Controlling for ability using test scores
提出一种半参数方法，利用标准化考试成绩控制能力，在回归中估计参数，无需参数化项目反应模型或项目级数据，适用于工资回归等实证研究。
Summary 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.