Who is the Key Player? A Network Analysis of Juvenile Delinquency

This article presents a methodology for empirically identifying the key player, whose removal from the network leads to the optimal change in aggregate activity level in equilibrium [Ballester, C., Calvo-Armengol, A., and Zenou, Y. (2006), "Who's Who in Networks. Wanted: The Key Player," Econometrica, 74: 1403-1417], allowing the network links to rewire after the removal of the key player. First, we propose an IV-based estimation strategy for the social-interaction effect, which is needed to determine the equilibrium activity level of a network, taking into account the potential network endogeneity. Next, to simulate the network evolution process after the removal of the key player, we adopt the general network formation model in Mele [(2017), "A Structural Model of Dense Network Formation," Econometrica, 85: 825-850] and extend it to incorporate the unobserved individual heterogeneity in link formation decisions. We illustrate the methodology by providing the key player rankings in juvenile delinquency using information on friendship networks among U.S. teenagers. We find that the key player is not necessarily the most active delinquent or the delinquent who ranks the highest in standard (not microfounded) centrality measures. We also find that, compared to a policy that removes the most active delinquent from the network, a key-player-targeted policy leads to a much higher delinquency reduction.