Beyond a Linear Relationship: Revisiting Minority Representation Hypotheses with a Semiparametric Approach

Standard methods often overlook non-linear complexities in the relationship between minority population size and substantive representation. To address this, we introduce spline regression and shape-constrained inference to test four prominent representational hypotheses using U.S. House roll call data (2009–2023). We find that Black representation follows a concave trajectory, with gains plateauing after a 10% population threshold, whereas Latino population share exerts no statistically significant influence. Furthermore, Black representation reveals stark regional heterogeneity: the Non-South mirrors the national concave trend, the Rim South exhibits a discrete representational bonus upon reaching majority status, and the Deep South remains statistically unresponsive to population changes. Ultimately, this research demonstrates the efficacy of semiparametric approaches in uncovering the nuanced dynamics of minority representation.