Microeconometrics with Partial Identi?cation

This chapter reviews the microeconometrics literature on partial identi?cation, focusing on the developments of the last thirty years. The topics presented illustrate that the available data combined with credible maintained assumptions may yield much information about a parameter of interest, even if they do not reveal it exactly. Special attention is devoted to discussing the challenges associated with, and some of the solutions put forward to, (1) obtain a tractable characterization of the values for the parameters of interest which are observationally equivalent, given the available data and maintained assumptions; (2) estimate this set of values; (3) conduct test of hypotheses and make con?dence statements. The chapter reviews advances in partial identi?cation analysis both as applied to learning (functionals of) probability distributions that are well-de?ned in the absence of models, as well as to learning parameters that are well-de?ned only in the context of particular models. A simple organizing principle is highlighted: the source of the identi?cation problem can often be traced to a collection of random variables that are consistent with the available data and maintained assumptions. This collection may be part of the observed data or be a model implication. In either case, it can be formalized as a random set. Random set theory is then used as a mathematical framework to unify a number of special results and produce a general methodology to carry out partial identi?cation analysis.