controlling for ability using test scores (replication data)
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.