An axiomatic approach to decoupling indicators for green growth

The concept of decoupling was introduced to measure and analyze the controversial trade-off between economic development and environmental sustainability; in particular, several empirical studies concern the construction and use of decoupling indicators. We elaborate on a descriptive comparison by Conte Grand (2016) of the three main ones, respectively D_O by OECD (2002), D_ε by Tapio (2005), and D_t by Lu et al. (2011), and introduce an axiomatic approach into the subject that articulates in the identification of some properties that appear indispensable or at least desirable for any decoupling indicator and in the assessment of their validity for the indices under scrutiny and/or in the construction of new indices that satisfy them. A graphical examination of the aggregation function level sets in the Cartesian plane is a relevant part of the method. Under such analysis, the index D_O turns out to show milder defects than D_ε and D_t. We then propose a suitable modification D_N in order to remove the defects and fulfill all the given compatible axioms; in particular, D_N is cumulative over sub-periods. It may also be opportune for a decoupling index to differentiate the treatment of the case when, during economic growth, environmental stress (e.g., polluting emissions) decreases from the case when it increases, although less than economy (the so-called absolute and relative decoupling, respectively), as well as to capture the rebound effect phenomenon, whereby the efforts to reduce environmental intensity may eventually result in a smaller overall environmental improvement than predicted or intended. To this end we build another index D_P by applying to D_N a correction (that can be calibrated via a global parameter) for the distance from what we define symmetric decoupling, the case when the variations of economy and of environmental pressure are inversely proportional. We conclude by testing the novel indices D_N and D_P against D_O on data from OECD (2017) of 103 world countries for the most recent completely available decade 2003–2013.