Introduction to the Special Issue on Inverse Problems in Econometrics

An inverse problem refers to the reconstruction of an object j ? typically a function ? from indirect noisy observations of it. Usually, one observes a noisy transformation of j through an operator. Solving an inverse problem consists in inverting such an operator, which may be challenging if the inverse problem is ill-posed. Ill-posed inverse problems arise in many applications in many fields. In structural econometrics, the importance of the theory of inverse problems has considerably increased over the last fifteen years. While some reference to such a theory was already previously present in econometrics, its intensive use starts much later, when econometricians recognized that the estimation of certain functional parameters in structural econometric models is an inverse problem. Since then, important contributions have been made which see the development and application of inverse problem techniques to econometric frameworks. As we explain below, the latter are different in many respects from classical frameworks of application of inverse problem techniques, as in medical image processing or quantum physics. References to the main contributions to inverse problems in econometrics can be found in the papers presented in this special issue.