A study on forecasting paths of genuine savings and wealth without and with carbon dioxide constraints: development of shadow price functions

This paper has developed a method for forecasting the future paths of genuine savings (GS) with and without carbon dioxide (CO₂) emissions constraints. GS calculations require shadow prices, which can be endogenously determined for variables and constraints in a model. However, in case of a ‘business as usual’ model (BAU), the shadow prices required for calculating GS without constraints show theoretically zero. This research derives the shadow prices required to measure GS for the BAU case as a function of several variables available in the optimal (economically efficient) case. This function is estimated from endogenously obtained variables from a model with environmental constraints. Subsequently, this function is used to calculate shadow prices with and without CO₂ constraints, which are further employed to compute future paths of GS according to two methods applied in the papers by Arrow et al. We successfully estimated GS (or GSnt; GS with changes in population and technology) under the BAU case, however, suggest that GS (or GSnt) measures depend, to a great extent, on the time span under consideration (truncation year) for wealth accounting and the accounting methods by Arrows’ papers used for its estimation. In some cases, especially according to the methodology used by Arrow’s paper in 2004 using adjusted consumption in wealth accounting, the sign of GS (or GSnt) changes from negative to positive when changes in total factor productivity are taken into consideration. These aspects should be explored before measuring (un)sustainability of a particular path based on the GS (or GSnt) indicator.