We study the behavior of batching by discretionary workers in the first stage of a two-stage queuing system and explore the trade-off it causes between their productivity and second stage wait times. Specifically, we focus on the behavior of batching admissions by emergency department (ED) physicians. Using data from a large hospital, we show that the probability of batching admissions is increasing in the hour of an ED physician's shift, and that batched patients experience a 4.7% longer delay from hospital admission to receiving an inpatient bed. Using a mediation analysis, we show that this effect is partially due to the increase in the coefficient of variation of inpatient bed requests caused by batching. However, we also find that batching admissions is associated with an average of 10.0% more patients seen in a shift, and a 2.6 minute reduction in a physician's average throughput time. An important implication of our work is that workers may induce delays in downstream stages, caused by practices that increase their productivity.