Assuming morale has not been diminished, members of a project that is perceived as slightly behind schedule will tend to work hard at catching up, thus increasing productivity. Similarly, members of a project that is perceived as slightly ahead of schedule often take vacation days, work less hours, read their email longer, and ease up in other ways, thus decreasing productivity. In other words, the cost estimation itself will affect the project outcome. Any specific project may expend less resources if it is slightly underestimated than if it is slightly overestimated.
Be careful, though! If project members believe that the schedule is ridiculously underestimated or that estimates are underestimated on purpose, then morale and productivity will decrease. Worse still, you, as a manager, might start to gain a reputation of being incompetent, manipulative, or both. If that happens then project members will begin to perceive all estimates, even good ones, as bad.
As long as a minor underestimate is a natural occurrence then there is no need to worry that it'll effect the schedule. Team productivity has a certain amount of flexibility to compensate as long as there are minor overestimates to balance things out.
Reference:
Abdel-Hamid, T., and Madnick, S., "Impact on Schedule Estimation on Software Project Behavior," IEEE Software, July 1986.
