We provide a new method of identifying the level of relative bargaining power in bilateral negotiations using exogenous variation in the degree of conflict between parties. Using daily births data, we study negotiations over birth timing. In doing so, we exploit the fact that fewer children are born on the "inauspicious" dates of February 29 and April 1; most likely, we argue, reflecting parental preferences. When these inauspicious dates abut a weekend, this creates a potential conflict between avoiding the inauspicious date (the parents' likely preference), and avoiding the weekend (the doctor's likely preference). Using daily births data, we estimate how often this conflict is resolved in favor of the physician. We show how this provides an estimate of how bargaining power is distributed between patients and physicians.