An axiomatic characterization of a generalized ecological footprint

ABSTRACT

The purpose of this paper is to propose an axiomatic characterization of ecological footprint indices. Using an axiomatic approach, we define a set of axioms representing the properties considered appropriate to ecological footprint measures in general. It can be shown that there exists a generalized index which is given by an arbitrary affine transformation of the land area appropriated to provide a country's share of consumption on world production. The footprint of a subset of countries is given by the sum of the individual footprints. As an implication, the well-known compound-based footprint index used by the Global Footprint Network can be characterized as a specification of the generalized index by an appropriate affine transformation. With respect to empirical applications the proposition of generalized and axiomatically characterized measures for the ecological burden by human activity may be considered as the main contribution of the paper.

KEYWORDS:

• Generalized ecological footprint index
• axiomatic characterization
• measurement theory
• overshoot day
• sustainable welfare

JEL CLASSIFICATION:

• C43
• Q01
• Q24
• Q54
• Q56

Acknowledgments

We are thankful to the two anonymous reviewers at the Journal of Ressource and Energy Economics and the reviewer at the Journal of Environmental Economics and Policy whose valuable suggestions helped to improve this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 In this context, the footprint index indicates the pressure exerted by human activity on the respective environment medium or via the respective pollutant.

2 It is assumed that the set of possible ecological states is unrestricted in the sense that $\{w\in \mathcal{W}|C_i\left(w\right)=c_i,A_i\left(w\right)=a_i,Y_i\left(w\right)=y_i,\text{ı}\in \mathrm{\Omega }\}$ is non-empty for $c_i,a_i,y_i\in {\mathbb{R}}_{+}$. This makes the domain of the index as wide as possible.

3 Consumption is defined as final demand by households, producers, and the state.

4 The most recent methodology even accounts for land productivity differences in time by extending the unit of measure to constant global hectares through a world-average intertemporal yield factor, expressed with reference to a selected base year. This step is aimed to avoid difficulties of interpretation in intertemporal comparison (Borucke et al. 2013).