I know science people use this a lot.
Do we economists care about it at all? If so, which one should be looked at? The one used by elsevier makes on sense.
One major problem with impact factors is that they can be (and are) manipulated. Quite a few journals will request or even demand that one cite papers pubbed in the journal in order to be pubbed. IF does not correct for self-citations or citations in the same journal. Commercial publishers encourage this as they base their subscription fees partly on the IF.
The most extreme case of such manipulation was Chaos, Solitons, and Fractals, pubbed by Elsevier, where only recently the founding editor, Mohammed El-Naschie, was finally forced out due to pressure from physicists (led by Joan Baez's cousin, John). El-Naschie pubbed over 250 papers by himself in his own journal, with later ones massively citing earlier ones. He had five of his own papers in one issue. While this is obviously an off-the-wall extreme case, milder versions of this are going on all the time, so one must take IF's with large grains of salt, although one rarely sees a journal be highly ranked by any measure that has a very low IF, say < .20.