Sharp identified sets for discrete variable IV models

Chesher, Andrew; Smolinski, Konrad

doi:10.1920/wp.cem.2010.1110

Cited by 7 publications

(6 citation statements)

References 19 publications

(19 reference statements)

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“…5 In particular, we show that the AS model is pointidentified when available entry variation is continuous, but only partially identified when such variation is discrete. This result parallels the typical finding that discrete regressors induce partial identification in nonparametric regression contexts; see, for example, Chesher (2005), Magnac and Maurin (2008), and Chesher and Smolinski (2010), among others. Among studies which consider partial identification in auctions specifically, our work is most similar in spirit to Haile and Tamer (2003), who relaxed assumptions on bidding behavior to obtain bounds on model fundamentals and counterfactual revenue in ascending auctions, and Tang (2011), who provided bounds on counterfactual revenue in auctions with affiliated values.…”

Section: Introductionsupporting

confidence: 85%

“…3 Note that while we derive sharp identified sets for AS fundamentals, we do not develop asymptotic distribution theory for these sets. In this respect, we follow prior studies such as Manski and Tamer (2002), Athey and Haile (2002), Haile and Tamer (2003), Chesher (2005), Berry andHaile (2010, 2012), Chesher and Smolinski (2010), and Chesher and Rosen (2013), among others. 4 To our knowledge, the only other study touching on nonparametric identification in the AS model is that of Marmer, Shneyerov, and Xu (2013), who proposed nonparametric specification tests for the S, LS, and AS models.…”

Section: Introductionmentioning

confidence: 99%

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Identification in Auctions With Selective Entry

2014

Econometrica

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This paper considers nonparametric identification of a two-stage entry and bidding model for auctions which we call the Affiliated-Signal (AS) model. This model assumes that potential bidders have private values, observe imperfect signals of their true values prior to entry, and choose whether to undertake a costly entry process. The AS model is a theoretically appealing candidate for the structural analysis of auctions with entry: it accommodates a wide range of entry processes, in particular nesting the Levin and Smith (1994) and Samuelson (1985) models as special cases. To date, however, the model's identification properties have not been well understood. We establish identification results for the general AS model, using variation in factors affecting entry behavior (such as potential competition or entry costs) to construct identified bounds on model fundamentals. If available entry variation is continuous, the AS model may be point identified; otherwise, it will be partially identified. We derive constructive identification results in both cases, which can readily be refined to produce the sharp identified set. We also consider policy analysis in environments where only partial identification is possible, and derive identified bounds on expected seller revenue corresponding to a wide range of counterfactual policies while accounting for endogenous and arbitrarily selective entry. Finally, we establish that our core results extend to environments with asymmetric bidders and nonseperable auction-level unobserved heterogeneity. * We are grateful to Co-Editor, Jean-Marc Robin, and three anonymous referees for their constructive comments that have greatly improved the paper. We also thank Yanqin Fan, Jeremy Fox, James Heckman, and participants in seminars at

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Section: Introductionsupporting

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Identification in Auctions With Selective Entry

2014

Econometrica

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“…when Y is a count or discrete response variable. The first two results were obtained in Chernozhukov and Hansen (2005), and the third result is in the spirit of results given in Chesher, Rosen, and Smolinski (2011);Chesher (2005); and Chesher and Smolinski (2010). The latter results are related to random set/optimal transport methods for identification analysis; see Beresteanu, Molchanov, and Molinari (2011);Ekeland, Galichon, and Henry (2010); Galichon and Henry (2009);and Galichon and Henry (2011).…”

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confidence: 67%

Quantile models with endogeneity

Chernozhukov¹,

Hansen²

2013

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Abstract. In this article, we review quantile models with endogeneity. We focus on models that achieve identification through the use of instrumental variables and discuss conditions under which partial and point identification are obtained. We discuss key conditions, which include monotonicity and full-rank-type conditions, in detail. In providing this review, we update the identification results of Chernozhukov and Hansen (2005). We illustrate the modeling assumptions through economically motivated examples. We also briefly review the literature on estimation and inference.

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“…There are antecedents to our work that partially identify quantities of interest in other models of discrete choice. Chesher (2010) and Chesher and Smolinski (2010) study ordered discrete outcome models with endogeneity. In this paper, we focus on choices from unordered sets of alternatives.…”

Section: Related Resultsmentioning

confidence: 99%

An instrumental variable model of multiple discrete choice

Chesher¹,

Rosen²,

Smolinski³

2013

Quantitative Economics

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This paper studies identification in multiple discrete choice models in which there may be endogenous explanatory variables, that is, explanatory variables that are not restricted to be distributed independently of the unobserved determinants of latent utilities. The model does not employ large support, special regressor, or control function restrictions; indeed, it is silent about the process that delivers values of endogenous explanatory variables, and in this respect it is incomplete. Instead, the model employs instrumental variable restrictions that require the existence of instrumental variables that are excluded from latent utilities and distributed independently of the unobserved components of utilities. We show that the model delivers set identification of latent utility functions and the distribution of unobserved heterogeneity, and we characterize sharp bounds on these objects. We develop easy‐to‐compute outer regions that, in parametric models, require little more calculation than what is involved in a conventional maximum likelihood analysis. The results are illustrated using a model that is essentially the conditional logit model of 41, but with potentially endogenous explanatory variables and instrumental variable restrictions. The method employed has wide applicability and for the first time brings instrumental variable methods to bear on structural models in which there are multiple unobservables in a structural equation.

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Sharp identified sets for discrete variable IV models

Cited by 7 publications

References 19 publications

Identification in Auctions With Selective Entry

Identification in Auctions With Selective Entry

Quantile models with endogeneity

An instrumental variable model of multiple discrete choice

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