Solving the Reflection Problem in Social Interaction Models with Endogeneity

30 Pages Posted: 13 Jun 2021 Last revised: 27 Apr 2022

See all articles by Zhongjian Lin

Zhongjian Lin

Emory University - Department of Economics

Xun Tang

Rice University - Department of Economics

Date Written: April 26, 2022

Abstract

We identify peer and contextual effects in social interactions models with endogenous covariates (e.g., self-selected treatments). Unobserved individual characteristics are correlated with these endogenous covariates and affect peer outcomes in the reduced form. Our method uses instruments for endogenous covariates, but does not require additional instruments for simultaneity in outcomes, which are often hard to find in linear-in-means models with contextual effects. Nor does our method require any exclusion restriction that some covariates have no contextual effects. The method can be applied to relax the Stable Unit Treatment Value Assumption (SUTVA) in the program evaluation literature, allowing individual treatments to influence the outcomes of other group members through both peer and contextual effects. We apply our method to estimate social effects in Grade 3 math scores of elementary school students in the State of Tennessee. Using lagged class sizes, teacher qualifications and students’ self-reported motivation scores as instruments for Grade 2 scores, we find significant evidence for positive peer effects and path dependence on G2 scores.

Keywords: Social Interactions, Endogeneity, Reflection Problem, Control Functions, Peer Effects, Academic Achievement.

JEL Classification: C31, C36, I21

Suggested Citation

Lin, Zhongjian and Tang, Xun, Solving the Reflection Problem in Social Interaction Models with Endogeneity (April 26, 2022). Available at SSRN: https://ssrn.com/abstract=3862178 or http://dx.doi.org/10.2139/ssrn.3862178

Zhongjian Lin (Contact Author)

Emory University - Department of Economics ( email )

1602 Fishburne Drive
Atlanta, GA 30322
United States

Xun Tang

Rice University - Department of Economics ( email )

6100 South Main Street
Houston, TX 77005
United States

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