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Binary Outcomes and Linear Interactions

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Abstract

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.

Suggested Citation

  • Vincent Boucher & Yann Bramoullé, 2020. "Binary Outcomes and Linear Interactions," AMSE Working Papers 2038, Aix-Marseille School of Economics, France.
  • Handle: RePEc:aim:wpaimx:2038
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    More about this item

    Keywords

    binary outcomes; linear probability model; peer effects; econometrics of games;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions

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