Discussion paper

DP15505 Binary Outcomes and Linear Interactions

Heckman and MaCurdy (1985) first showed that binary outcomes are compatible with linear econometric
models of interactions. This key insight was unduly discarded by the literature on the econometrics of games.
We consider general models of linear interactions in binary outcomes that nest linear models of peer effects in
networks and linear models of entry games. We characterize when these models are well defined. Errors must
have a specific discrete structure. We then analyze the models’ game-theoretic microfoundations. Under
complete information and linear utilities, we characterize the preference shocks under which the linear model
of interactions forms a Nash equilibrium of the game. Under incomplete information and independence, we
show that the linear model of interactions forms a Bayes-Nash equilibrium if and only if preference shocks
are iid and uniformly distributed. We also obtain conditions for uniqueness. Finally, we propose two simple
consistent estimators. We revisit the empirical analyses of teenage smoking and peer effects of Lee, Li, and
Lin (2014) and of entry into airline markets of Ciliberto and Tamer (2009). Our reanalyses showcase the
main interests of the linear framework and suggest that the estimations in these two studies suffer from
endogeneity problems.


Boucher, V and Y Bramoullé (2020), ‘DP15505 Binary Outcomes and Linear Interactions‘, CEPR Discussion Paper No. 15505. CEPR Press, Paris & London. https://cepr.org/publications/dp15505