Technological vs. Ecological switch and the environmental Kuznets curve

Empirical research has mainly consisted in examining a wide variety of pollutants for evidence of the inverted U-shaped pattern, resulting in the conclusion that such a shape is valid for many local and flow pollutants. From the technical point of view, the problem sounds at first glance strongly asymmetric, the technological switch involving explicit timing decisions while ecological switches are essentially based on a posited threshold pollution level. The challenge is first analytical because the general optimal control problem involved is nontrivial. It is also computational because comparing eight possible solutions is very demanding. A natural approach is to decompose the problem into several sub-problems for given timing variables, to solve each of them, and then to identify the optimal timings. With one timing variable, two sub-problems are involved corresponding to the resulting two time intervals, before and after the switch.