Scholars of bureaucratic politics have long posited that politicians face a trade-off between appointing competent bureaucrats and selecting politically loyal ones. However, measuring this purported trade-off presents significant challenges—does it genuinely exist, and, if so, how substantial is it? In this study, I leverage individual-level data on the careers of approximately 30,000 Chilean central government bureaucrats, encompassing all hires across nearly all ministries during a centre-left presidential administration. This dataset is combined with their university admission test scores and centre-left party membership status to provide a precise measurement of the trade-off. Using mixed models to account for agency heterogeneity, I find that in lower-qualification positions, party members and non-members exhibit similar test scores. However, in professional and managerial roles, a noticeable gap emerges: party members rank approximately five to nine percentiles lower in ability than non-members in equivalent positions within the bureaucratic hierarchy. Furthermore, I show that this preference for centre-left party members disappears under centre-right administrations. Importantly, the observed gap is not primarily driven by differences in professional qualifications between party members and non-members but persists within professions. These findings strengthen the interpretation that the results reflect a preference for hiring politically loyal bureaucrats. By examining politicians’ revealed preferences, this analysis quantifies the cognitive "shadow price" of political loyalty, providing a novel measure of the trade-off between competence and loyalty in bureaucratic hiring.