The sampling properties of the usual estimator of marginal product from a CobbDouglas production function are studied under the assumption of normally distributed errors. The asymptotic normality of these estimators is demonstrated and certain special cases are considered for which the asymptotic distribution is particularly simple. An alternative estimator of marginal product is suggested which has both a smaller bias and greater precision than the usual estimator. Estimators of the variance-covariance matrix of all marginal product estimators mentioned are given. These are accurate to order n-1. A GREAT deal of attention is given nowadays to the statistical properties of estimators of parameters in simultaneous equations models. By contrast, little attention is given to the statistical properties of estimators of parameters in simpler economic models. One such model that has been virtually ignored by statisticians is the Cobb-Douglas production function. The usefulness of this function in the cross section analysis of an industry should not be underrated although, as with all models, care must be taken to ensure that the data to which the function is fitted correspond reasonably well with the assumptions, both economic and statistical, implied by the function. The purpose of the present paper is to consider some of the statistical properties of estimators of marginal product obtained from a CobbDouglas function. Section 2 will discuss the estimator most frequently used (see, for example, Tintner and Brownlee [8] and Heady [4]). The third section will discuss alternative estimators which reduce bias to order n-2 where n is the size of sample. These alternative estimators may be useful when the sample size is small and the variability of observed production about the fitted Cobb-Douglas function is large. The fourth section considers the problem of estimating the variance matrices of the estimators discussed in Sections 2 and 3. A numerical illustration is given in Section 5.