Identification and Estimation by Penalization in Nonparametric Instrumental Regression

Florens, Jean‐Pierre; Johannes, Jan; Bellegem, Sébastien Van

doi:10.1017/s026646661000037x

Cited by 54 publications

(42 citation statements)

References 20 publications

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“…Our paper also extends the work [1,2,6,7] by allowing for more general nonlinear unknown operator m, more flexible regularization and more general source condition. Finally, our results extend those of [8][9][10][11][12][13] from linear ill-posed inverse problems to nonlinear ill-posed inverse problems.…”

Section: Chen X and Pouzo Dsupporting

confidence: 78%

On nonlinear ill-posed inverse problems with applications to pricing of defaultable bonds and option pricing

Chen

Pouzo

2009

Sci. China Ser. A-Math.

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This paper considers the estimation of an unknown function h that can be characterized as a solution to a nonlinear operator equation mapping between two infinite dimensional Hilbert spaces. The nonlinear operator is unknown but can be consistently estimated, and its inverse is discontinuous, rendering the problem ill-posed. We establish the consistency for the class of estimators that are regularized using general lower semicompact penalty functions. We derive the optimal convergence rates of the estimators under the Hilbert scale norms. We apply our results to two important problems in economics and finance: (1) estimating the parameters of the pricing kernel of defaultable bonds; (2) recovering the volatility surface implied by option prices allowing for measurement error in the option prices and numerical error in the computation of the operator.

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Section: Chen X and Pouzo Dsupporting

confidence: 78%

On nonlinear ill-posed inverse problems with applications to pricing of defaultable bonds and option pricing

Chen

Pouzo

2009

Sci. China Ser. A-Math.

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“…This bound is a "source condition" under Assumption 3 b) and is similar to conditions used by Florens, Johannes and Van Bellegem (2010) and others. Under Assumption 3 a) it is similar to norms in generalized Hilbert scales, for example, see Engl, Hanke, and Neubauer (1996) and Chen and Reiß (2010).…”

Section: Local Identification In Hilbert Spacesmentioning

confidence: 66%

Local identification of nonparametric and semiparametric models

Chen¹,

Chernozhukov²,

Lee³

et al. 2011

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Abstract. In parametric models a sufficient condition for local identification is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We show that there are corresponding sufficient conditions for nonparametric models. A nonparametric rank condition and differentiability of the moment conditions with respect to a certain norm imply local identification. It turns out these conditions are slightly stronger than needed and are hard to check, so we provide weaker and more primitive conditions. We extend the results to semiparametric models. We illustrate the sufficient conditions with endogenous quantile and single index examples. We also consider a semiparametric habit-based, consumption capital asset pricing model. There we find the rank condition is implied by an integral equation of the second kind having a one-dimensional null space.JEL Classification: C12, C13, C23

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“…the Tikhonov regularization estimation approach in Hall and Horowitz (2005) and Darolles, Fan, Florens and Renault (2011). See also Carrasco, Florens and Renault (2006), Florens, Johannes and Van Bellegem (2011) and Gagliardini and Scaillet (2012) for further motivation. For a general estimation method in ill-posed problems with penalization see Chen and Pouzo (2012).…”

Section: Identificationmentioning

confidence: 99%

On the identification of structural linear functionals

Escanciano¹,

Li²

2013

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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 This paper asks which aspects of a structural Nonparametric Instrumental Variables Regression (NPIVR) can be identified well and which ones cannot. It contributes to answering this question by characterizing the identified set of linear continuous functionals of the NPIVR under norm constraints. Each element of the identified set of NPIVR can be written as the sum of a common "identifiable component" and an idiosyncratic "unidentifiable component". The identified set for any continuous linear functional is shown to be a closed interval, whose midpoint is the functional applied to the "identifiable component". The formula for the length of the identified set extends the popular omitted variables formula of classical linear regression. Some examples illustrate the wide applicability and utility of our identification result, including bounds and a new identification condition for point-evaluation functionals. The main ideas are illustrated with an empirical application of the effect of children on labor-market outcomes for women. Terms of use: Documents in

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Identification and Estimation by Penalization in Nonparametric Instrumental Regression

Cited by 54 publications

References 20 publications

On nonlinear ill-posed inverse problems with applications to pricing of defaultable bonds and option pricing

On nonlinear ill-posed inverse problems with applications to pricing of defaultable bonds and option pricing

Local identification of nonparametric and semiparametric models

On the identification of structural linear functionals

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