This was part of Assessing the Economic and Environmental Consequences of Climate Change
Carbon prices and forest preservation over space and time in the Brazilian Amazon
Jose Scheinkman, Columbia University
Friday, March 31, 2023
In this research, we build and analyze a spatial/dynamic model of socially efficient land allocation in the Brazilian Amazon, and assess the consequences of imposing alternative social costs of carbon emissions on the spatial/dynamic allocation of land use. We show how to incorporate the stochastic evolution of agricultural prices, and we explore the consequences of ambiguity in the location-specific productivities on the socially efficient policy.
We pose the model in continuous time. The cross-sectional heterogeneity in productivities and the natural state constraints on land allocation preclude standard recursive methods for solving so-called Hamilton-Jacobi-Bellman (HJB) equations. Instead, we use and extend methods from Modified Predictive Control (MPC) that were originally developed in control theory and engineering to study multi-plant production in real time. The inequality constraints on the states are approximated using an interior point method. These MPC alogorithms allow for uncertainty specified as a Markov process and are implemented by incorporting a shorter uncertainty horizon than the overall control horizon as a means of approximation. We also explore parameter ambiguity from the standpoint of the social planner by making a model-determined robustness adjustment to the subjective probabilities for the unknown parameters. We are once again pushed to use numerical methods, in this case a Metropolis Hasting algorithm implemented as a Markov Chain Monte Carlo (MCMC) simulator. In this way, we confront what is sometimes referred as ``deep uncertainty.’'
Our results show that with modest transfers per ton of net CO2, Brazil would find it optimal to choose policies that produce substantial capture of GHG in the next 30 years, suggesting that the management of tropical forests could play an important role on climate change mitigation in the near future.
Joint work with J. Assunção, L. Hansen and Todd Munson