SOUTH AFRICA’S

METHODOLOGICAL APPENDIX
SELECTION OF PEERS
Global peer cities were selected based on economic
characteristics and competitiveness factors.
Classifying and identifying peers allows policymakers
and stakeholders to better understand the position of
their economies in a globalized context as well as to
conduct constructive benchmarking.
To select peers we utilized a combination of principal
components analysis (PCA), k-means clustering, and
agglomerative hierarchical clustering. 1 These commonly
used data science techniques allowed us to
group metro areas with their closest peers given a set
of economic and competitiveness indicators. For this
report we selected 14 economic variables: population,
nominal GDP, real GDP per capita, productivity
(defined as output per worker), total employment,
share of the population in the labor force, and
industry share of total GDP (8 sectors). 2 We included
seven additional variables that measure one of the
four quantitative dimensions of the competitiveness
analysis framework used in this report. The variables
included are: share of the population with tertiary
education (talent), stock of Greenfield foreign direct
investment (FDI) (trade), number of international
passengers in 2014 (infrastructure), number of highly
cited papers between 2010 and 2013 (innovation),
mean citation score between 2010 and 2013 (innovation),
and average internet download speed in 2014
(infrastructure).
Our analysis proceeded in three steps. First, we
applied PCA to reduce the number of dimensions
of our data by filtering variables that are highly
interrelated while retaining as much variance as
possible. PCA generates “components” by applying
a linear transformation to all the variables. 3 To
successfully perform our clustering algorithm we
selected the number of components that explain
80 to 90 percent of the variance of a dataset. For
this report we selected the first seven components,
which accounted for 84 percent of the total variation
of the data.
The second stage applied a k-means algorithm to the
seven components, a process which calculates the
distance of every observation in our dataset to each
other, then generates a cluster centroid and assigns
each data point to the closest cluster. 4 K-means
repeats this procedure until a local solution is
found. This algorithm provides a good segmentation
of our data and under most circumstances it is a
sufficient method for partitioning data. 5 However
k-means sometimes generates clusters with multiple
observations, thus obscuring some of the closest
economic relationships between metro areas. To
improve the results of k-means we implemented
a third step, hierarchical clustering, which follows
a similar approach to k-means. Hierarchical
clustering calculates Euclidean distances to all
other observations, but generates a more granular
clustering that permits clearer peer-to-peer
comparison.
BROOKINGS
METROPOLITAN
POLICY
PROGRAM
42