Pathological Outcomes of Observational Learning

“Pathological Outcomes of Observational Learning”, Smith and Sorensen (Econometrica, 2000)

Informational herding may well be the most cited micro theory literature in the last thirty years. It explores how Bayes-rational individuals learn sequentially from the discrete actions of others. Ironically, hundreds or thousands of papers in this arena succumb to the problem they study. The literature started out with a bang — a claim based on a multinomial signal family that herding produces (1) cascades, (2) a positive probability of incomplete learning, and (3) an eventual “herd” of people copying one another. My early paper with Peter Sorensen proved that two these three conclusions were artifacts of the multinomial signal family. The generally true true results are actually more intriguing — for typical signal distributions, people generally never stop learning and yet herds arise — a perpetual string of identical actions. And when this signal family has unbounded likelihood ratios, learning is correct.

Unlike earlier informational herding papers, we also admit heterogeneous preferences. Not only may type-specific `herds’ eventually arise, but a new robust possibility emerges: confounded learning. Beliefs may converge to a limit point where history offers no decisive lessons for anyone, and each type’s actions forever nontrivially split between two actions.

To verify that our identified limit outcomes do arise, we exploit the Markov-martingale character of beliefs. Learning dynamics are stochastically stable near a fixed point in many Bayesian learning models like this one.

Dynamics of Social Learning

Dynamics of Social Learning