Production functions that take into account uncertainty can be empirically estimated by taking a state contingent view of the world. Where there is no a priori information to allocate data amongst a small number of states, the estimation may be carried out with finite mixtures model. The complexity of the estimation almost guarantees a large number of local maxima for the likelihood function. However, it is shown, with examples, that a variation on the traditional method of finding starting values substantially improves the estimation results. One of the major benefits of the proposed method is the reliable estimation of a decision maker's ability to substitute output between states, justifying a preference for the state contingent approach over the use of a stochastic production function.