Regressions with Test Scores as Covariates

Ben Williams, GWU

Abstract:

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.