Controlling for ability using test scores

Benjamin Williams

Journal of Applied Econometrics, 2019, vol. 34, issue 4, 547-565

Abstract: 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.

Date: 2019
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