Cost function estimation under production uncertainty is problematic because the relevant cost is conditional on unobservable expected output. If input demand functions are also stochastic, then a nonlinear errors-in-variables model is obtained and standard estimation procedures typically fail to attain consistency. But by exploiting the full implications of the expected profit maximization hypothesis that gives rise to ex ante cost functions, it is shown that the errors-in-variables problem can be effectively removed, and consistent estimation of the parameters of interest can be achieved. A Monte Carlo experiment illustrates the advantages of the proposed procedure as well as the pitfalls of other existing estimators.