Modeling the Marginal Value of Rainforest Losses: A Dynamic Value Function Approach

A rainforest can be modeled as a dynamic asset subject to various risks, including risk of fire. Any small part of the forest can be in one of two states: either untouched by forest fire, or already damaged by fire, in which case there is both a local forest loss and increased dryness over a broader area. In this paper, two Bellman equations are constructed, one for unharmed forest and a second for already burnt forest. The analysis solves the two equations for the total expected asset values in each of the two states, assuming that asset returns have a constant growth rate over time. The equations are used for deriving the marginal value of standing (unburnt) rainforest, equivalent to the expected discounted value loss when losing a small additional forest patch. The paper shows that marginal forest value is increased by the additional dryness and forest fire risk that follow from forest fragmentation when additional forest is lost locally. Both forest fires and dryness here serve as “multipliers” to the basic services return loss, within and outside the forest. The paper also presents a framework for calibrating the impact of the forest fire risk component on forest value.