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Author: Williams, Benjamin
Resulting in 2 citations.
1. Williams, Benjamin
Controlling for Ability Using Test Scores
Journal of Applied Econometrics published online (10 January 2019): DOI: 10.1002/jae.2683.
Also: https://onlinelibrary.wiley.com/doi/10.1002/jae.2683
Cohort(s): NLSY79
Publisher: Wiley Online
Keyword(s): Monte Carlo; Test Scores/Test theory/IRT

Permission to reprint the abstract has not been received from the publisher.

This paper proposes a semiparametric method to control for ability using standardized test scores, or other item response assessments, in a regression model. The proposed method is based on a model in which the parameter of interest is invariant to monotonic transformations of ability. I show that the estimator is consistent as both the number of observations and the number of items on the test grow to infinity. I also derive conditions under which this estimator is root‐n consistent and asymptotically normal. The proposed method is easy to implement, does not impose a parametric item response model, and does not require item level data. I demonstrate the finite sample performance in a Monte Carlo study and implement the procedure for a wage regression using data from the NLSY1979.
Bibliography Citation
Williams, Benjamin. "Controlling for Ability Using Test Scores." Journal of Applied Econometrics published online (10 January 2019): DOI: 10.1002/jae.2683.
2. Williams, Benjamin
Identification of a Nonseparable Model under Endogeneity Using Binary Proxies for Unobserved Heterogeneity
Quantitative Economics 10,2 (May 2019): 527-563.
Also: https://onlinelibrary.wiley.com/doi/10.3982/QE674
Cohort(s): NLSY79
Publisher: Wiley Online
Keyword(s): Armed Forces Qualifications Test (AFQT); Cognitive Ability; Educational Attainment; Heterogeneity; Modeling; Test Scores/Test theory/IRT

Permission to reprint the abstract has not been received from the publisher.

In this paper, I study identification of a nonseparable model with endogeneity arising due to unobserved heterogeneity. Identification relies on the availability of binary proxies that can be used to control for the unobserved heterogeneity. I show that the model is identified in the limit as the number of proxies increases. The argument does not require an instrumental variable that is excluded from the outcome equation nor does it require the support of the unobserved heterogeneity to be finite. I then propose a nonparametric estimator that is consistent as the number of proxies increases with the sample size. I also show that, for a fixed number of proxies, nontrivial bounds on objects of interest can be obtained. Finally, I study two real data applications that illustrate computation of the bounds and estimation with a large number of items.
Bibliography Citation
Williams, Benjamin. "Identification of a Nonseparable Model under Endogeneity Using Binary Proxies for Unobserved Heterogeneity." Quantitative Economics 10,2 (May 2019): 527-563.