Duality methods utilizing a profit function framework are employed to estimate the output elasticity of ambient ozone levels on cash grain farms in Illinois. While duality methods have been recommended as a cure to many of the statistical problems of direct estimation of production functions, multicollinearity may still be a problem. A method for utilizing stochastic information on parameters of a seemingly unrelated system of equations, which is implied by profit function estimation, is developed and applied to measuring the impact of ozone. Such an approach may be necessary in measuring other environmental effects because of a lack of regressor variability.