Estimating parameters of constrained optimization models in a consistent way requires a different set of methods than is available in a typical econometric toolkit. We identify three complications likely to arise in this context, and suggest solutions to those complications: (i) the bi-level programming character, (ii) ill-posedness, and (iii) derivation of estimator properties. The solutions suggested involve a combination of numerical techniques and utilization of out-of-sample information via Bayesian techniques. The proposed framework is also suitable for typical empirical problems arising in trade analysis such as the estimation of trade equilibrium models and data balancing exercises.