Both the theoretical and empirical literature on the estimation of allocative and technical inefficiency has grown enormously. To minimize aggregation bias, ideally one should estimate firm and input-specific parameters describing allocative inefficiency. However, identifying these parameters has often proven difficult. For a panel of Chilean hydroelectric power plants, we obtain a full set of such parameters using Gibbs sampling, which draws sequentially from conditional generalized method of moments (GMM) estimates obtained via instrumental variables estimation. We find an economically significant range of firm-specific efficiency estimates with differing degrees of precision. The standard GMM approach estimates virtually no allocative inefficiency for industry-wide parameters.