Inference on parameter sets in econometric models

Victor Chernozhukov

This paper provides confidence regions for minima of an econometric criterion function Q([theta]). The minima form a set of parameters, [theta]I, called the identified set. In economic applications, [theta]I represents a class of economic models that are consistent with the data. Our inference procedures are criterion function based and so our confidence regions, which cover [theta]I with a prespecified probability, are appropriate level sets of Qn([theta]), the sample analog of Q([theta]). When [theta]I is a singleton, our confidence sets reduce to the conventional confidence regions based on inverting the likelihood or other criterion functions. We show that our procedure is valid under general yet simple conditions, and we provide feasible resampling procedure for implementing the approach in practice. We then show that these general conditions hold in a wide class of parametric...