change in food, timber and biofuels industries, this is one of four core uncertainties a↵ecting competition for global land use (Steinbuks and Hertel, 2013). To quantify the uncertainty in agricultural yields, we construct stochastic crop productivity index that captures two key uncertainty sources: technological progress and global climate change (Lobell et al., 2009; Licker et al., 2010; Foley et al., 2011).<sup>5</sup> Following Rosenzweig et al. (2014), we use projections from climate and crop simulation models, as well as the survey of recent agro-economic and biophysical studies to calibrate the index.

We simulate the results of the perfect foresight model under di↵erent realizations of the crop productivity index, focusing our attention on the current century. We then 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. When the uncertainty in crop productivity is incorporated into the model, we see an additional redistribution of land resources aimed at o↵setting the impact of potentially lower yields. Owing to intertemporal substitution, some of that redistribution takes place even in the absence of the actual changes in the states of climate or technology a↵ecting crop yields. Moreover, the range of these alternative optimal paths of cropland is considerably smaller than the magnitude of possible land conversion resulting from the scenario analysis based on deterministic model simulations. This result indicates that the scenario analysis may significantly overstate the magnitude of expected agricultural land conversion under uncertain crop yields.

Besides the methodological innovation, our study also contributes to the growing environmental economics literature that analyzes the intertemporal allocation of land and other natural resources under uncertainty and irreversibility constraints. Most of that literature focuses on a particular type of resource or sector, where intertemporal issues are significant and cannot be ignored. One example of this literature is forestry management in the context of uncertain fire risks and climate mitigation policies (Sohngen and Mendelsohn, 2003, 2007; Daigneault et al., 2010). Another example is natural land conservation decisions under irreversible biodiversity losses (Conrad, 1997, 2000; Bulte et al., 2002; Leroux et al., 2009). While these models are undoubtedly helpful for understanding the broad implications of uncertainty on the intertemporal allocation of land resources, they fail to account for the e↵ect of uncertainty in supply and demand drivers on the optimal allocation of land resources in the long run. Our study is perhaps most closely related to the recent work of Lanz et al. (2017) who develop a two-sector stochastic Schumpeterian growth model with the endogenous allocation of global land use. They find, like our paper does, that optimal allocation of global land use requires more cropland conversion when the uncertainty in agricultural productivity is present. Lanz et al. (2017), however, focused on endogenous population dynamics, labor allocation, and technological progress, whereas our paper is concerned about the endogenous allocation of multiple types of land use and corresponding land-based goods and services. Our paper also advances on methodological grounds by introducing a novel algorithm that overcomes the computational difficulties of solving multidimensional stochastic land use models, which made Lanz et al. (2017) significantly

> 5Climate change will likely a↵ect the productivity of other land resources, such as forestland. Several recent modeling studies (see, e.g., Tian et al. (2016) and references therein) have suggested that climate change is likely to result in higher forest growth and greater timber yields, as well as in more forest dieback, with the net e↵ects varying over time and space. Incorporating these e↵ects is beyond the scope of this study and is left for future research.

4