Empirical models with social interactions or peer effects allow the out- come of an individual to depend on the outcomes, choices, treatments, and/or characteristics of the other individuals in the group. We document the subtle re- lationship between the data and the objects of interest in models with interactions in small groups, and show that some econometric assumptions, that are direct ex- tensions from models of individualistic treatment response, implicitly entail strong behavioral assumptions. We point out two such econometric assumptions, EITR, or empirical individual treatment response, and EGTR, or empirical group treatment response. In some cases EITR and/or EGTR are inconsistent with a class of plau- sible economic models for the interaction under consideration; in other cases these econometric assumptions imply significant assumptions on behavior that are not necessarily implied by economic theory. We illustrate this using relevant examples of interaction in immunization and disease, and in educational achievement. We conclude that it is important for applications in this class of models with small group interactions to recognize the restrictions some assumptions impose on behav- ior.

kt2-october2012.pdfThe linear-in-means model is often used in applied work to empirically study the role of social interactions and peer effects. We document the subtle relationship between the parameters of the linear-in-means model and the parameters relevant for policy analysis, and study the interpretations of the model under two different scenarios. First, we show that without further assumptions on the model the direct analogs of standard policy relevant parameters are either undefined or are complicated functions not only of the parameters of the linear-in-means model but also the parameters of the distribution of the unobservables. This complicates the interpretation of the results. Second, and as in the literature on simultaneous equations, we show that it is possible to interpret the parameters of the linear-in-means model under additional assumptions on the social interaction, mainly that this interaction is a result of a particular {\it economic game}. These assumptions that the game is built on rule out economically relevant models. We illustrate this using examples of social interactions in educational achievement. We conclude that care should be taken when estimating and especially when interpreting coefficients from linear in means models.

kt2-june16lim.pdfIdentification in econometric models maps prior assumptions and the data to information about a parameter of interest. The partial identification approach to inference recognizes that this process should not result in a binary answer that consists of whether the parameter is point identified. Rather, given the data, the partial identification approach characterizes the informational content of various assumptions by providing a menu of estimates, each based on different sets of assumptions, some of which are plausible and some of which are not. Of course, more assumptions beget more information, so stronger conclusions can be made at the expense of more assumptions. The partial identification approach advocates a more fluid view of identification and hence provides the empirical researcher with methods to help study the spectrum of information that we can harness about a parameter of interest using a menu of assumptions. This approach links conclusions drawn from various empirical models to sets of assumptions made in a transparent way. It allows researchers to examine the informational content of their assumptions and their impacts on the inferences made. Naturally, with finite sample sizes, this approach leads to statistical complications, as one needs to deal with characterizing sampling uncertainty in models that do not point identify a parameter. Therefore, new methods for inference are developed. These methods construct confidence sets for partially identified parameters, and confidence regions for sets of parameters, or identifiable sets.

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