A cost valuation model based on a stochastic representation of the IPAT equation

Within the framework of models for human-driven environmental impact based on the IPAT equation, we develop a model for the evolution of impact (expressed in terms of carbon dioxide emissions) and for the valuation of the economic cost associated to its reduction. We use a stochastic representation of the IPAT equation that is alternative to the STIRPAT model. This first step leads to a stochastic differential equations model that describes trends in carbon dioxide emissions on the basis of economic and demographic dynamics. As an example, we estimate the model parameters for the United States. We then use this framework to build a model for the assessment of the economic costs related to a reduction of carbon dioxide emissions for a country committed to respect an international agreement, such as the Kyoto protocol. In particular, we show that the adherence to an environmental treaty may be traced back to a problem of cost valuation and to a decision under risk. This allows us to use the mathematical tools that have been developed in quantitative finance, in the context of option pricing, to determine the expected investment that is required to reduce the emissions of a country by a certain amount and within a well-defined temporal frame. © Springer Science+Business Media, LLC 2008