How does informational heterogeneity affect the quality of forecasts?

We investigate a toy model of inductive interacting agents aiming to forecast a continuous, exogenous random variable E. Private information on E is spread heterogeneously across agents. Herding turns out to be the preferred forecasting mechanism when heterogeneity is maximal. However in such conditions aggregating information efficiently is hard even in the presence of learning, as the herding ratio rises significantly above the efficient market expectation of 1 and remarkably close to the empirically observed values. We also study how different parameters (interaction range, learning rate, cost of information and score memory) may affect this scenario and improve efficiency in the hard phase.