A social interaction model with both in-group and out-group effects

ABSTRACT

This paper studies social interaction models with both in-group and out-group effects. The in-group effect follows the standard setup in the literature, while the out-group effect is introduced by assuming the economic outcome also depends on its out-group average value. We present a network game with limited information of outside groups that rationalizes the econometric model. We show that both effects are identified under a set of mild regularity conditions. We propose to estimate the model using the two-stage least squares (2SLS) method and establish the asymptotic normality of the estimators. The finite sample performance of the estimators is investigated through Monte Carlo simulations.

KEYWORDS:

• Social interaction models
• in-group effects
• out-group effects
• 2SLS

JEL CLASSIFICATION:

• C31
• C51

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed here.

Notes

¹ A $n\times n$ adjacency matrix $W$ is defined as follows. If $i$ and $j$ are connected, then $W_{ij}=1$, otherwise $W_{ij}=0$.

² It is a convention in the literature of social interaction models to assume that the individual characteristics $X$ are nonstochastic; seeLee (2004) andLee (2007), among many others.

³ In the example of student’s academic achievement, $y_i$ will be student $i$‘s GPA, $x_i$ will be a vector of exogenous variables that may affect student’s academic achievement, such as age and parents’ education. ${\sum }_{j\in G(i)}{W}_{G(i),ij}{y}_j$ is the average GPA of student $i$‘s connected friends, and ${\bar{y}}_{-G(i)}$ is the average GPA outside student $i$‘s classroom.

⁴ The identification results can be derived similarly for models with fixed effects but estimation procedure would be much more complicated; see Lee (2007) for more details. We leave Equation (1)(1) $y_i={\lambda }_1\sum _{j\in G(i)}{W}_{G(i),ij}{y}_j+{\lambda }_2{\bar{y}}_{-G(i)}+x_i^{\mathrm{T}}\beta +{\in }_i,$(1) with group-specific fixed effects as a future research direction.

⁵ The only reference we find is Tchuente (2019) who considers the identification and estimation of social interaction effect in the classic social interaction model, i.e. there only exists the in-group effect.

Additional information

Funding

This work was supported by the Humanities and Social Sciences Research Projects of Department of Education of Zhejiang Province [Y202146231].