Instrumental Variables Estimation

Rather than considering possible pairings of observations (as in Section 1.4), an alternative method could be proposed, following Bramoulle et al. (2009), which takes individuals as separate observations and asks whether players are influenced by those with whom they shared a table, by taking the mean of all the weights chosen by these ‘table contacts’, and including this average as a regressor.

It would be necessary in this case to use an instrumental variables (IV) specification as opposed to ordinary least squares, because if it was assumed that participants allocated to the same table during the ACP were influenced by one-another, then it would be possible that the player in question also influenced the responses of each of his neighbors, meaning that their average response would be subject to reverse causality.

works. ‘Correlated’ effects refer to the case where players who are directly linked in a network are more likely to behave in similar ways. Aside from this effect, it is also possi- ble to distinguish between ‘exogenous’ effects, where the characteristics of each player have an effect on the behavior of those other players to whom the player is directly linked, and ‘endogenous’ effects, where the behavior of each player has an influence on those around them.

While correlated effects can be ruled out in this case, thanks to the randomized nature of the ACP seating assignment, Manski (1993) highlighted potential problems in distin- guishing between the exogenous and endogenous effects. Bramoulle et al. (2009) showed, however, that in the absence of correlation effects, it is possible to separately identify the exogenous and endogenous effects by using an instrumental variables approach under certain conditions on the network. One such condition is that the network contains ‘in- transitive triads’. The presence of an intransitive triad implies that you can find a playeri, who is linked to another playerj, who in turn is linked to some other playerk, but where no direct link exists between players iand k. In such cases, any influence between players iand k must come through their mutual links with playerj. This makes it possible to use the characteristics of player k as instruments for the actions of player j in explaining the behavior of player i.

One potential advantage of such an IV specification over the dyadic models reported in Section 1.4 is that the direction of causality is explicitly accounted for. This method therefore identifies the effect of a one-point increase in the average weight assigned to a criterion among those players with whom each player shared a table on their own weighting choice. This could be considered more interpretable than the effect on a pairing that is reported in dyadic regressions. Furthermore, in this case, the weights associated with each criterion are treated in separate regressions. This offers the prospect of a more detailed breakdown of which criteria could be driving the results from the dyadic regressions, where the dependent variable was calculated by aggregating across all 11 criteria.

A key requirement for using this estimation procedure, however, is that in such a model the characteristics of players with whom any player inever shared a table (playerk in the illustration above) must have a strong enough impact on the behavior of player j to be

considered a valid instrument. In this experiment, this is not found to be the case, so the results are merely summarized here for the sake of brevity.

Table 1.5 in the Appendix shows the results of IV regressions of the form described above, where the characteristics used to instrument the endogenous regressor (the average weighting choice among each player’s direct table contacts) are the gender, age and edu- cation status of those players who could have influenced the player in question via some intransitive triad. Coefficients are generally found to be positive, which could be inter- preted as suggesting that if a player shares tables with other participants who on average assign a higher weight to the criterion under consideration, then that player too will assign a higher weight on average to the same criterion. In most cases, however, results are found to be insignificant at the 5% level. More importantly, as alluded to above, theF-statistics associated with the first-stage regressions range from 0.322 to 3.943, which suggests that using intransitive triads in this way does not provide instruments with a sufficient influence over the weighting choices of other players to provide meaningful estimates.

It is possible to conduct similar regressions, with the inclusion of additional controls for ‘cultural variables’ (as were used in Tucker and Gastil (2013)) and political leaning (both self-reported and inferred from other survey questions). While the coefficients associated with the average weighting choice of neighbors are generally positive, which would support the findings of the dyadic regressions reported in Section 1.4, these results are generally not found to be statistically significant and are again based on instruments that are found to be too weak to provide meaningful results. Detailed tables reporting these findings are therefore omitted from this chapter.