Two-Step Estimation of Incomplete Information Social Interaction Models With Sample Selection

ABSTRACT

This article considers linear social interaction models under incomplete information that allow for missing outcome data due to sample selection. For model estimation, assuming that each individual forms his/her belief about the other members’ outcomes based on rational expectations, we propose a two-step series nonlinear least squares estimator. Both the consistency and asymptotic normality of the estimator are established. As an empirical illustration, we apply the proposed model and method to National Longitudinal Study of Adolescent Health (Add Health) data to examine the impacts of friendship interactions on adolescents’ academic achievements. We provide empirical evidence that the interaction effects are important determinants of grade point average and that controlling for sample selection bias has certain impacts on the estimation results. Supplementary materials for this article are available online.

KEY WORDS:

• Incomplete information
• Rational expectation
• Sample selection
• Series estimation
• Social interactions.

Supplementary Materials

Supplement1: Proofs of the main theorems.

Supplement2: Proofs of technical lemmas and additional numerical results.

(UBES_S_1394861.pdf)

Acknowledgments

I am grateful to Editor Rajeev Dehejia, the associate editor, and three anonymous referees for their constructive comments, which greatly improved the article. I also thank Michihito Ando, Yasuyuki Todo, and the participants of the seminars at Kwansei University, Tokyo University, and Waseda University for their valuable suggestions.

Funding

This work was supported financially by JSPS Grant-in-Aid for Young Scientists B-15K17039.

This research uses data from Add Health, a program project 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 due Ronald R. Rindfuss and Barbara Entwisle for assistance in the original design. Information on how to obtain the 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 analysis.