the modeling approach of Steinbuks and Hertel (2013) has several important limitations, which we attempt to address in this paper. First, they adopt a very simplistic approach to quantifying uncertainty in crop yields, focusing on rather simplistic representation of climate impacts, and ignoring uncertainty in the evolution of agricultural technology. Second, their model is perfect foresight and assumes risk-neutral agents, and thus ignores the impact of future uncertainty on optimal allocation of global land use.

The model we develop is a long-run dynamic stochastic partial equilibrium framework in which the societal objective function being maximized places value on food production, liquid fuels (including biofuels), timber production and biodiversity. A non-homothetic AIDADS utility function represents model preferences, and, as society becomes wealthier, places greater value on eco-system services, and smaller value on additional consumption of food, energy and timber products. The forestry sector is characterized by multiple forest vintages, which add considerable computational complexity in the context of this dynamic stochastic analysis. To meet the significant computational challenge of this high-dimensional problem, we use recent state of art methods in parallel dynamic programming and implement them on a supercomputer.

To quantify the uncertainty in climate impacts on agricultural yields we follow the methodological approach of Rosenzweig et al. (2014). Our estimates are based on the results from Decision Support System for Agrotechnology Transfer (DSSAT) crop simulation model for four major crops, run globally on a 0.5 degree grid and weighted by agricultural output under different GHG forcing scenarios using outputs from five different global climate models. Our estimates of uncertainty in agricultural technology is based on recent agro-economic and biophysical studies assessing the potential for closing yield gaps and advances in plant breeding.

The model is solved over the period 2005-2204, with an emphasis on the first century. The model baseline accurately reflects developments in global land use over the 10 years that have already transpired, while also incorporating projections of population, income and demand growth from a variety of international agencies. We show the results of the perfect foresight model, whereby climate and technology shocks to crop yields are absent and compare and contrast them with the results of the dynamic stochastic model, where the uncertainty in crop yields is brought to the model’s optimization stage. Our model baseline results suggest that, in the near term decades, there is a significant expansion in the area dedicated to food crops due to rapid population growth and increasing demand for food at subsistence level. The expansion in cropland is largely associated with a accelerated loss of unmanaged natural forests, whereas managed forest lands are little changed. In the second half of the coming century slower population growth, and technology improvements in crop yields and food processing result in a smaller demand for crop land. By 2100 cropland area is just 4 percent larger than in 2004. Managed and protected natural forest land areas grow significantly by the end of the century, reflecting rising real incomes, and growing demand for timber products and ecosystem services. The results of the dynamic stochastic analysis are consistent with the expected hypothesis that 4