Crop yields tend to be spatially and temporally correlated due to the systemic nature of land and weather conditions. Recent concern has been focused on whether climate change such as increasing extreme weather events would affect crop yield and yield volatility (Goodwin 2001, Ozaki, et al. 2008). In this paper, a spatio-temporal Conditional Autoregressive Model (ST-CAR model) (Mariella and Tarantino, 2010) will be used to analyze the impact of climate change on crop yield and yield volatility. State level crop yield data from 1950 to 2014 is collected for this study. As an extension of the standard CAR model, a space-time autoregressive matrix will be used in the ST-CAR model to handle both spatial dependence between states and temporal dependence among the examined period. Specifically, the spatial correlation parameter in ST-CAR model varies along time, making it possible to reveal the potential impact of climate change on spatial correlation. Future yield projections will be generated and used in the FASOM model to conduct a welfare analysis. Preliminary results of segment regression shows that breakpoints exist for many states in the US for the last few decades, indicating the potential impact of climate change on yield and yield volatility.