What about local agriculture? If you ship your food for free, won't that hurt their economy?

We are in constant communication with our partners on the ground regarding just such an issue. It doesn't do good for us to go into a situation where we're causing harm. Our NGOs will tell us that their region is suffering a drought and the crops have been destroyed, and what little food they do have available is too expensive for the local people. If there is a viable agricultural commodity in an area, the situation wouldn't be desperate enough for an appeal from an NGO, and we take steps to determine the actual need.