reach 70–80% of the genetic yield potential ceiling. Based on these observations from the agronomic literature, we specify the following logistic function determining the evolution of the crop productivity index over time: where _✓_ 0<sup>_c_is the value of the crop productivity index in period 0, which we calibrate to match</sup> observed weighted yields in key staple crops (corn, rice, soybeans, and wheat), _✓T_<sup>_c_is the crop</sup> yield potential in the end of the current century, that is, “the yield an adapted crop cultivar can achieve when crop management alleviates all abiotic and biotic stresses through optimal crop and soil management” (Evans and Fischer, 1999), and _c_ is the logistic convergence rate to achieving potential crop yields.

Though the initial value of the crop productivity index is known with certainty, potential crop yields are highly uncertain. We assume that potential crop yields are a↵ected by a two-dimensional stochastic process of climate and technological shocks, _J_ 1 _,t_ , and _J_ 2 _,t_ , respectively. For the technological shock, _J_ 2 _,t_ , we assume that there are three states of technology: “bad” (indexed by _J_ 2 _,t_ = 1), “medium” (indexed by _J_ 2 _,t_ = 2), and “good” (indexed by _J_ 2 _,t_ = 3). In the optimistic (i.e., “good”) state of advances in crop technology, we assume that yields continue to grow linearly throughout the coming century, eliminating the yield gap by 2100. In the “medium” state of technology, rather than closing the yield gap by 2100, average yields in 2100 are just three-quarters of yield potential at that point in time. In the “bad” state of technology, there is no technological progress, and the crop yields stay the same as at the beginning of the coming century.

For the climate shock, _J_ 1 _,t_ , we assume it is a Markov chain with five possible states at each time _t_ . To construct these states, we use the results of Rosenzweig et al. (2014), who conducted a globally consistent, protocol-based, multi-model climate change assessment for major crops with the explicit characterization of uncertainty.<sup>23</sup> Based on this assessment, we construct five states that correspond to quintiles of the distribution of di↵erent outcomes of four global crop simulation models and five global climate models, with and without CO2 fertilization e↵ects for potential crop yields by 2100. Under two optimistic states of the world, we observe a 2 and 15 percent increases in potential crop yields relative to model baseline, respectively, whereby significant CO2 fertilization e↵ects o↵set the negative e↵ects of climate change. For the next two states, we see a 15 and 19 percent declines in potential crop yields relative to model baseline whereby CO2 fertilization e↵ects are assumed to be either small or non-existent, and the negative e↵ects of climate change tend to prevail. Finally, under the most pessimistic state of the world, drastic adverse e↵ects of climate change combined with the absence of any CO2 fertilization e↵ects result in a 36 percent decline in potential crop yields relative to model baseline.

Further details of constructing climate and technological states can be found in the

> 23 Given the partial equilibrium nature of FABLE, we cannot directly capture all sources of GHG emissions and, therefore, endogenize their e↵ect on global land use. However, as global land use emissions account for less than a quarter of global GHG emissions (IPCC, 2014b), climate-induced changes in land use will be relatively small to have a major e↵ect on global temperatures.

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