Measuring World Better Life Frontier: A Composite Indicator for OECD Better Life Index

The OECD Better Life initiative recently released a comprehensive set of 11 indicators of well-being covering a group of countries. Each individual indicator corresponds to a key topic that is essential to well-being. However, the problem of aggregating them is left to users of this dataset. Using these as individual indicators, we propose a composite indicator of overall well-being, which is intended to measure the performance of each country in terms of providing well-being to its people. The 'benefit of the doubt' approach (BOD), a well-known aggregation tool based on a weighed sum, assigns the most favourable weights for each entity under investigation. BOD may also be considered to evaluate the performance of each entity in terms of its efficiency. Regarding individual indicators as outputs, it constructs the benchmark production frontier from observed individual indicators. A composite indicator based on BOD equals the distance between each entity's individual indicator and the production frontier, indicating its efficiency. It is widely considered that the well-being of a country's people stems from its productive base, which is characterized by capital assets and social infrastructures. Thus, the productive base can be considered the input used to produce well-being, which is reflected by individual indicators. Therefore, when we apply BOD to aggregate individual well-being indicators across countries, we implicitly assume that all countries have the same productive base, as BOD addresses only the output and neglects the input. This inaccurate assumption leads to a distored performance measure. Data envelopment analysis (DEA), in which BOD has its roots, is a tool to measure the efficiency of each entity by allowing for differences in inputs as well as outputs across entities. DEA also measures efficiency by using the distance to the production frontier; however, unlike BOD, DEA constructs the production frontier more accurately by utilizing the information of inputs as well as outputs, leading to a better performance measure. We apply DEA to aggregate 11 individual well-being indicators into a composite indicator using the World Bank's estimates of each country's productive base. The composite indicator based on BOD is distributed similarly to and is highly correlated with the existing Human Development Indicator (HDI). It is also positively correlated with GDP per capita. On the other hand, we show that the composite indicator based on DEA is neg