Susanne M. Schennach

Estimating the Technology of Cognitive and Noncognitive Skill Formation.

This paper formulates and estimates multistage production functions for childrens cognitive and noncognitive skills. Skills are 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 production technologies based on nonlinear factor models with endogenous inputs. A by-product of our approach is a framework for evaluating childhood and schooling interventions that does not rely on arbitrarily scaled test scores as outputs and recognizes the differential effects of the same bundle 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 in the production of cognitive skills. It increases slightly in later stages of the life cycle in the production of noncognitive skills. This finding has important implications for the design of policies that target the disadvantaged. For some configurations of disadvantage and for some outcomes, it is optimal to invest relatively more in the later stages of childhood than in earlier stages.

Point estimation with exponentially tilted empirical likelihood

Parameters defined via general estimating equations (GEE) can be estimated by maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72 (2004) 219--255] have recently shown that this EL estimator exhibits desirable higher-order asymptotic properties, namely, that its

Nonparametric Regression In The Presence Of Measurement Error

O(n^{-1})

Quantile Regression With Mismeasured Covariates

bias is small and that bias-corrected EL is higher-order efficient. Although EL possesses these properties when the model is correctly specified, this paper shows that, in the presence of model misspecification, EL may cease to be root n convergent when the functions defining the moment conditions are unbounded (even when their expectations are bounded). In contrast, the related exponential tilting (ET) estimator avoids this problem. This paper shows that the ET and EL estimators can be naturally combined to yield an estimator called exponentially tilted empirical likelihood (ETEL) exhibiting the same

Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information

O(n^{-1})

Regressions with Berkson errors in covariates - a nonparametric approach

bias and the same

Entropic Latent Variable Integration via Simulation

O(n^{-2})

Estimating nonseparable models with mismeasured endogenous variables

variance as EL, while maintaining root n convergence under model misspecification.

Estimating the Technology of Cognitive and Noncognitive Skill Formation

We introduce a nonparametric regression estimator that is consistent in the presence of measurement error in the explanatory variable when one repeated observation of the mismeasured regressor is available. The approach taken relies on a useful property of the Fourier transform, namely, its ability to convert complicated integral equations into simple algebraic equations. The proposed estimator is shown to be asymptotically normal, and its rate of convergence in probability is derived as a function of the smoothness of the densities and conditional expectations involved. The resulting rates are often comparable to kernel deconvolution estimators, which provide consistent estimation under the much stronger assumption that the density of the measurement error is known. The finite-sample properties of the estimator are investigated through Monte Carlo experiments.This work was made possible in part through financial support from the National Science Foundation via grant SES-0214068. The author is grateful to the referees and the co-editor for their helpful comments.

The Economics of Pollution Permit Banking in the Context of Title IV of the 1990 Clean Air Act Amendments

This paper establishes that the availability of instrumental variables enables the identification and the consistent estimation of nonparametric quantile regression models in the presence of measurement error in the regressors. The proposed estimator takes the form of a nonlinear functional of derivatives of conditional expectations and is shown to provide estimated quantile functions that are uniformly consistent over a compact set.