This working paper, authored by Itzhak Krinsky and A. Leslie Robb, explores the statistical properties of elasticities derived from Translog and Generalized Leontief cost functions. The authors propose a simulation exercise to compare the empirical distributions of factor demand elasticities with linear approximations. They find that the linear approximations often significantly underestimate the standard deviations of these elasticities, leading to potential errors in statements about their precision. The study uses a three-factor production process characterized by a cost function and shares equations for both the Translog and Generalized Leontief cost functions. The results highlight the importance of caution when using linear approximations to estimate the dispersion of non-linear functions of random variables. The paper also includes tables detailing the parameter information and simulation results for both cost functions, providing a comprehensive comparison between the linear approximations and the empirical distributions.This working paper, authored by Itzhak Krinsky and A. Leslie Robb, explores the statistical properties of elasticities derived from Translog and Generalized Leontief cost functions. The authors propose a simulation exercise to compare the empirical distributions of factor demand elasticities with linear approximations. They find that the linear approximations often significantly underestimate the standard deviations of these elasticities, leading to potential errors in statements about their precision. The study uses a three-factor production process characterized by a cost function and shares equations for both the Translog and Generalized Leontief cost functions. The results highlight the importance of caution when using linear approximations to estimate the dispersion of non-linear functions of random variables. The paper also includes tables detailing the parameter information and simulation results for both cost functions, providing a comprehensive comparison between the linear approximations and the empirical distributions.