In this paper we consider the specification and estimation of the Cobb-Douglas production function model. After reviewing the "traditional" specifying assumptions for the model which are based on deterministic profit maximization, we develop a model in which profits are stochastic and in which maximization of the mathematical expectation of profits is posited. "Sampling theory" and Bayesian estimation techniques for this model are presented.
Dreze, J., Kmenta, J., & Zellner, A. (1966). Specification and estimation of Cobb-Douglas production function models. Econometrica, 34(4), 784-795. https://hdl.handle.net/2078.5/77064 (Original work published 1966)