A Spectral Method for Deconvolving a Density

Carrasco, Marine; Florens, Jean‐Pierre

doi:10.1017/s026646661000040x

Cited by 52 publications

(55 citation statements)

References 45 publications

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“…See, for example, Proposition 8 of Carrasco and Florens (2011). By similar reasoning, the adjoint operator C * of C is injective as well.…”

Section: B1 Identificationmentioning

confidence: 79%

Identification and estimation of nonparametric panel data regressions with measurement error

Wilhelm¹

2015

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This paper provides a constructive argument for identification of nonparametric panel data models with measurement error in a continuous explanatory variable. The approach point identifies all structural elements of the model using only observations of the outcome and the mismeasured explanatory variable; no further external variables such as instruments are required. In the case of two time periods, restricting either the structural or the measurement error to be independent over time allows past explanatory variables or outcomes to serve as instruments. Time periods have to be linked through serial dependence in the latent explanatory variable, but the transition process is left nonparametric. The paper discusses the general identification result in the context of a nonlinear panel data regression model with additively separable fixed effects. It provides a nonparametric plug-in estimator, derives its uniform rate of convergence, and presents simulation evidence for good performance in finite samples. * First version: January 31, 2011. I am particularly indebted to Susanne Schennach, Chris Hansen, Alan Bester, and Azeem Shaikh, and thank them for their advice, encouragement and comments. I also thank Stephane Bonhomme, Federico Bugni, Jean-Marie Dufour, Kirill Evdokimov, Jean-Pierre Florens, Xavier D'Haultfoeuille, James Heckman, Roger Koenker, Arthur Lewbel, Elie Tamer and participants of various conferences and seminars for helpful discussions. Remaining errors are my own. I gratefully acknowledge financial support from the ESRC Centre for Microdata Methods and Practice at IFS (ES/I0334021/1).

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“…See, for example, Proposition 8 of Carrasco and Florens (2011). By similar reasoning, the adjoint operator C * of C is injective as well.…”

Section: B1 Identificationmentioning

confidence: 79%

Identification and estimation of nonparametric panel data regressions with measurement error

Wilhelm¹

2015

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“…A similar formula has been derived by Carrasco and Florens (2005) for the density deconvolution problem. Such a characterization is new in the nonparametric IV regression setting.…”

Section: Mean Integrated Square Errormentioning

confidence: 77%

“…A similar heuristic approach has been successfully applied in Carrasco and Florens (2005) for density deconvolution. Theoretical properties of such a selection procedure are still unknown, and beyond the scope of this paper.…”

Section: An Empirical Examplementioning

confidence: 99%

Tikhonov regularization for nonparametric instrumental variable estimators

Gagliardini

Scaillet

2012

Journal of Econometrics

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We study a Tikhonov Regularized (TiR) estimator of a functional parameter identi…ed by conditional moment restrictions in a linear model with both exogenous and endogenous regressors. The nonparametric instrumental variable estimator is based on a minimum distance principle with penalization by the norms of the parameter and its derivative. After showing its consistency in the Sobolev norm we derive the expression of the asymptotic Mean Integrated Square Error. The convergence rate with optimal value of the regularization parameter is characterized in two examples. We illustrate our theoretical …ndings and the small sample properties with simulation results. Finally, we provide an empirical application to estimation of an Engel curve, and discuss a data driven selection procedure for the regularization parameter.

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“…Devroye, 1989, Carrasco andFlorens, 2010). This condition can be satisfied by various distributions including the Type-I extreme value distribution and normal distribution.…”

Section: Bundle Choice (Example 2)mentioning

confidence: 97%

“…They use tensor products of integral transforms to study nonparametric identification of random coefficient densities. Using their framework, one may show that 14) where…”

Section: Alternative Specific Coefficientsmentioning

confidence: 99%

Nonparametric identification of random coefficients in endogenous and heterogeneous aggregate demand models

Dunker¹,

Hoderlein²,

Kaido³

2017

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This paper studies nonparametric identification in market level demand models for differentiated products with heterogeneous consumers. We consider a general class of models that allows for the individual specific coefficients to vary continuously across the population and give conditions under which the density of these coefficients, and hence also functionals such as welfare measures, is identified. Building on earlier work by Berry and Haile (2013), we show that key identifying restrictions are provided by (i) a set of moment conditions generated by instrumental variables together with an inversion of aggregate demand in unobserved product characteristics; and (ii) the variation of the product characteristics across markets that is exogenous to the individual heterogeneity.We further show that two leading models, the BLP-model (Berry, Levinsohn, and Pakes, 1995) and the pure characteristics model , require considerably different conditions on the support of the product characteristics.

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A Spectral Method for Deconvolving a Density

Cited by 52 publications

References 45 publications

Identification and estimation of nonparametric panel data regressions with measurement error

Identification and estimation of nonparametric panel data regressions with measurement error

Tikhonov regularization for nonparametric instrumental variable estimators

Nonparametric identification of random coefficients in endogenous and heterogeneous aggregate demand models

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