Modeling market-level effects of disturbance risks in age structured forests

The intensity and frequency of catastrophic forest disturbances, such as wildfires, are predicted to continue increasing into the future. Market-level models can be used to assess the effects of such disturbances on timber production and on other ecosystem services provided by forests. This paper examines catastrophic disturbances in the context of age structured forests and compares stochastic and deterministic approaches to modeling equilibrium harvesting. We define the deterministic model as the certainty equivalent form of the stochastic model. Forest transition dynamics are modeled using two age classes. In each period, some share of forestland is subject to destruction, following either an IID stochastic process or determined by the expected value of the same stochastic process. Our analysis and characterization of the two models yield new theoretical results. We show that the equilibrium cycles vanish due to the presence of such disturbances. We also derive a close connection between market-level models with disturbances and the standard stand-level model with risk. We use dynamic programming to solve the state dependent policy functions for both stochastic and deterministic cases and use simulations to compare the paths of the expected timber supply, timber prices, and land allocation to young and old age classes. Our results suggest a close similarity between the stochastic and deterministic policies. This provides a justification for using the certainty equivalent specification to approximate stochastic models, even in more complex settings.