Instrumental variables estimators typically must satisfy monotonicity conditions to be interpretable as capturing local average treatment effects. Building on previous research that suggests monotonicity is unlikely to hold in the context of school entrance age effects, we develop an approach for identifying the magnitude of the resulting bias. We also assess the impact on monotonicity bias of bandwidth selection in regression discontinuity (RD) designs, finding that "full sample" instrumental variables estimators may outperform RD in many cases. We argue that our approaches are applicable more broadly to numerous settings in which monotonicity is likely to fail.