Peer Effects and Social
Networks in Education
Presented by Jianwen Zou
1. Model
• Preferences
1. Model
• The Katz–Bonacich network centrality:
• The vector of Katz–Bonacich centralities is:
• We can then write the vector of Katz–Bonacich:
1. Model
• Equilibrium
• best reply function for each i = 1, ..., n:
1. Model
• Equilibrium
• Suppose that φω(g) < 1. Then, the individual equilibrium outcome is
uniquely defined and given by:
2. Data
• 2.1 Data:
• a unique database on friendship networks from Add Health
• Friendship networks
• Educational achievements
2. Data
3.1 Empirical strategy
• The empirical counterpart of (5) and (6) is:
3.2. Identification of peer effects
• The role of network-fixed effects
3.2. Identification of peer effects
• The role of peer groups with individual level variation
• Peer effects are identified if the structural parameters (μ, φ) uniquely
determine the reduced-form coefficients in (10).
3.2. Identification of peer effects
• The role of specific controls:
• find proxies for typically unobserved individual characteristics
• To control for differences in leadership propensity across adolescents
• capture differences in attitude towards education and parenting
• conditional on school-fixed effects
3.2. Identification of peer effects
• Estimation strategy
• First, we estimate our empirical model defined by equation (9) for
each network in our dataset
• Discard which network does not satisfy the condition 𝜙𝑘 < 1/ω(𝑔𝑘 ).
• Then stack the remind networks and estimate model (9) by running a
pseudo-panel data estimation
4.1. Empirical results
• A one-standard deviation increase in the Katz–Bonacich index
translates into roughly 7% of a standard deviation in education
outcome
4.1. Empirical results
6. ALTERNATIVE MEASURES OF UNIT
CENTRALITY
• Degree centrality:
• Closeness centrality:
• Betweenness centrality:
6. ALTERNATIVE MEASURES OF UNIT
CENTRALITY
7. DIRECTED NETWORKS
• The indegree of student i, denoted by 𝑔𝑖+ , is the number of
nominations student i receives from other students, that is 𝑔𝑖+ =
𝑗 𝑔𝑖𝑗
• We consider only the indegree to define the Katz–Bonacich centrality
measure
• Result is in the last column in Table 3