We revisit and rehabilitate linear models of interactions in binary outcomes. Building on Heckman and MaCurdy (1985), we characterize when these models are statistically well defined. We then characterize and assess their game-theoretic microfoundations. We show that linear models of interactions admit sensible microfoundations under incomplete information and independence, but unconventional ones under complete information. We propose two simple estimators and 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 highlight the main advantages of the linear framework and suggest that the estimations in these two studies suffer from endogeneity problems.
Vincent Boucher: Laval University, CRREP, CREATE.
Yann Bramoullé: Aix-Marseille University.
We thank Habiba Djebbari, Arthur Lewbel, participants at seminars and conferences for their helpful comments, and Aureo de Paula for invaluable feedback. This work was supported by the French National Research Agency Grant ANR-17-EURE-0020. This research uses data from Add Health, a program directed by Kathleen Mullan Harris and designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan Harris at the University of North Carolina at Chapel Hill, and funded by Grant P01-HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development, with cooperative funding from 23 other federal agencies and foundations. Special acknowledgment is given to Ronald R. Rindfuss and Barbara Entwisle for assistance in the original design. Information on how to obtain Add Health data files is available on the Add Health website http://www.cpc.unc.edu/addhealth). No direct support was received from Grant P01-HD31921 for this research. Replication codes are available at https:
//github.com/vincentboucherecn/linearbinaryinteractions. We used Hlavac (2018) for some tables.