  In the classical herding literature, agents receive a private signal
regarding a binary state of nature, and sequentially choose an action, after
observing the actions of their predecessors. When the informativeness of
private signals is unbounded, it is known that agents converge to the correct
action and correct belief. We study how quickly convergence occurs, and show
that it happens more slowly than it does when agents observe signals. However,
we also show that the speed of learning from actions can be arbitrarily close
to the speed of learning from signals. In particular, the expected time until
the agents stop taking the wrong action can be either finite or infinite,
depending on the private signal distribution. In the canonical case of Gaussian
private signals we calculate the speed of convergence precisely, and show
explicitly that, in this case, learning from actions is significantly slower
than learning from signals.
