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### Abstract

Many studies have done econometric estimates of how climate alters crop yields and or land rents in an effort to gain information on potential effects of climate change. However, an important related factor, the atmospheric carbon dioxide (CO2) concentration, and in fact a driver of climate change is ignored. This means the prior econometric estimates are biased as they infer what will happen under climate change from observations in the recent past, but without consideration of CO2 effects. Furthermore although CO2 has been varying, it has proceeded at a very linear pace and cannot be disentangled from technological progress using historical crop yield data. This paper is designed to overcome this issue and estimate the consequences that CO2 has and will have in conjunction with climate change. The paper also partitions yield growth into temporal CO2 and climate change affected components and begins to address an issue of how climate change and its drivers will affect rates of technological progress. Moreover, we also factor in a number of conditions regarding to extreme events. This allows us 1) to estimate the consequences of such factors on yields; 2) to project given forecasts of climate change induced shifts in those factors what the implications are for yield distributions; and 3) carry this into welfare and technological change analyses. First, we use a stochastic production function approach of the type suggested by Just and Pope (1978, 1979) estimated with a three-step feasible generalized least squares approach to estimate the effect of climate change and CO2 fertilization on crop yields. The observational data of crop yields and planted acreage are collected from the USDA-National Agricultural Statistics Service. State-level climate data used in this study are obtained from the National Oceanic and Atmospheric Administration. The free-air CO2 enrichment (FACE) experimental data are obtained from the USDA Agricultural Research Service and SOYFACE, University of Illinois. Next, to investigate the implication of future climate change on crop yield and its variability, we employ our estimated coefficients together with future climate change projected by standard GCMs used in the IPCC (2007) with the IPCC SRES scenario A1B. Finally, to explore the market outcomes and welfare implications of economic units given climate-induced shifts in yields across US regions, we plug in our projected percentage changes of mean crop yields into the agricultural sector model (ASM), a price endogenous, spatial equilibrium mathematical programming of the agricultural sector in the US. Our initial results find that yields of C-3 crops, soybeans, cotton, and wheat, positively respond to the elevated CO2, while yields of C-4 crops, corn and sorghum do not. However, we find that C-4 crops indirectly benefit from elevated CO2 in times and places of drought stress. We find the effect of crop technological progress to mean yields is non-linear with inverted-U shape in all crops, except cotton. Our study also reveals that ignoring the atmospheric CO2 in econometric model of crop yield studies is likely to overestimate the pure effect of climate change on crop yields as CO2 enhances those yields. For climate change impact, the average climate conditions and their variability appear to contribute in a statistically significant way to both average crop yields and their variability. Moreover, generally we find that the effect of CO2 fertilization generally outweighs the effect of climate change on mean crop yields in many regions. In terms of market outcomes and welfare distribution, we find the yield growth under the combined climate change and CO2 effect tends to decrease price in 2050. Planted acreage of all crops in North Plains, except wheat winter, is projected to increase, while it tends to decrease in South Plains, Lake States, Delta States, Southeast, and Mountains for almost all crops. Overall consumers’ surplus is projected to increase, while producers’ surplus is heterogeneously affected across US regions, but in total decreases by about $4.72 billion. Overall the total US welfare is increased about$ 2.27 billion compared to the base scenario. There are several clear implications of above findings. For example, 1) returns to agricultural research should be reevaluated in the light of climate change influences as for example aggressive CO2 mitigation will decrease returns; 2) models using econometric methods to predict future crop yields should be aware that ignoring CO2 fertilization may overestimate the real effect of climate change on crop yields; and 3) welfare losses for producers under climate change are likely with consumers gaining.