Asymptotic Properties for a Class of Partially Identified Models

Beresteanu, Arie; Molinari, Francesca

doi:10.2139/ssrn.956084

Cited by 107 publications

(202 citation statements)

References 66 publications

(58 reference statements)

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“…6 Inference is more challenging than estimation as the current literature is inconclusive about the type of con dence interval that should be used in a partial identi cation analysis. There are a number of papers that propose con dence intervals that cover the identi ed set (interval between upper and lower bound) with a xed probability (for example Chernozhukov et al (2007) and Beresteanu and Molinari (2008)). Imbens and Manski (2004) propose a con dence interval which does not cover the identi ed set with xed probability but rather the parameter of interest is covered with xed probability.…”

Section: Miv-boundsmentioning

confidence: 99%

The Effect of Parents’ Schooling on Child’s Schooling: A Nonparametric Bounds Analysis

Haan

2011

Journal of Labor Economics

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The effect of parents' schooling on child's schooling: a nonparametric bounds analysis de Haan, M. Link to publication Citation for published version (APA):de Haan, M. (2010). The effect of parents' schooling on child's schooling: a nonparametric bounds analysis. Amsterdam: Amsterdam School of Economics. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Download date: 10 May 2018The e ect of parents' schooling on child's schooling:A nonparametric bounds analysis Monique de Haan * Abstract A strong positive relation between parents' schooling and child's schooling does not necessarily re ect a causal relation. The recent empirical literature has used di erent approaches to identify intergenerational schooling e ects and produces contradictory ndings. This paper uses a new approach to investigate the e ect of parents' schooling on child's schooling: a nonparametric bounds analysis. By relying on a set of relatively weak and in part testable assumptions, this paper obtains informative bounds on the average causal impact of mother's and father's schooling on the schooling of their child. The tightest bounds, which are obtained using monotone instrumental variables, show that increasing mother's or father's schooling to a college degree has a positive e ect on child's schooling which is signi cantly di erent from zero, but substantially lower than the OLS estimates.

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Section: Miv-boundsmentioning

confidence: 99%

The Effect of Parents’ Schooling on Child’s Schooling: A Nonparametric Bounds Analysis

Haan

2011

Journal of Labor Economics

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“…Both of them are mainly focused on statistical inference. One is given by the work of Beresteanu andMolinari (2006, 2008). They study a class of partially identified models in which the sharp identification region of the parameter vector of interest can be written as a transformation of the Aumann expectation of a properly defined random set.…”

Section: Overviewmentioning

confidence: 99%

“…They then define the notion of "core determining" classes of sets, to find a manageable class of sets for which to check that the dominance condition is satisfied. 6 In order to establish sharpness of the identification region of the parameters of a best linear predictor with interval outcome data, Beresteanu andMolinari (2006, 2008) use the same result involving the capacity functional of a random set due to Artstein (1983) that we use in this paper.…”

Section: Overviewmentioning

confidence: 99%

Sharp identification regions in games

Beresteanu¹,

Molchanov²,

Molinari³

2008

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We study identification in static, simultaneous move finite games of complete information, where the presence of multiple Nash equilibria may lead to partial identification of the model parameters. The identification regions for these parameters proposed in the related literature are known not to be sharp. Using the theory of random sets, we show that the sharp identification region can be obtained as the set of minimizers of the distance from the conditional distribution of game's outcomes given covariates, to the conditional Aumann expectation given covariates of a properly defined random set. This is the random set of probability distributions over action profiles given profit shifters implied by mixed strategy Nash equilibria. The sharp identification region can be approximated arbitrarily accurately through a finite number of moment inequalities based on the support function of the conditional Aumann expectation. When only pure strategy Nash equilibria are played, the sharp identification region is exactly determined by a finite number of moment inequalities. We discuss how our results can be extended to other solution concepts, such as for example correlated equilibrium or rationality and rationalizability.We show that calculating the sharp identification region using our characterization is computationally feasible. We also provide a simple algorithm which finds the set of inequalities that need to be checked in order to insure sharpness. We use examples analyzed in the literature to illustrate the gains in identification afforded by our method.

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“…However, there is one precedent to the use of the Aumann expectation as a key tool to describe fundamental features of partially identi…ed models. This is the work of Molinari (2006, 2008), who were the …rst to illustrate the bene…ts of using elements of random sets theory to conduct identi…cation analysis and statistical inference for incomplete econometric models in the space of sets, in a manner which is the exact analog of how these tasks are commonly performed for point identi…ed models in the space of vectors.…”

Section: Introductionmentioning

confidence: 99%

“…They then de…ne the notion of "core determining"classes of sets, to …nd a manageable class of sets for which to check that the dominance condition is satis…ed. Beresteanu and Molinari (2006) use Artstein's (1983 result to establish sharpness of the identi…cation region of the parameters of a best linear predictor with interval outcome data.…”

Section: Introductionmentioning

confidence: 99%

Sharp identification regions in models with convex moment predictions

Beresteanu¹,

Molchanov²,

Molinari³

2010

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We provide a tractable characterization of the sharp identi…cation region of the parameters in a broad class of incomplete econometric models. Models in this class have set valued predictions that yield a convex set of conditional or unconditional moments for the observable model variables. In short, we call these models with convex moment predictions. Examples include static, simultaneous move …nite games of complete and incomplete information in the presence of multiple equilibria; best linear predictors with interval outcome and covariate data; and random utility models of multinomial choice in the presence of interval regressors data. Given a candidate value for ; we establish that the convex set of moments yielded by the model predictions can be represented as the Aumann expectation of a properly de…ned random set. The sharp identi…cation region of ; denoted I ; can then be obtained as the set of minimizers of the distance from a properly speci…ed vector of moments of random variables to this Aumann expectation. Algorithms in convex programming can be exploited to e¢ ciently verify whether a candidate is in I : We use examples analyzed in the literature to illustrate the gains in identi…cation and computational tractability a¤orded by our method.

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Asymptotic Properties for a Class of Partially Identified Models

Cited by 107 publications

References 66 publications

The Effect of Parents’ Schooling on Child’s Schooling: A Nonparametric Bounds Analysis

The Effect of Parents’ Schooling on Child’s Schooling: A Nonparametric Bounds Analysis

Sharp identification regions in games

Sharp identification regions in models with convex moment predictions

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