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At its heart, social learning asks how effective people can be at pooling their individual information. The question is most interesting — and most realistic — when there are constraints on learning from

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others. One such constraint, which inspired the herding literature, is that sometimes people may observe others’ choices but not the beliefs that led to them. Another constraint, which is the focus of this paper, is that people may see a summary of others’ choices, such as aggregate sales data, or a statistic on the news. A summary such as this will often do a poor job of summarizing the information content of others’ choices. The data that an observer would need to form a better summary is not just the individual choices, but also their context: when each choice was made, which prior choices it relied on, and so forth. We show that when people learn from summaries of past actions, they cannot correct for a type of echo chamber effect (recent actions rely on older ones) that tends to give the earliest actions too much influence. This inertia can slow learning down so much that, for practical purposes, it is effectively incomplete. The inertial effect of old actions grows more pernicious in a changing world (the moving target model), but it can also become beneficial (e.g., with heterogeneous tastes, or a self reliance bias) when a decisionmaker wishes her samplees had paidmore heed to the past.

Our model can also be applied if people observe others’ actions individually but treat them equally in forming a mental summary statistic. Equal treatment might arise because contextual information is missing (as we suggest in our sample average model). Another rationale, not pursued in this paper, is that people have clues about context but either underestimate the need to correct for correlation among the actions they sample orfind it too difficult. In this case, forming a sample average could be a cognitively simple rule of thumb.

For savvy learners with partial context on the choices they see, the first order correction would be to try to discount older choices, since their information is likely to be redundant. In this sense, a higher (exogenous) frequency of sampling recent versus old choices in our model could be interpreted as a proxy for better information about context. As expected, social learning is faster when people are able to collect observations with less redundancy. However, this reduced-form interpretation is not a substitute for an explicit model of inference from partially ordered data. Further work along these lines appears challenging, but would be welcome.48

Poor information about the dependencies among people’s choices is a problem for applied mi- croeconomists as well as for the people they study. Certain aspects of our model (sequences of cohorts of agents, normally distributed errors) bear a loose similarity to simple econometric models of repeated cross-section data. While our model is not ready to estimate, it suggests a tractable way to build modest assumptions about what people know into structural empirical models of social learning.

Our analysis relies heavily on the tractability of continuous actions paired with normal errors. Developing a similar model with discrete actions, such as the binary action models that have been a workhorse of the herding literature, would seem to require substantially different methods. That

4 8_{One intermediate approach, developed in an earlier version of this paper, is to retain the observation of a sample}

average but to allow the agent to choose the composition of this sample (within certain constraints). This structure is motivated by a screening story: for example our sprinter from the introduction might be able to screen older blogs out of her sample based on hairstyles or dated pop culture references, just as she might be able to avoid blogs that are more focused on distance running. One can show that agents generally prefer to screen for recent actions, but if the screening technology is imperfect, the slow learning results in the paper still apply.

said, there is no obvious reason why the factors that contribute to fast or slow learning in our model would not play a roughly similar role if actions were discrete. Other adaptations are more direct. For example, in our model, an agent’s action is his (posterior) point estimate of the unknown parameter. Thus, it could be recast as a model of learning from others’ beliefs rather than from their actions without changing the mathematics.49 Opportunities to observe summary statistics about other people’s beliefs — in the form of prediction markets, online product ratings, and so forth — have proliferated of late, and learning from the “wisdom of crowds” has seized the imagination of the popular press.50 However, crowds and markets can also make mistakes and propagate stale information.51 _{Our model provides a framework for thinking about how the wisdom of crowds may} sometimes be underwhelming due to the inertia of early mistakes.