Instrumental Variable Treatment of Nonclassical Measurement Error Models

Hu, Yingyao; Schennach, Susanne M.

doi:10.1111/j.0012-9682.2008.00823.x

Cited by 315 publications

(415 citation statements)

References 44 publications

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“…Drawing on the analyses of Schennach (2004a) and Hu and Schennach (2008), we establish identification of the technology of skill formation. We relax the strong independence assumptions for error terms in the measurement equations that are maintained in Cunha and Heckman (2008) and Carneiro, Hansen, and Heckman (2003).…”

Section: Introductionmentioning

confidence: 99%

Estimating the technology of cognitive and noncognitive skill formation

Cunha¹,

Heckman²,

Schennach³

2010

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527

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This paper formulates and estimates multistage production functions for child cognitive and noncognitive skills. Output is determined by parental environments and investments at different stages of childhood. We estimate the elasticity of substitution between investments in one period and stocks of skills in that period to assess the benefits of early investment in children compared to later remediation. We establish nonparametric identification of a general class of nonlinear factor models. A by-product of our approach is a framework for evaluating childhood interventions that does not rely on arbitrarily scaled test scores as outputs and recognizes the differential effects of skills in different tasks. Using the estimated technology, we determine optimal targeting of interventions to children with different parental and personal birth endowments. Substitutability decreases in later stages of the life cycle for the production of cognitive skills. It increases in later stages of the life cycle for the production of noncognitive skills. This finding has important implications for the design 10 To focus on the main contribution of this paper, we focus on investment in children. Thus we assume that θ T+1 is the adult stock of skills for the rest of life contrary to the evidence reported in Borghans, Duckworth, Heckman, and ter Weel (2008). The technology could be extended to accommodate adult investment as in Ben-Porath (1967) or its generalization (Heckman, Lochner, and Taber, 1998). 12 This formulation assumes that measurements a ∈ {1, 2, 3} proxy only one factor. Carneiro, Hansen, and Heckman (2003) consider alternative specifications, but in a much less general econometric model. The key idea in all factor approaches is one normalization of the factor loading for each factor in one measurement to set the scale of the factor and some measurements for each measurement of type a dedicated to each factor. It is clear that even within the framework of this paper, as long as some of each of the measurements of type a satisfy the assumptions in this paper, one can identify the factor loadings of the remaining measurements that do not satisfy the assumptions if, for example, the factors are mutually independent. 22 See the Web Appendix for a more detailed derivation of the likelihood function and filtering equations (see Web Appendix Section 3 and Web Appendix Section 6.4). Section 6.4 presents the full model with heterogeneity and investment equations.

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Section: Introductionmentioning

confidence: 99%

Estimating the technology of cognitive and noncognitive skill formation

Cunha¹,

Heckman²,

Schennach³

2010

Self Cite

527

992

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“…Theorem 1 in Hu and Schennach (2008) then allows us to conclude that the joint distribution of (h(X * ), X, Y, Z) is identified. However, in order to identify the distribution of (X * , X, Y, Z), we need to identify h(·).…”

Section: Appendix: Proofsmentioning

confidence: 95%

“…Let variables from Hu and Schennach (2008) be denoted by the corresponding uppercase letter with tildes and make the following assignments: (X * ,X,Ỹ ,Z) = (h(X * ), Z, Y, X). We now verify the 5 assumptions of Theorem 1 in Hu and Schennach (2008).…”

Section: Appendix: Proofsmentioning

confidence: 99%

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Regressions with Berkson errors in covariates - a nonparametric approach

Schennach¹

2013

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This paper establishes that so-called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with Berkson-type measurement error in the regressors. An estimator is proposed and proven to be consistent. Its practical performance and feasibility are investigated via Monte Carlo simulations as well as through an epidemiological application investigating the effect of particulate air pollution on respiratory health. These examples illustrate that Berkson errors can clearly not be neglected in nonlinear regression models and that the proposed method represents an effective remedy.

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“…While the above treatment covers proxies for instruments whose measurement errors satisfy conditional mean or independence assumptions, more general proxies contaminated by either "nonclassical"or "Berkson-type" 3 measurement errors could be treated by adapting the techniques of Hu and Schennach (2008) or Schennach (2007), respectively.…”

Section: Asymptotics: Pxi Casementioning

confidence: 99%

Local indirect least squares and average marginal effects in nonseparable structural systems

Schennach

White

Chalak

2012

Journal of Econometrics

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We study the scope of local indirect least squares (LILS) methods for nonparametrically estimating average marginal e¤ects of an endogenous cause X on a response Y in triangular structural systems that need not exhibit linearity, separability, or monotonicity in scalar unobservables. One main …nding is negative: in the fully nonseparable case, LILS methods cannot recover the average marginal e¤ect. LILS methods can nevertheless test the hypothesis of no e¤ect in the general nonseparable case. We provide new nonparametric asymptotic theory, treating both the traditional case of observed exogenous instruments Z and the case where one observes only error-laden proxies for Z. Acknowledgement 0.1 We thank Stefan Hoderlein, Xun Lu, Andres Santos, and Suyong Song for helpful comments and suggestions. Any errors are the authors' responsibility. S. M. Schennach acknowledges support from the National Science Foundation via grants SES-0452089 and SES-0752699. This is a revised version of a paper titled "Estimating Average Marginal E¤ ects in Nonseparable Structural Systems." JEL Classi…cation Numbers: C13, C14, C31.

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Instrumental Variable Treatment of Nonclassical Measurement Error Models

Cited by 315 publications

References 44 publications

Estimating the technology of cognitive and noncognitive skill formation

Estimating the technology of cognitive and noncognitive skill formation

Regressions with Berkson errors in covariates - a nonparametric approach

Local indirect least squares and average marginal effects in nonseparable structural systems

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