  Agents learn about a changing state using private signals and their
neighbors' past estimates of the state. We present a model in which Bayesian
agents in equilibrium use neighbors' estimates simply by taking weighted sums
with time-invariant weights. The dynamics thus parallel those of the tractable
DeGroot model of learning in networks, but arise as an equilibrium outcome
rather than a behavioral assumption. We examine whether information aggregation
is nearly optimal as neighborhoods grow large. A key condition for this is
signal diversity: each individual's neighbors have private signals that not
only contain independent information, but also have sufficiently different
distributions. Without signal diversity $\unicode{x2013}$ e.g., if private
signals are i.i.d. $\unicode{x2013}$ learning is suboptimal in all networks and
highly inefficient in some. Turning to social influence, we find it is much
more sensitive to one's signal quality than to one's number of neighbors, in
contrast to standard models with exogenous updating rules.
