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Count Data Models with Heterogeneous Peer Effects under Rational Expectations

Aristide Houndetoungan

TL;DR

This paper tackles the challenge of estimating peer effects for count outcomes under rational expectations with heterogeneous peer effects across observed groups. It develops a microfounded static incomplete-information network model with a flexible, semiparametric payoff and nonlinear count outcomes, and establishes identification under a friends-of-friends condition that extends to nonlinear settings. Parameters are consistently estimated via Nested Pseudo-Likelihood, and the approach is evaluated through Monte Carlo experiments and an empirical application to Add Health data, where gender differences in peer responsiveness are evident and the semiparametric specification outperforms SAR-Tobit under nonquadratic costs. The work highlights the risk of misspecification in linear-in-means or SAR-Tobit approaches for counts and provides an R package, CDatanet, to facilitate practical implementation in applied settings.

Abstract

This paper develops a peer effect model for count responses under rational expectations. The model accounts for heterogeneity in peer effects across groups based on observed characteristics. Identification is based on the linear model condition that requires the presence of friends of friends who are not direct friends. I show that this identification condition extends to a broad class of nonlinear models. Parameters are estimated using a nested pseudo-likelihood approach. An empirical application to students' extracurricular participation reveals that females are more responsive to peers than males. An easy-to-use R package, CDatanet, is available for implementing the model.

Count Data Models with Heterogeneous Peer Effects under Rational Expectations

TL;DR

This paper tackles the challenge of estimating peer effects for count outcomes under rational expectations with heterogeneous peer effects across observed groups. It develops a microfounded static incomplete-information network model with a flexible, semiparametric payoff and nonlinear count outcomes, and establishes identification under a friends-of-friends condition that extends to nonlinear settings. Parameters are consistently estimated via Nested Pseudo-Likelihood, and the approach is evaluated through Monte Carlo experiments and an empirical application to Add Health data, where gender differences in peer responsiveness are evident and the semiparametric specification outperforms SAR-Tobit under nonquadratic costs. The work highlights the risk of misspecification in linear-in-means or SAR-Tobit approaches for counts and provides an R package, CDatanet, to facilitate practical implementation in applied settings.

Abstract

This paper develops a peer effect model for count responses under rational expectations. The model accounts for heterogeneity in peer effects across groups based on observed characteristics. Identification is based on the linear model condition that requires the presence of friends of friends who are not direct friends. I show that this identification condition extends to a broad class of nonlinear models. Parameters are estimated using a nested pseudo-likelihood approach. An empirical application to students' extracurricular participation reveals that females are more responsive to peers than males. An easy-to-use R package, CDatanet, is available for implementing the model.
Paper Structure (30 sections, 9 theorems, 26 equations, 5 figures, 10 tables)

This paper contains 30 sections, 9 theorems, 26 equations, 5 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Microeconomic Foundations
  3. Incomplete Information Network Game
  4. Bayesian Nash Equilibrium
  5. Econometric Model
  6. Econometric Model
  7. Identification
  8. Estimation
  9. Monte Carlo Experiments
  10. Empirical Application
  11. Data
  12. Empirical Results
  13. Counterfactual Analysis
  14. Conclusion
  15. Proofs
  16. ...and 15 more sections

Key Result

Proposition 2.1

Under Assumptions ass_cost--ass_dist_e, $U_i^e(.)$ has a unique maximizer, $y_i^{\ast} \in \mathbb{N}_R$, almost surely (a.s.). Moreover, $y_i^{\ast} = r$ if and only if $U_i^e\left(r\right) > \max\left\{ U_i^e\left(r- 1\right), U_i^e\left(r + 1\right)\right\}$.

Figures (5)

  • Figure 1: Illustration of the identification
  • Figure 2: Simulated data using the count data model with social interactions
  • Figure 3: Distribution of the number of extracurricular activities
  • Figure 4: Counterfactual analysis results
  • Figure D.1: Histograms of the observed and simulated dependent variables

Theorems & Definitions (14)

  • Proposition 2.1
  • Remark 2.1
  • Proposition 2.2
  • Proposition 2.3
  • Remark 3.1
  • Definition 3.1
  • Proposition 3.1
  • Proposition 3.2
  • Proposition 3.3
  • Lemma A.1
  • ...and 4 more