Modeling the marginal value of rainforest losses: A dynamic value function approach

The economic value of a rainforest is modeled as a dynamic asset subject to fire risk and potential increase in dryness. I solve two Bellman equations, for unburnt and for already burnt forest, to derive analytically tractable expressions for the total expected, spatially differentiated, asset value of the forest in each state assuming constant growth and forest loss rates over time. I derive the marginal expected discounted value loss when losing a small additional piece of forest, at any alternative site in the forest. Marginal forest value is found to increase when the risk of forest fire increases due to forest fragmentation when forest is lost locally; and also when forest dryness, affecting forest values negatively, increases upon forest fragmentation. Both forest fire risk and dryness serve as “multipliers” on the basic services return loss, both within and outside of the forest. Increased forest fire risk is found to reduce average rainforest value by reducing their future expected lifespans and current returns; but to increase marginal forest value by making primary forest loss avoidance more valuable. I calibrate the model including the impact of the forest fire risk component on forest value, with multipliers in a typical range 1.3–1.5.