tion income increases (Foley et al., 2011). By the end of the coming century, the production of livestock in the baseline scenario increases by about 1.5 times compared to 2004, reaching 1.28 billion tons. Given the important contribution of the livestock feed in the production of livestock, we can see its production is smaller in the pessimistic scenario and larger in the optimistic scenario. The di↵erence in livestock production between the optimistic and pessimistic scenarios accounts for about 550 million tons. This range is similar to the dynamic stochastic model. As the significance of animal feed in livestock production grows over time, the e↵ect of uncertain crop yields becomes more pronounced. Similar to the result for food crops, the most extreme paths of crop productivity account for about a third of all variation in livestock production.

Production of timber in the deterministic model also expands with the growing demand for timber products and further improvements in forest yields (panel e). By 2100, production of merchantable timber crops reaches 3.2 billion tons in the deterministic baseline scenario, which is twice as large as in 2004. The consumption of ecosystem services declines in the near decades, as unmanaged natural forest lands are converted to croplands (panel f). It then increases throughout the remaining part of the coming century as the demand for ecosystem services increases, and more natural forest lands become institutionally protected. By 2100 consumption of ecosystem services is 36 percent larger than in 2004. Crop productivity has a very small e↵ect on consumption paths of merchantable timber and ecosystem services in either deterministic or stochastic models. This result is not very surprising as the crop productivity does not directly a↵ect the production of either timber or ecosystem services, whereas indirect land use change e↵ects are relatively small in this stochastic application of the FABLE model.

# **6 Conclusions**

This paper demonstrates how the uncertainties associated with nonstationary biophysical processes and technological change can be incorporated into an economic analysis of the optimal allocation of natural resources in the long run. In doing so, it introduces a novel computational method, ENLCEQ, for solving nonstationary dynamic high-dimensional stochastic problems and applies it to FABLE, a recently developed multi-sectoral dynamic model of global land use.

For illustrative purposes, the study focuses on uncertainty in future crop yields, one of the core uncertainties a↵ecting the evolution of global land use in the long run. Combining scenarios from global climate models and high-resolution output from spatial crop simulation models for four major crops, it comes up with a plausible range of realizations of climate shocks and their e↵ect on future crop yields. These estimates are supplemented with an extensive survey of recent agro-economic and biophysical studies assessing the potential for closing yield gaps as well as attaining further advances in potential yields through plant breeding.

The paper’s key insight is to illustrate the magnitude of optimal land conversion decisions in the context of di↵erent realizations of the stochastic crop productivity. Consistent with the economic theory of natural resource management under uncertainty, the agricultural productivity shocks, due either to adverse climate impacts or unexpected limits on 24