In this article, it is shown how the parameters of a transport model can be estimated in a way that, in contrast to previously used methods, utilizes observations of regional prices as well as of trade costs. The proposed method uses bi-level programming to minimize a weighted least squares' criterion under the restriction that the estimated parameters satisfy the Kuhn-Tucker conditions for an optimal solution of the transport model. We use Monte-Carlo simulations to trace out some properties of the estimator and compare it with a traditional calibration method. The analysis shows that the proposed technique estimates prices as well as trade costs more efficiently.