user_name, there's actually quite a bit of literature trying to estimate discount rates (recently, hyperbolic discounting has been a big area of research; you might see work by Laibson, Caplin and Leahy, or McCrary). You're right that it's imposible to "know" someone's discount factor, but you can certainly back it out of behavior, given standard assumptions about utility functions and rationality. To parameterize simple models, people often assume b is about 0.95, though of course it's important to do sensitivity analysis around that estimate.
In (graduate level and research) economics, the standard way to express a stream of consumption is U(c(t))+bU(c(t+1))+b^2U(c(t+2))... Since this board is about graduate economics, I think it's a reasonable framework to use
