Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure

Berry, Steven; Haile, Philip A.

doi:10.2139/ssrn.2630221

Cited by 9 publications

(20 citation statements)

References 26 publications

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“…INTRODUCTION THE NOTATION AND MAINTAINED HYPOTHESES (Assumption 1) of the model are as given in Berry and Haile (2018). Here we demonstrate that, if Y is the pre-image under r of any bounded open connected subset of R J , log densities satisfying the requirements of Corollary 2 in Berry and Haile (2018) form a dense open subset of all log densities on R J that are twice continuously differentiable and possess a local maximum. This is true even when instruments vary only over an arbitrarily small open ball.…”

mentioning

confidence: 61%

“…We prove Lemma 10 by constructing an arbitrarily small perturbation of 7 Although we focus on genericity of the conditions required by Berry and Haile's (2018, Corollary 2), Lemmas 10 and 12 below imply that F M is a dense open subset of F (see Corollary 1 in Berry and Haile (2018)). 8 Such w f must exist since around any local max is an open ball on which ln f (u * ) is (at least weakly) maximal.…”

Section: Then We Havementioning

confidence: 99%

“…The proof of Lemma 5 in Berry and Haile (2018) showed that, for some compact set Σ with nonempty interior, there exists c such that (i) the upper contour set A(c Σ) = {u ∈ Σ : ln f (u) ≥ c} lies in the interior of Σ and (ii) the restriction of ln f to A(c Σ) attains a maximumc = ln f (u * ) > c at its unique critical point. Let…”

Section: S22 Openmentioning

confidence: 99%

“…Given any open set S ⊂ R J that is bounded and connected, let Y S denote the pre-image of S under r. Because r is continuous, Y S is open; and because r has continuous inverse (see the proof of Lemma 1 in Berry and Haile (2018)), Y S is connected. Boundedness of S and G implies that there is a finite set Z S ⊂ Z J such that…”

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confidence: 99%

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Identification of Nonparametric Simultaneous Equations Models With a Residual Index Structure

Berry¹,

Haile²

2018

Econometrica

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Berry and Haile (2018) considered identification in a class of nonparametric simultaneous equations models, providing several combinations of sufficient conditions on the joint density of structural errors and the support of instruments. We show here that, even when the instruments vary only over a small open ball, the requirements on the joint density may be viewed as mild in at least one formal sense.

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mentioning

confidence: 61%

Section: Then We Havementioning

confidence: 99%

Section: S22 Openmentioning

confidence: 99%

mentioning

confidence: 99%

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Identification of Nonparametric Simultaneous Equations Models With a Residual Index Structure

Berry¹,

Haile²

2018

Econometrica

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“…One is the vector (β it , α it ) of random coefficients on x jt and p jt . These random coefficients allow heterogeneity in preferences that can explain why consumers tend to substitute 1 We will also make some use of a recent literature on the identification of simultaneous equations, as represented by Matzkin (2008), Matzkin (2015) and Berry & Haile (2015).…”

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confidence: 99%

Identification in differentiated product markets

Berry¹,

Haile²

2015

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract Empirical models of demand for-and, often, supply of-differentiated products are widely used in practice, typically employing parametric functional forms and distributions of consumer heterogeneity. We review some recent work studying identification in a broad class of such models. This work shows that parametric functional forms and distributional assumptions are not essential for identification. Rather, identification relies primarily on the standard requirement that instruments be available for the endogenous variables-here, typically, prices and quantities. We discuss the kinds of instruments needed for identification and how the reliance on instruments can be reduced by nonparametric functional form restrictions or better data. We also discuss results on discrimination between alternative models of oligopoly competition. Terms of use: Documents in EconStor may

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Generalized instrumental variable models, methods, and applications

Chesher

Rosen

2020

Handbook of Econometrics

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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.

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Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure

Cited by 9 publications

References 26 publications

Identification of Nonparametric Simultaneous Equations Models With a Residual Index Structure

Identification of Nonparametric Simultaneous Equations Models With a Residual Index Structure

Identification in differentiated product markets

Generalized instrumental variable models, methods, and applications

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