Set Identification, Moment Restrictions, and Inference

Abstract

For the last ten years, the topic of set identification has been much studied in the econometric literature. Classical inference methods have been generalized to the case in which moment inequalities and equalities define a set instead of a point. We review several instances of partial identification by focusing on examples in which the underlying economic restrictions are expressed as linear moments. This setting illustrates the fact that convex analysis helps not only in characterizing the identified set but also for inference. In this perspective, we review inference methods using convex analysis or inversion of tests and detail how geometric characterizations can be useful.

Entry games for the airline industry 1

“…Another solution consists in using the recent literature on moment inequalities and set identification (see Tamer, 2009 or Bontemps andMagnac, 2017, for a survey). It is out of the scope of this chapter to introduce formally this econometric solution but the general idea is to bound the probability of each outcome.…”

A geometric approach to inference in set-identified entry games

“…The support function provides a collection of moment inequalities, but these moment inequalities have a particular structure and are exploited differently than in the general moment inequality literature (see, in particular, the two surveys by Molchanov and Molinari (2015) and Bontemps and Magnac (2017)).…”

Partial Identification of Economic Mobility: With an Application to the United States

“…Understanding mobility patterns in the US is important as there is convincing evidence that income inequality has been increasing in the US. 4 However, the welfare impact of this rise depends crucially on the level of economic mobility. Shorrocks (1978Shorrocks ( , p. 1013 argues that "evidence on inequality of incomes or wealth cannot be satisfactorily evaluated without knowing, for example, how many of the less a-uent will move up the distribution later in life.…”

“…Available at http://faculty.smu.edu/millimet/code.html 4. The level of income inequality in the US has followed a U-shaped pattern over the past century(Picketty and Saez 2003; Kopczuk et al 2010; Atkinson and Bourguignon 2015).…”