Identification in econometric models maps prior assumptions and the data to information about a parameter of interest. The partial identification approach to inference recognizes that this process should not result in a binary answer that consists of whether the parameter is point identified. Rather, given the data, the partial identification approach characterizes the informational content of various assumptions by providing a menu of estimates, each based on different sets of assumptions, some of which are plausible and some of which are not. Of course, more assumptions beget more information, so stronger conclusions can be made at the expense of more assumptions. The partial identification approach advocates a more fluid view of identification and hence provides the empirical researcher with methods to help study the spectrum of information that we can harness about a parameter of interest using a menu of assumptions. This approach links conclusions drawn from various empirical models to sets of assumptions made in a transparent way. It allows researchers to examine the informational content of their assumptions and their impacts on the inferences made. Naturally, with finite sample sizes, this approach leads to statistical complications, as one needs to deal with characterizing sampling uncertainty in models that do not point identify a parameter. Therefore, new methods for inference are developed. These methods construct confidence sets for partially identified parameters, and confidence regions for sets of parameters, or identifiable sets.
