Transformation-Induced Bias: Unbiased Coefficients Do Not Imply Unbiased Quantities of Interest

Abstract

Political scientists commonly focus on quantities of interest computed from model coefficients rather than on the coefficients themselves. However, the quantities of interest, such as predicted probabilities, first differences, and marginal effects, do not necessarily inherit the small-sample properties of the coefficient estimates. Indeed, unbiased coefficient estimates are neither necessary nor sufficient for unbiased estimates of the quantities of interest. I characterize this transformation-induced bias, calculate an approximation, illustrate its importance with two simulation studies, and discuss its relevance to methodological research.