each indicator category. Moreover,
at Level 1 of aggregation, countries with more than 25%
missing values were dropped.
2. Level 2: Geometric aggregation was applied to the indicator
categories to allow only partial compensability between
indicators in each dimension. Like in Level 1, the 25% rule on missing values was applied to the dimensions with more than missing values was applied to the dimensions with more than
four indicator categories, i.e., resource efficiency and green
economic opportunities.
3. Level 3: Geometric aggregation was applied on the
dimensions and the 25% rule on missing values was not
applied. At this level of aggregation, no dimension was
allowed to easily substitute the other dimensions to improve
the Green Growth Index.

Python software was used to conduct all the analysis described
above, except for the correlation analysis which was done in Prism
(GraphPad Software). Detailed discussion on the steps involved in
constructing the Green Growth Index is provided in chapter 5 of
GGGI Technical Report Number 5, Green Growth Index: Concepts,
Methods, Applications (Acosta et al. 2019).