Tough Shift: The Temporal Dynamics of Police Discretion

A central concern in studying state agents is how incentives and constraints shape effort. In shift work, fatigue typically reduces productivity as shifts progress. In policing, however, accounts propose the opposite: officers exploit discretion at shift end to generate overtime (“collars for dollars”). We test this claim using traffic enforcement, where officers exercise discretion but face clear opportunity costs near shift end. Leveraging five years of Phoenix Police traffic stop data (N=292,184; officers N=2,919) and officer fixed effects, we estimate the causal impact of shift timing on enforcement. Contrary to the overtime hypothesis, we find a 14.9% decline in stop frequency at shift end. We also document higher selectivity, consistent with declining capacity or motivation rather than overtime-seeking. These results introduce a temporal dimension to theories of discretion, refine principal–agent models of police behavior, and provide evidence of a systematic “discretion curve'' across shifts.