Some Interpretation of the Linear-in-Means Model of Social Interactions

Abstract

The linear-in-means model is often used in applied work to empirically study the role of social interaction 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 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.