Responsibility, inequality, efficiency, and equity in four sustainability paradigms: insights for the global environment from a cross-development analytical model

Abstract

This paper develops a theoretical framework to assess the feasibility of global environmental sustainability solutions based on one or more value changes. The framework represents four sustainability paradigms (weak sustainability WS, a-growth AG, de-growth DG, strong sustainability SS) and five value changes (i.e. a sense of responsibility for nature, future generations, or the current generation in developing countries; aversion to inequality for the current generation or future generations). It defines solutions in terms of consumption, environment use, and welfare for representative individuals in both developed (OECD) and developing (non-OECD) countries. Solutions are characterised by efficiency (i.e. Pareto and Kaldor–Hicks) with respect to welfare and by intra- and inter-generational equality for consumption, environment use, and welfare, by confirming internal consistency and consistency with alternative equity approaches for utilitarianism (i.e. Harsanyi), egalitarianism (i.e. Arneson for welfare; Dworkin for consumption or environment use; Sen for consumption and environment use), and contractarianism (i.e. Rawls). Theoretical and operational insights are described for alternative sustainability paradigms and equity approaches. In terms of feasibility based on improved technology, decreased population, and modified consumption, the ordering is responsibility for future generations > responsibility for the current generation in developing countries > aversion to inequality for the current generation > aversion to inequality for future generations and AG > SS > DG > WS: responsibility for nature is unfeasible. In terms of internal consistency, responsibility for future generations > responsibility for the current generation in developing countries = aversion to inequality for the current generation = aversion to inequality for future generations and SS > AG > DG; WS is internally inconsistent. In terms of consistency with an equity approach, responsibility for future generations > responsibility for the current generation in developing countries = aversion to inequality for future generations > aversion to inequality for the current generation and SS > AG > DG > WS.

Appendices

Appendix 1: List of variable names

• α_F: the future preference for consumption

• α_N: the preference for consumption in OECD countries

• α_S: the preference for consumption in non-OECD countries

• β_N: the degree of concern for nature in OECD countries

• β_S: the degree of concern for nature in non-OECD countries

• γ_N: the degree of concern for future generations in OECD countries

• γ_S: the degree of concern for future generations in non-OECD countries

• δ_N: the degree of concern for the current non-OECD generation in OECD countries

• ε: the degree of aversion to intra-generational inequality

• ζ: the degree of aversion to inter-generational inequality

• η: per capita equilibrium use of the environment consistent with the current world population

• θ_N: the use of the environment for each consumption unit for the OECD current generation

• θ_S: the use of the environment for each consumption unit for the non-OECD current generation

• θ_F: the use of the environment for each consumption unit for the future generation

• E_C: population-weighted per capita use of the environment by the current generation

• E_F: per capita use of the environment by the future generation

• E_N: per capita use of the environment in the current OECD generation

• E_S: per capita use of the environment in the current non-OECD generation

• p_N: proportion of the global population in the OECD countries

• p_S: proportion of the global population in the non-OECD countries

• U: overall utility as dependent on consumption

• U_C: population-weighted utility for the current generation as dependent on consumption

• U_F: utility for the future generations as dependent on consumption

• U_N: utility for the current OECD generation as dependent on consumption

• U_S: utility for the current non-OECD generation as dependent on consumption

• W: overall welfare as dependent on environment use

• W_C: population-weighted welfare of the current generation as dependent on environment use

• X_C: population-weighted per capita consumption in the current generation

• X_F: per capita consumption in the future generation

• X_N: per capita consumption in the OECD current generation

• X_S: per capita consumption in the non-OECD current generation

Appendix 2: Use of a shared common environment

In the case of n countries at a similar development level, and which share a common environment (e.g. a closed sea), the model changes as follows:

$$U_{{\rm F}} = {\text{X}}_{{\rm F}}^{{\alpha_{{\rm F}} }} \;{\text{with}}\; \alpha_{{\rm F}} = \frac{1}{n}\mathop \sum \limits_{i}^{n} \alpha_{i} \quad {\text{and}}\quad X_{{\rm F}} = \eta /\theta_{{\rm F}} \;{\text{with}}\;\theta_{{\rm F}} = \frac{1}{n}\mathop \sum \limits_{i}^{n} \theta_{i}$$

$$U_{{C_{i} }} = X_{i}^{{\alpha_{i} }} \left( {\sum p_{i} E_{i} } \right)^{{ - \beta_{i} }} U_{{\rm F}}^{{\gamma_{i} }} \left( {\sum p_{j} U_{{{{\rm C}}_{j} }} } \right)^{{\delta_{i} }}$$

$$U_{{\rm C}} = \left[ {\left( {\sum p_{i} U_{{{{\rm C}}_{i} }} } \right)^{1 - \varepsilon } } \right]^{{1/\left( {1 - \varepsilon } \right)}}$$

$$U = \left[ {U_{{\rm C}}^{1 - \zeta } + U_{{\rm F}}^{1 - \zeta } } \right]^{{1/\left( {1 - \zeta } \right)}}$$

$$W_{{\rm C}} = \left[ {\left( {\sum p_{i} E_{i} } \right)^{1 - \varepsilon } } \right]^{{1/\left( {1 - \varepsilon } \right)}}$$

$$W = \left[ {E_{{\rm C}}^{1 - \zeta } + E_{{\rm F}}^{1 - \zeta } } \right]^{{1/\left( {1 - \zeta } \right)}}$$

where i refers to a sum which includes all n countries, whereas j refers to a sum that excludes country i. Note that this system of equations could be solved for X_i to check for the existence of a sustainability solution at current preferences. Alternatively, it could be solved for a set of consumption preferences (i.e. α_i, β_i, γ_i, δ_i, ε, ζ) at current consumption levels to check which country should change its preferences to a greater extent. Moreover, U_F ≥ U_i could be used instead of U_F ≥ U_C. Finally, the model could be solved in a cooperative context, in which δ_i could be positive. Alternatively, it could be solved in a non-cooperative context, in which δ_i is set to 0.

Appendix 3: Statistical analysis for the environmental ethics

In this section, I will estimate the significance and size of the five main secular environmental ethics for sustainability (i.e. responsibility for nature β, for future generations γ, and for the current generation in developing countries δ; aversion to inequality for the current generation ε and for future generations ζ). To do so, I will rely on the same dataset discussed in Sect. 4 (i.e. 145 countries) and the formulas introduced in Sect. 3. The additional data used in this analysis are presented in Table S1 of the Supplementary Materials II. In particular, formulas involving the parameters α, β, γ, and δ suggest the need to use a logarithmic transformation of the dependent variables (i.e. ln U_N and ln U_S for OECD and non-OECD countries, respectively) and independent variables (i.e. ln GDP_S, ln EF_S, and ln U_F for non-OECD countries, and ln GDP_N, ln EF_N, ln U_S, and ln U_F for OECD countries), and then to estimate the two equations linear model for ln U_N and ln U_S using a three-stage least-squares regression. Note that all parameters are assumed to be positive. In summary, I will estimate the following two equations:

$${ \ln } U_{S} = \alpha_{{\rm S}} {\text{ln GDP}}_{{\rm S}} - \beta_{{\rm S}} {\text{ln EF}}_{{\rm S}} + \gamma_{{\rm S}} {\text{ln}}U_{{\rm F}} + \xi_{{\rm S}}$$

And

$${ \ln } U_{{\rm N}} = \alpha_{{\rm N}} {\text{ln GDP}}_{{\rm N}} - \beta_{{\rm N}} {\text{ln EF}}_{{\rm N}} + \gamma_{{\rm N}} {\text{ln }}U_{{\rm F}} + \delta_{{\rm N}} {\text{ln }}U_{{\rm S}} + \xi_{{\rm N}}$$

where ξ_S and ξ_N are the estimation residuals. Note that I estimated ln U_S and ln U_N by using the consumption expenditures as a percentage of GDP as a proxy for α, the environmental protection expenditures as a percentage of GDP as a proxy for β, the R&D expenditures as a percentage of GDP as a proxy for γ, and the foreign aid expenditures as a percentage of GDP as a proxy for δ. Moreover, I estimated U_F by using world average values for α. Finally, I expect a positive sign for all parameters apart from those attached to ln E_F. Estimation results are presented in Table 9.

Table 9 Impacts of the environmental ethics parameters on welfare: β_N and β_S are attached to lnefn and lnefs, respectively; γ_N and γ_S are attached to lnuf in the first and second estimations, respectively; and δ_N is attached to lnus in the first estimation

Thus, the parameters either have the expected sign (i.e. responsibility to nature β and for future generations γ, with β_N ≈ β_S and γ_N ≈ γ_S, as well as for α, with α_N ≈ α_S) or are non-significant (i.e. responsibility for the current generation in developing countries δ_N).

Next, the formulas involving parameters ε and ζ suggest the need to use a logarithmic transformation of the independent variable (i.e. ln U) and then to estimate a nonlinear equation by applying nonlinear least-squares regression to the fitted values obtained from the previous regressions. Note that I estimated ln U (the overall utility) by using 1 − the Gini coefficient as a proxy for ε, and 1 − the government debt as a percentage of GDP as a proxy for ζ, with these coefficients constrained in [0, 1]. That is, if the observed government debt as a percentage of GDP is larger than 100%, ζ is assumed to be 0. Moreover, I performed the estimation by using 1–ε and 1–ζ. Finally, both ε and ζ are assumed to be constrained in [0, 1]. In summary, I will estimate the following equation:

$${ \ln } U = \frac{1}{1 - \zeta } {\text{ln}}\left\{ {\left[ {\left( {0.18 U_{{\rm N}} } \right)^{1 - \varepsilon } + \left( {0.82 U_{{\rm S}} } \right)^{1 - \varepsilon } } \right]^{1 - \zeta /1 - \varepsilon } + U_{{\rm F}}^{1 - \zeta } } \right\} + \psi$$

where ψ is the estimation residual, and 0.18 and 0.82 are the proportions of the world’s population in OECD and non-OECD countries, respectively, in 2012. Note that I expect a positive sign for all parameters. Estimation results are presented in Table 10.

Table 10 Impacts of the environmental ethics parameters on welfare: aversion to inequality for current generations ε and future generations ζ, with ep = 1 − ε, and ze = 1 − ζ

Thus, the estimated concern for the current generation is negative but non-significant (i.e. ε = –13.619 + 1), whereas the estimated concern for future generations is in (0,1) and significant (i.e. ζ = –0.287 + 1).

In summary, the reliability (i.e. significance and size) rankings in the statistical results are intuitive for sustainability (i.e. ζ > β > γ > δ > ε). However, combining this reliability ranking with the feasibility ranking obtained in the numerical simulations (i.e. γ > δ > ε > ζ > β) leads to a pessimistic conclusion about sustainability: the most reliable factors (i.e. ζ > β) are unfeasible, whereas the most feasible factors (i.e. γ > δ) are unreliable to achieve sustainability.