Estimating outlier-robust regression models is challenging because model specification and outlier definition are interdependent, yet empirical research typically treat them separately. We propose a framework that jointly aligns a well-defined research question with appropriate model specification and robust estimation. Reexamining the relationship between CEO equity incentives and innovation, we show that conventional least-squares estimates produce unstable results: vega effects vary with functional forms, while delta effects are highly sensitive to influential observations. Our framework reconciles these inconsistencies, producing consistently positive and significant vega effects alongside generally insignificant delta effects, thereby highlighting the importance of a holistic approach.
Ho et al. (2026) studied this question.