Predicting the impact of climate change on crop yield is difficult, in part because the production function mapping weather to yield is high dimensional and nonlinear. We compare three approaches to predicting yields: (i) deep neural networks (DNNs), (ii) traditional panel-data models, and (iii) a new panel-data model that allows for unit and time fixed-effects in both intercepts and slopes in the agricultural production function - made feasible by a new estimator developed by Keane and Neal (2020) called MO-OLS. Using U.S. county-level corn yield data from 1950-2015, we show that both DNNs and MO-OLS models outperform traditional panel data models for predicting yield, both in-sample and in a Monte Carlo cross-validation exercise. However, the MO-OLS model substantially outperforms both DNNs and traditional panel-data models in forecasting yield in a 2006-15 holdout sample. We compare predictions of all these models for climate change impacts on yields from 2016 to 2100.