The Marginal Coefficient: A New Approach for Identifying Observation Level Sensitivities

Many constructs of interest to accounting researchers relate to the sensitivity of one variable to another. Examples include the earnings response coefficient, earnings persistence, and earnings timeliness. These constructs are typically measured at the sample level using ordinary least squares (OLS). Because OLS quantifies sensitivity-based constructs at the sample level, it does not allow researchers to explore how variation in sensitivities within a sample affects economic outcomes of interest, which is a common research objective. Researchers have adopted a number of approaches to estimate observation level sensitivities. Each approach captures a portion of the total variation in sensitivities by capitalizing on one or more known sources of variation. We introduce an approach for estimating observation level sensitivities that reflects the variation from known sources captured by traditional approaches as well as the variation from unknown sources and randomness. This approach measures observation level sensitivities based on each observation’s contribution to the sample coefficient. Using the earnings response coefficient context, we show that sensitivity estimates based on our approach subsume and capture substantially more of the within-sample variation in sensitivities than those from existing approaches, are associated in predicted ways with previously documented determinants, and explain economic outcomes.