Inference for identifiable parameters in partially identified econometric models

Romano, Joseph P.; Shaikh, Azeem M.

doi:10.1016/j.jspi.2008.03.015

Cited by 218 publications

(321 citation statements)

References 21 publications

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“…3 Two papers in the literature of partially identified models touch upon the idea of profiling without using the term: Romano and Shaikh (2008) and Santos (2012). The former proposes a sub-sampling-based confidence set for a point-identified profile of the parameters under high-level conditions, while we design a bootstrap-based confidence set for a potentially partially-identified profile of the model parameter under low-level conditions.…”

Section: Introductionmentioning

confidence: 99%

Estimating demand for differentiated products with error in market shares

Gandhi¹,

Lu²,

Shi³

2013

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In this paper we introduce a new approach to estimating differentiated product demand system that allows for error in market shares as measures of choice probabilities. In particular, our approach allows for products with zero sales in the data, which is a frequent phenomenon that arises in product differentiated markets but lies outside the scope of existing demand estimation techniques. Although we find that error in market shares generally undermine the standard point identification of discrete choice models of demand, we exploit shape restrictions on demand implied by discrete choice to generate a system of moment inequalities that partially identify demand parameters. These moment inequalities are fully robust to the variability in market shares yet are also adaptive to the information revealed by market shares in a way that allows for informative inferences. In addition, we construct a profiling approach for parameter inference with moment inequalities, making it feasible to study models with a large number of parameters (as typically required in demand applications) by focusing attention on a profile of the parameters, such as the price coefficient. We use our approach to study consumer demand from scanner data using the Dominick's Finer Foods database, and find that even for the baseline logit model, demand elasticities nearly double when the full error in market shares is taken into account.

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Section: Introductionmentioning

confidence: 99%

Estimating demand for differentiated products with error in market shares

Gandhi¹,

Lu²,

Shi³

2013

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“…In both cases, Chernozhukov, Hong and Tamer (2007) use a criterion approach for the definition of the identified set and subsampling techniques for estimation and inference (see also Romano and Shaikh, 2008). In the moment inequality set-up, Rosen (2008) develops simple testing pro-cedures and Bugni (2010) and Canay (2010) investigate the properties of canonical bootstrap and modifications of it.…”

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confidence: 99%

Set identified linear models

Bontemps¹,

Magnac²,

Maurin³

2011

139

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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. Terms of use: Documents in AbstractWe analyze the identification and estimation of parameters β satisfying the incomplete linear moment restrictions E(z (xβ − y)) = E(z u(z)) where z is a set of instruments and u(z) an unknown bounded scalar function. We first provide empirically relevant examples of such a set-up. Second, we show that these conditions set identify β where the identified set B is bounded and convex. We provide a sharp characterization of the identified set not only when the number of moment conditions is equal to the number of parameters of interest but also in the case in which the number of conditions is strictly larger than the number of parameters. We derive a necessary and sufficient condition of the validity of supernumerary restrictions which generalizes the familiar Sargan condition. Third, we provide new results on the asymptotics of analog estimates constructed from the identification results. When B is a strictly convex set, we also construct a test of the null hypothesis, β 0 ∈ B, whose size is asymptotically correct and which relies on the minimization of the support function of the set B − {β 0 } . Results of some Monte Carlo experiments are presented.

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“…When covariates are discrete, the number of inequality restrictions that define the identified set are finite, and potentially applicable methods include those of Andrews and Soares (2007), Beresteanu and Molinari (2008), Bugni (2007), Canay (2007), CHT, Galichon and Henry (2009), Romano and Shaikh (2008), and Rosen (2008). When the covariates are continuous, the restrictions defining the identified set embody uncountably many conditional inequality restrictions.…”

Section: Specifically For Each Pair Smentioning

confidence: 99%

Set identification via quantile restrictions in short panels

Rosen¹

2009

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This paper studies the identifying power of conditional quantile restrictions in short panels with fixed effects. In contrast to classical fixed effects models with conditional mean restrictions, conditional quantile restrictions are not preserved by taking differences in the regression equation over time. This paper shows however that a conditional quantile restriction, in conjunction with a weak conditional independence restriction, provides bounds on quantiles of differences in time-varying unobservables across periods. These bounds carry observable implications for model parameters which generally result in set identification. The analysis of these bounds includes conditions for point identification of the parameter vector, as well as weaker conditions that result in identification of individual parameter components.

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Inference for identifiable parameters in partially identified econometric models

Cited by 218 publications

References 21 publications

Estimating demand for differentiated products with error in market shares

Estimating demand for differentiated products with error in market shares

Set identified linear models

Set identification via quantile restrictions in short panels

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