This paper examines the statistical properties of elasticities derived from translog and generalized Leontief cost functions. Itzhak Krinsky and A. Leslie Robb argue that linear approximations of elasticity formulas are not reliable for estimating the variance of elasticities, as they can significantly underestimate the true variability. Instead, they propose a simulation approach to estimate the empirical distributions of factor demand elasticities. The authors use a three-factor production process characterized by a cost function of the form K = g(Q, P₁, P₂, P₃), where K is total cost, Pᵢ is the price of the ith factor, and Q is output. They consider two functional forms: the translog (TL) cost function and the generalized Leontief (GL) cost function. For each, they derive the share equations and calculate the own and cross-price elasticities of factor demand. The authors simulate the distribution of elasticities by drawing random samples from a multivariate normal distribution with mean and variance-covariance matrix based on estimated parameters. They compare the results of this simulation with linear approximations of the variances. The simulation results show that the linear approximations significantly underestimate the true standard deviations of the elasticities, sometimes by as much as a thousand times. The authors also examine the normality of the simulated distributions. They find that the translog model's distributions are more normal than those of the GL model. They conclude that simulation methods are more reliable for estimating the statistical properties of elasticities than linear approximations, and recommend their use for more accurate statistical inference.This paper examines the statistical properties of elasticities derived from translog and generalized Leontief cost functions. Itzhak Krinsky and A. Leslie Robb argue that linear approximations of elasticity formulas are not reliable for estimating the variance of elasticities, as they can significantly underestimate the true variability. Instead, they propose a simulation approach to estimate the empirical distributions of factor demand elasticities. The authors use a three-factor production process characterized by a cost function of the form K = g(Q, P₁, P₂, P₃), where K is total cost, Pᵢ is the price of the ith factor, and Q is output. They consider two functional forms: the translog (TL) cost function and the generalized Leontief (GL) cost function. For each, they derive the share equations and calculate the own and cross-price elasticities of factor demand. The authors simulate the distribution of elasticities by drawing random samples from a multivariate normal distribution with mean and variance-covariance matrix based on estimated parameters. They compare the results of this simulation with linear approximations of the variances. The simulation results show that the linear approximations significantly underestimate the true standard deviations of the elasticities, sometimes by as much as a thousand times. The authors also examine the normality of the simulated distributions. They find that the translog model's distributions are more normal than those of the GL model. They conclude that simulation methods are more reliable for estimating the statistical properties of elasticities than linear approximations, and recommend their use for more accurate statistical inference.