Reciprocity in a social network: evidence from a natural field experiment

I use a natural field experiment to test for the presence of reciprocity in the context of a social network. Over the course of a year, I randomly sent birthday greetings to the online friends of a Facebook user. I find that sending a birthday greeting to a Facebook friend causes an increase of 50 percent in the probability that the friend will reciprocate when the birthday of the sender arrives. I also find that the tendency to reciprocate is decreasing in time. The likelihood that a birthday congratulation will be reciprocated increases by almost three times as much when the birthday of the sender is one month away than when it is six months away.