Results of Principal Components Analysis (PCA) and Analytic Hierarchy Process (AHP) on weights

1. Principal Components Analysis

Weights for the indicators can be estimated using Principal Components Analysis (PCA). PCA puts together indicators which correlate well into groups in order to account for the highest possible variation in each direction (i.e., positive or negative) with as less indicators as possible. One of the relevant results for estimating PCA weights are the rotated factor loadings using a given rotation method. In this case the GGPM team used the varimax rotation. This method allows the construction of weights for each category (Nicoletti et al. 2000), but it does not reflect the theoretical importance of each indicator. It simply normalizes the share of the variance for each indicator. The method to calculate the weight Wj of each factor j is as follows:
Equation 1

Where Fij is the factor loading of each indicator i on each factor j.

The squared factor loadings for each indicator i and each factor j were calculated and then scaled to the unity sum (Sij). The Sij with the highest value for indicator i and for a given factor j is chosen to estimate the weight:
Equation 2

Finally, to get the weight wj of each indicator i is derived by
multiplying the unity sum by the weight of the respective factor:
Equation 3

This method was repeated for the indicators in other dimensions. For illustration of this method, please refer to OECD and JRC Handbook on constructing composite indicators (2008).

The results are presented in Figure A4.1. Except for two indicators, all other indicators for efficient and sustainable resource use have relatively equal weights (13-17 percent). Similarly, except for one indicator, all other indicators for green economic opportunities have relatively equal weights (ca. 27-29 percent). In the case of natural capital protection and social inclusion, about half of the indicators have relatively equal weights (5-9 percent).

Legend:

Efficient and sustainable resource use
EE1: Ratio of total primary energy supply to GDP (MJ per \$2011 PPP GDP); EE2: Share of renewables to total final energy consumption (Percent); EW1: Water use efficiency (USD per m3); EW2: Share of freshwater withdrawal to available freshwater resources (Percent); SL1: Average soil organic carbon content (Tons per hectare); SL2: Share of organic agriculture to total agricultural land area (Percent); ME1: Total domestic material consumption (DMC) per unit of GDP (DMC kg per GDP); ME2: Total material footprint (MF) per capita (MF tons per capita).

Natural capital protection EQ1: PM2.5 air pollution, mean annual population weighted exposure (Micrograms per m3); EQ2: DALY rate as affected by unsafe water sources (DALY lost per 100,000 persons); EQ3: Municipal solid waste (MSW) generation per capita (Tons per year per capita); GE1: Ratio of CO2 emissions to population, excluding AFOLU (Metric tons per capita); GE2: Ratio of non-CO2 emissions to population, excluding AFOLU (Tons per capita); GE3: Ratio of non-CO2 emissions in agriculture to population (Gigagrams per 1000 persons); BE1: Average proportion of Key Biodiversity Areas covered by protected areas (Percent); BE2: Share of forest area to total land area (Percent); BE3: Soil biodiversity, potential level of diversity living in soils  (Index); CV1: Red list index (Index); CV2: Tourism and recreation in coastal and marine areas (Score); CV3: Share of terrestrial and marine protected areas to total territorial areas (Percent).

Green economic opportunities
GV1: Adjusted net savings, minus natural resources and pollution damages (Percent GNI); GT1: Share of export of environmental goods (OECD & APEC class.) to total export (Percent); GJ1: Share of green employment in total manufacturing employment (Percent); GN1: Share of patent publications in environmental technology to total patents (Percent).

Social inclusion
AB1: Population with access to safely managed water and sanitation (Percent); AB2: Population with access to electricity and clean fuels/ technology (Percent); AB3: Fixed Internet broadband and mobile cellular subscriptions (Number per 100 people); GB1: Proportion of seats held by women in national parliaments (Percent); GB2: Ratio of female to male with account in financial institution, age 15+ (Percent); GB3: Getting paid, covering laws and regulations for equal gender pay (Score); SE1: Inequality in income based on Atkinson (Index); SE2: Ratio of urban to rural, access to safely managed water/sanitation & electricity (Percent); SE3: Share of youth not in education, employment or training, aged 15-24 years (Percent); SP1: Proportion of population above statutory pensionable age receiving pension (Percent); SP2: Healthcare access and quality index (Index); SP3: Proportion of urban population living in slums (Percent).

2. Principal Components Analysis

Analytic Hierarchy Process (AHP) is a participatory and multicriteria decision-making approach that indicates the relative importance of indicators based on their pairwise comparisons (Dedeke, 2013; Pakkar, 2014). For example, for the resource efficiency dimension, experts were asked which of these they consider more important: energy efficiency or land use efficiency. Then, they had to give the level of importance of one indicator over the other as follows: 1 = equal importance, 2 = weak difference in importance, 3 = moderate importance, 4 = moderate plus, 5 = strong importance, 6 = strong plus, 7 = very strong importance, 8 = very, very strong importance, and 8 = extreme importance. An AHP Excel Template developed by Goepel (2018) was used to analyze the responses of the experts to the questionnaire. Additional analyses were conducted to assess the consistency of the experts’ opinions on the ratings and weights. In addition to the weights, the AHP Excel template generates a consensus index that ranges from 0 percent, which means there was no consensus among experts, to 100 percent, which means there was full consensus among experts. Figure A4.2 presents the level of consensus among the experts on the weights assigned to the indicators based on the AHP survey (more detailed results are in Acosta et al. 2019). The consensus values range from zero to 100 percent, where the latter implies a unanimous opinion on the weights (Figure A4.2). The consensus was highest among the experts in Asia Pacific and lowest in Africa. Asia Pacific had at least 80 percent consensus for their weights, with highest agreement on weights assigned to social inclusion. In the case of Africa, the highest consensus was for resource efficiency at 68 percent and lowest for social inclusion at only 51 percent. The very low consensus on social inclusion is not surprising because the region has one of the most complex social issues to address. The levels of consensus among the experts in Latin America and the Caribbean (LAC) were around 75 percent in all dimensions, except for the natural capital protection which was only 67 percent.

Appendix References:

Acosta, L.A., R.J. Mamiit, C. Ho, I. Gunderson, O. Anastasia, M. Angawi, C.O. Balmes, N. Desta, N. Krairiksh, H.W. Lakew, J.L.A. Loustaunau, P. Martinez, K. Ram-Indra, and C. Shrestha. (2018). Assessment of feedback from regional expert consultations on the Green Growth Index (Phase 2). GGGI Technical Report, The Global Green Growth Institute, Seoul, Republic of Korea.

Dedeke. (2013). Estimating the Weights of a Composite Index Using AHP: Case of the Environmental Performance Index, British Journal of Arts and Social Sciences, Vol.11 No.II, p. 199-221, ISSN: 2046- 9578, www.bjournal.co.uk/BJAS.aspx

Goepel. (2018). Implementation of an Online Software Tool for the Analytic Hierarchy Process (AHP-OS). International Symposium on the Analytic Hierarchy Process, Hong Kong, July 13 – July 15,  2018. Available in: https://www.isahp.org/uploads/isahp18_proceeding_1370731_001.pdf

Nicoletti G., Scarpetta S. and Boylaud O. (2000), Summary indicators of product market regulation with an extension to employment protection legislation, OECD, Economics department working papers No. 226, ECO/WKP(99)18. http://www.oecd.org/eco/eco

OECD and JRC. (2008). Handbook on constructing composite indicators: Methodology and use guide. Statistics Directorate and the Directorate for Science, Technology and Industry of the Organisation for Economic Co-operation and Development (OECD) and the Econometrics and Applied Statistics Unit of the Joint Research Centre (JRC) of the European Commission. Available in: https://www.oecd.org/sdd/42495745.pdf

Pakkar. (2014). Using data envelopment analysis and analytic hierarchy process to construct composite indicators. Journal of Applied Operational Research (2014) 6(3), 174-18.