Peering into the mist: social learning over an opaque observation network

I present a model of social learning over an exogenous, directed network that may be readily nested within broader macroeconomic models with dispersed information and combines the attributes that agents (a) act repeatedly and simultaneously; (b) are Bayes-rational; and (c) have strategic interaction in their decision rules. To overcome the challenges imposed by these requirements, I suppose that the network is opaque: agents do not know the full structure of the network, but do know the link distribution. I derive a specific law of motion for the hierarchy of aggregate expectations, which includes a role for network shocks (weighted sums of agents' idiosyncratic shocks). The network causes agents' beliefs to exhibit increased persistence, so that average expectations overshoot the truth following an aggregate shock. When the network is sufficiently (and plausibly) irregular, transitory idiosyncratic shocks cause persistent aggregate effects, even when agents are identically sized and do not trade.