بهره وری کل عوامل و منحنی کوزنتس محیط زیست: نظر برخی از شهود

Chimeli and Braden [Chimeli, Ariaster B., Braden, John B., 2005. Total factor productivity and the Environmental Kuznets Curve. Journal of Environmental Economics and Management 49, 366–380] derive a necessary and sufficient condition under which inter-country differences in total factor productivity can yield an Environmental Kuznets Curve. They argue that their results emphasize the importance of differences in total factor productivity across countries as well as the need for decreasing returns to scale in pollution-abating technologies for the existence of an Environmental Kuznets Curve. We show that their Proposition 1 is equivalent to Proposition 2 in Lieb [Lieb, Christoph M., 2002. The Environmental Kuznets Curve and satiation: a simple static model. Environment and Development Economics 7, 429–448]. This implies that, even in Chimeli and Braden's model, contemporaneous changes in the marginal rate of substitution between environmental quality and consumption on the demand side and the marginal rate of transformation between these goods on the supply side drive the pollution–income relationship. This is a very general condition that does not rely on either differences in total factor productivity or decreasing returns to scale in abatement, and which is widely applicable.

Chimeli and Braden (2005) show that differences in total factor productivity can yield a U-shaped relationship between environmental quality and income in a cross section of countries, a relationship implied by the Environmental Kuznets Curve (EKC) hypothesis. Several authors have empirically tested the EKC hypothesis using either cross-sectional data (for example Gawande et al., 2000 and Khanna and Plassmann, 2004) or data that cover a relatively short time period (for example, Torras and Boyce, 1998), and Chimeli and Braden's result provides a theoretical justification for these tests.

Expression (3) is a very general condition for an EKC in the types of models developed by C&B and Lieb. It illustrates that only appropriate joint changes of MRS and MRT may yield an EKC. By itself, expression (3) does not imply any particular driving force behind the EKC. This suggests that C&B's result is not driven by differences in total factor productivity, per se, but rather by differences in income/resources, regardless of what the source of those differences might be. C&B find that decreasing returns to scale in environmental protection yields a cross-sectional EKC across countries because they ensure that additional environmental expenditures increase the cost of improving environmental quality by more when environmental effort is low than when it is high (C&B, p.372). However, the equivalence between C&B's and Lieb's results suggests that such decreasing returns to scale simply ensure that − MRSCC,P > − 1 / ρ · dMRTC,P / dC|dP = 0 when total factor productivity is small but that the inequality reverses at higher levels of total factor productivity. Although C&B's observation is certainly correct, this condition can be fulfilled through alternative restrictions on either preferences or the pollution function as well.