Generalized instrumental variable models, methods, and applications

Abstract

This chapter sets out the extension of the scope of the classical IV model to cases in which unobserved variables are set-valued functions of observed variables. The resulting Generalized IV (GIV) models can be used when outcomes are discrete while unobserved variables are continuous, when there are rich speci…cations of heterogeneity as in random coe¢ cient models, and when there are inequality restrictions constraining observed outcomes and unobserved variables. There are many other applications and classical IV models arise as a special case. The chapter provides characterizations of the identi…ed sets delivered by GIV models. It gives details of the application of GIV analysis to models with an interval censored endogenous variable and to binary outcome models-for example probit models-with endogenous explanatory variables. It illustrates how the identi…ed sets delivered by GIV models can be represented by moment inequality characterizations that have been the focus of recently developed methods for inference. An empirical application to a binary outcome model of female labor force participation is worked through in detail.

Econometrics with Partial Identification

“…In particular, as I show throughout the chapter, the methods allow for simple and tractable characterizations of sharp identification regions. The collection of these results establishes that indeed this is a useful tool to carry out econometrics with partial identification, as exemplified by its prominent role both in this chapter and in Chapter XXX in this Volume by Chesher and Rosen (2019), which focuses on general classes of instrumental variable models. The random sets approach complements the more traditional one, based on mathematical tools for (single valued) random vectors, that proved extremely productive since the beginning of the research program in partial identification.…”

“…Key Insight 3.2: The preceding discussion allows me to draw a novel connection between the two characterizations in Manski and Tamer (2002), and the distinction put forward by Chesher and Rosen (2017b) and Chesher and Rosen (2019, Chapter XXX in (3.5). This notion of potential observational equivalence parallels one of the notions used to obtain sufficient conditions for point identification in the semiparametric literature (as in, e.g.…”

“…Later sections in this chapter illustrate how Theorem A.1 delivers the sharp identification region in other more complex instances of partial identification of probability distributions, as well as in structural models. In Chapter XXX in this Volume, Chesher and Rosen (2019) apply Theorem A.1 to obtain sharp identification regions for functionals of interest in the important class of generalized instrumental variable models.…”

“…Haile and Tamer's 2003 bounds exploit the information contained in the marginal distributions G i:n for each i and n. However, in Identification Problem 3.8 additional information can be extracted from the joint distribution of ordered bids Chesher and Rosen (2017b). obtain the sharp identification region H P [Q] using random set methods(Artstein's characterization in Theorem A.1) applied to a quantile function representation of the order statistics.…”

Estimating Endogenous Effects on Ordinal Outcomes

“…The single equation IV model is incomplete because it does not uniquely pin down the value of all endogenous variables as a function of exogenous observed and unobserved variables. Such models are generally partially identifying, and results from Chesher and Rosen (2017) are applied to characterize the resulting identified sets.…”