Regressions with Test Scores as Covariates

Ben Williams, GWU


Responses to individual items from test scores, psychological assessments and survey questionnaires are often aggregated, and these “scores” are then included in regression analyses in order to control for a latent trait. This practice is econometrically sound if the number of items is large enough. A separate issue is that regression results are dependent on the scale of the test score. To address this problem I will describe a semiparametric method that is invariant to monotonic transformations of ability. I will present theoretical results and Monte Carlo simulations as guidance to how large is large enough for both standard regression results and the semiparametric regression estimator. I will also describe a simple nonparametric bias-corrected OLS estimator that reduces the bias substantially when the number of items is small. I will illustrate these results with wage regressions using data from the NLSY1979.