A Corn Yield Function Considering the impact of water and weather

Agriculture is a resource-intensive activity. It currently uses a substantial portion of the Earth’s natural resources: crop production, pasture and livestock grazing systems occupy around 40% of total land area, nitrogen fertilizer applied to agricultural land comprises more than half of the global reactive nitrogen attributable to human activity and agricultural production consumes more fresh water than any other human activity since it accounts for 80% of all freshwater consumption (Cassman 2003). Water is one of the key determinants of agricultural land productivity, adequate water supply to crops is essential to achieve maximum yield and greater stability, enabling also greater scope for diversification. The success of irrigation in improving food security and fostering rural welfare during the last decades has been extremely important but an inappropriate management of it can contribute to a series of environmental problems. The achievement of the required sustained (and sustainable) growth in agricultural production over the next 40 years calls for understanding the current and future enhancers and constraints of agricultural productivity. As water becomes scarcer it is important to estimate the real contribution that water has for agricultural productivity given the whole set of variables that are present in the farming production process, including also the amount of fertilizer and chemicals used, the environment where the process is held (such as temperature, precipitation and soil organic matter) and the farmers profit maximizing behavior. The objective of this study is to measure the contribution that the amount of water irrigated has on agricultural productivity in addition to the effect of weather and the traditional inputs. The data set used in this study consists on data from a survey done to farmers in three different Natural Resources Districts (NRDs) in the state of Nebraska during the period 2004 to 2011. The chosen NRDs are spread over the 41st parallel along East, Center and West Nebraska accounting for important weather (temperatures and precipitation) and soil variability. The data set consists of more than 30,000 observations with information on actual yield, type of crop, inches of water employed, nitrogen applied and manure rates. Additionally we include estimations on temperature (measured in intervals of degree days), precipitation and soil organic matter. Using these variables, this research develops an econometric production function that assumes a semi transcendental logarithmic technology. Particular interest is given to the amount of water used and its interactions with the remaining variables. We do not know of any other similar study done at this level of aggregation and with this great amount of observations. The hypothesized production function follows the form: Where for each field Yi represents the log of the biomass produced at year t for all the crops, Xit is a vector of the log of the amount of water used, amount of fertilizer used, amount of manure used and the time trend at year t, Kit is soil organic matter for year t and rit is a vector of rainfall an 2 degree days intervals (dd30-35 and dd35-40) for year t. By estimating the production elasticities from this translog specification we are able to obtain the effect of water and the other inputs in our hypothesized biomass yield function at each data point. Initial results quantify the critical importance that the amount of irrigated water has on agricultural productivity. As expected the amount of water used has a positive effect on the expected yield, for every extra inch of water pumped the yield is expected to increase by 6.74 percent. Results also highlight the significant negative effect of higher temperatures, a full day of temperatures over 35ºC is expected to decrease the yield in 33.1 percent but this harmful negative effect can be decreased by the use of irrigation. Results also highlight and quantify the importance of the use of Nitrogen as fertilizer. As a next step in this analysis, we plan to use the already available information on nitrogen and electricity prices to improve our estimation; by incorporating share equations we will be able to account for the economic behavior of the producer (as well as the physical relations between the inputs) and additionally to study the effect that price changes due to market or policy modifications can have on factor allocation (in the short run) or in technical change (induced by price changes in the long run).