My research has been aimed at creating a tight connection between econometrics and economic theory, relaxing, at the same time, the parametric restrictions that one typically imposes when estimating a model. When doing applied work, one may decide to make parametric assumptions because of computational benefits, scarcity of data, or other important considerations. Analyzing what can be inferred when such assumptions are not in place allows one to learn what type of conclusions do not depend on such parametric specifications. A tight connection between econometrics and economic theory allows one to interpret estimates in terms of the elements of the model, and to evaluate counterfactuals under environments where some of the elements in the model do not change. It also allows one to determine whether observations are consistent with any particular model.