Semiparametric estimation of binary response models with endogenous regressors

Rothe, Christoph

doi:10.1016/j.jeconom.2009.04.005

Cited by 58 publications

(48 citation statements)

References 43 publications

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“…To illustrate this idea in a general setting, suppose that the estimator used to generate the covariates satisfies the following asymptotically linear representation, which is similar to conditions used e.g. in Rothe (2009) or Ichimura and Lee (2010). The assumption can be shown to be satisfied for a wide range of nonparametric, semiparametric, and fully parametric estimation procedures (we also discuss two representative examples below).…”

Section: Application To Semiparametric Estimationmentioning

confidence: 99%

“…Rothe, 2009). Suppose again that the function r 0 is a nonparametric regression function that satisfies D = r 0 (X r ) + ζ with E(ζ|X r ) = 0 and E(ζ 2 |X r ) < ∞.…”

Section: The Asymptotic Variance and The Bootstrapmentioning

confidence: 99%

“…See their references for a list of examples, and Andrews (1995), Song (2008) and Sperlich (2009) for related results. Examples of semiparametric applications with generated covariates include Olley and Pakes (1996), Heckman, Ichimura, and Todd (1998), Li and Wooldridge (2002), Levinsohn and Petrin (2003), Blundell and Powell (2004), Linton, Sperlich, and Van Keilegom (2008), Rothe (2009), Escanciano, Jacho-Chávez, and Lewbel (2012) and Caetano, Rothe, and Yildiz (2014), among many others. Song (2013) studies a class of semiparametric models with generated covariates that have a single-index structure, and shows that adaptive estimation is possible in such models under weak conditions (see also Song (2012)).…”

Section: Introductionmentioning

confidence: 99%

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Semiparametric Estimation With Generated Covariates

2015

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We study a general class of semiparametric estimators when the infinite-dimensional nuisance parameters include a conditional expectation function that has been estimated nonparametrically using generated covariates. Such estimators are used frequently to e.g. estimate nonlinear models with endogenous covariates when identification is achieved using control variable techniques. We study the asymptotic properties of estimators in this class, which is a non-standard problem due to the presence of generated covariates. We give conditions under which estimators are root-n consistent and asymptotically normal, derive a general formula for the asymptotic variance, and show how to establish validity of the bootstrap.JEL Classification: C14, C31

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Section: Application To Semiparametric Estimationmentioning

confidence: 99%

“…Rothe, 2009). Suppose again that the function r 0 is a nonparametric regression function that satisfies D = r 0 (X r ) + ζ with E(ζ|X r ) = 0 and E(ζ 2 |X r ) < ∞.…”

Section: The Asymptotic Variance and The Bootstrapmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Semiparametric Estimation With Generated Covariates

2015

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“…, θ J ,∆ n could be the first order conditions for a semiparametric weighted least squares estimator of index parameters as in Ichimura and Lee (1991) or when J = 1,∆ n could be the first order conditions for semiparametric weighted least squares or maximum likelihood estimators as those in Ichimura (1993) and Klein and Spady (1993), respectively. Similarly, if X := (X ⊤ 1 , X ⊤ 2 , Z ⊤ 1 , Z ⊤ 2 ) ⊤ and W (X) = (Z ⊤ 1 θ 1 + X ⊤ 2 θ 2 , X 2 − g(Z 1 , Z 2 )), then∆ n could be the first order conditions for semiparametric weighted least squares or maximum likelihood estimators that uses 'control function' approaches as in Escanciano, Jacho-Chávez and Lewbel (2011) and Rothe (2009) respectively. Alternatively, if W (X) = X 1 ⊂ X,∆ n also has the form of test statistics designed to test nonparametrically the significance of a subset of covariates as in Delgado and González Manteiga (2001).…”

Section: And If E[y |X] Fulfills the Index Condition E[y |X] = E[y |Wmentioning

confidence: 99%

Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing

Escanciano

Jacho-Chávez

Lewbel

2014

Journal of Econometrics

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A new uniform expansion is introduced for sums of weighted kernel-based regression residuals from nonparametric or semiparametric models. This result is useful for deriving asymptotic properties of semiparametric estimators and test statistics with data-dependent bandwidth, random trimming, and estimated weights. An extension allows for generated regressors, without requiring the calculation of functional derivatives. Example applications are provided for a binary choice model with selection, including a new semiparametric maximum likelihood estimator, and a new directional test for correct specification of the average structural function. An extended Appendix contains general results on uniform rates for kernel estimators, additional applications, and primitive sufficient conditions for high level assumptions.

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“…Blundell and Powell (2004) and Rothe (2009) applied the control variable approach to semiparametric binary response models. Lee (2007) set forth an estimation strategy using a control variable approach for a triangular system of equations for conditional quantiles with an additive nonparametric first stage.…”

Section: Introductionmentioning

confidence: 99%

Quantile regression with censoring and endogeneity

Fernández‐Val¹,

Chernozhukov²,

Kowalski³

2011

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Abstract. In this paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are nonadditive in the unobservables. The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity. For computation, we extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the estimation of the control variable. We give generic regularity conditions for asymptotic normality of the CQIV estimator and for the validity of resampling methods to approximate its asymptotic distribution. We verify these conditions for quantile and distribution regression estimation of the control variable. Our analysis covers two-stage (uncensored) quantile regression with nonadditive first stage as an important special case. We illustrate the computation and applicability of the CQIV estimator with a Monte-Carlo numerical example and an empirical application on estimation of Engel curves for alcohol.Date: March 17, 2014. We thank Denis Chetverikov and Sukjin Han for excellent comments and capable research assistance. We are grateful to Richard Blundell for providing us the data for the empirical application. We thank the editor Cheng Hsiao, two referees, and seminar participants at EIEF, Georgetown, Rochester, and Penn State for useful comments. We gratefully acknowledge research support from the NSF.

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Semiparametric estimation of binary response models with endogenous regressors

Cited by 58 publications

References 43 publications

Semiparametric Estimation With Generated Covariates

Semiparametric Estimation With Generated Covariates

Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing

Quantile regression with censoring and endogeneity

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