An IPAT-type Model of Environmental Impact Based on Stochastic Differential Equations

Emilio Zagheni, University of California, Berkeley
Francesco C. Billari, Università Bocconi

This work adds to the literature examining human-driven climate change within the framework of IPAT-based models. Starting from the well-known IPAT identity, we develop a stochastic differential equations model that describes the trend of the environmental impact, expressed as CO2 emissions, on the basis of the dynamics of population and affluence. Our theoretical scheme has then been used to develop a model for the assessment of the costs that a country has to bear, if committed to respect an international agreement on emissions reduction. We show that the adherence to an environmental treaty may be traced back to a problem of cost valuation in a risk situation: this allows us to exploit the mathematical tools developed in the field of finance to determine the expected investment that a country is supposed to make in order to reduce its emissions of a certain amount, within a well-defined temporal frame.