Table 9 Minimum and maximum bounds around the true coefficients of the Horowitz–Manski and Manski–Tamer estimators of the OLS endogenous social interactions model with non-closed groups and individuals excluded from their own peer group. 50 Monte Carlo simulations, 5 missing values in each simulation
From: Partial identification of nonlinear peer effects models with missing data
Group size | No. of groups | HM | MT | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\({\bar{\theta }}_{\min }-\theta\) | \({\bar{\theta }}_{\max }-\theta\) | \(\bar{\theta }_{\min }-\theta\) | \({\bar{\theta }}_{\max }-\theta\) | ||||||||||||||
k | b | d | J | k | b | d | J | k | b | d | J | k | b | d | J | ||
5 missing values | |||||||||||||||||
 5 | 50 | \(-\)0.13 | \(-\)0.03 | \(-\)0.09 | \(-\)0.05 | 0.17 | 0.01 | 0.07 | 0.05 | \(-\)0.13 | \(-\)0.03 | \(-\)0.09 | \(-\)0.05 | 0.17 | 0.01 | 0.07 | 0.05 |
 5 | 100 | \(-\)0.09 | \(-\)0.02 | \(-\)0.06 | \(-\)0.02 | 0.07 | 0.01 | 0.02 | 0.03 | \(-\)0.09 | \(-\)0.02 | \(-\)0.06 | \(-\)0.02 | 0.07 | 0.01 | 0.02 | 0.03 |
 5 | 200 | \(-\)0.05 | \(-\)0.01 | \(-\)0.03 | \(-\)0.01 | 0.03 | 0.00 | 0.00 | 0.02 | \(-\)0.05 | \(-\)0.01 | \(-\)0.03 | \(-\)0.01 | 0.03 | 0.00 | 0.01 | 0.02 |
 5 | 500 | \(-\)0.02 | \(-\)0.01 | \(-\)0.01 | 0.00 | 0.01 | 0.00 | 0.01 | 0.01 | \(-\)0.02 | \(-\)0.01 | \(-\)0.01 | 0.00 | 0.01 | 0.00 | 0.01 | 0.01 |
 10 | 50 | \(-\)0.05 | \(-\)0.02 | \(-\)0.04 | \(-\)0.03 | 0.12 | 0.00 | 0.03 | 0.03 | \(-\)0.05 | \(-\)0.02 | \(-\)0.04 | \(-\)0.03 | 0.12 | 0.00 | 0.03 | 0.03 |
 10 | 100 | \(-\)0.03 | 0.00 | \(-\)0.02 | \(-\)0.02 | 0.06 | 0.01 | 0.01 | 0.01 | \(-\)0.03 | 0.00 | \(-\)0.02 | \(-\)0.02 | 0.06 | 0.01 | 0.02 | 0.01 |
 10 | 200 | \(-\)0.02 | 0.00 | \(-\)0.01 | \(-\)0.01 | 0.01 | 0.00 | 0.01 | 0.01 | \(-\)0.02 | 0.00 | \(-\)0.01 | \(-\)0.01 | 0.01 | 0.00 | 0.01 | 0.01 |
 10 | 500 | \(-\)0.01 | 0.00 | 0.00 | \(-\)0.01 | 0.01 | 0.00 | 0.01 | 0.00 | \(-\)0.01 | 0.00 | 0.00 | \(-\)0.01 | 0.01 | 0.00 | 0.01 | 0.00 |
 25 | 50 | \(-\)0.06 | 0.00 | \(-\)0.01 | 0.00 | 0.00 | 0.01 | 0.02 | 0.02 | \(-\)0.06 | \(-\)0.01 | \(-\)0.01 | \(-\)0.01 | 0.02 | 0.01 | 0.02 | 0.02 |
 25 | 100 | \(-\)0.01 | \(-\)0.01 | 0.00 | \(-\)0.01 | 0.03 | 0.00 | 0.02 | 0.00 | \(-\)0.01 | \(-\)0.01 | \(-\)0.01 | \(-\)0.01 | 0.03 | 0.00 | 0.02 | 0.00 |
 25 | 200 | \(-\)0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | \(-\)0.01 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.01 | 0.00 |
 25 | 500 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
7 missing values | |||||||||||||||||
 5 | 50 | \(-\)0.15 | \(-\)0.04 | \(-\)0.16 | \(-\)0.09 | 0.30 | 0.02 | 0.08 | 0.06 | \(-\)0.15 | \(-\)0.04 | \(-\)0.16 | \(-\)0.09 | 0.30 | 0.02 | 0.08 | 0.06 |
 5 | 100 | \(-\)0.10 | \(-\)0.02 | \(-\)0.06 | \(-\)0.04 | 0.13 | 0.01 | 0.05 | 0.03 | \(-\)0.10 | \(-\)0.02 | \(-\)0.06 | \(-\)0.04 | 0.13 | 0.01 | 0.05 | 0.03 |
 5 | 200 | \(-\)0.07 | \(-\)0.01 | \(-\)0.03 | \(-\)0.01 | 0.03 | 0.00 | 0.02 | 0.02 | \(-\)0.07 | \(-\)0.01 | \(-\)0.03 | \(-\)0.01 | 0.03 | 0.00 | 0.02 | 0.02 |
 5 | 500 | \(-\)0.02 | \(-\)0.01 | \(-\)0.02 | 0.00 | 0.03 | 0.00 | 0.00 | 0.01 | \(-\)0.02 | \(-\)0.01 | \(-\)0.02 | 0.00 | 0.03 | 0.00 | 0.01 | 0.01 |
 10 | 50 | \(-\)0.11 | \(-\)0.02 | \(-\)0.05 | \(-\)0.03 | 0.11 | 0.01 | 0.06 | 0.04 | \(-\)0.11 | \(-\)0.02 | \(-\)0.05 | \(-\)0.03 | 0.11 | 0.01 | 0.06 | 0.04 |
 10 | 100 | \(-\)0.08 | \(-\)0.01 | 0.00 | \(-\)0.02 | 0.04 | 0.00 | 0.05 | 0.02 | \(-\)0.08 | \(-\)0.01 | \(-\)0.01 | \(-\)0.02 | 0.04 | 0.00 | 0.05 | 0.02 |
 10 | 200 | \(-\)0.02 | \(-\)0.01 | \(-\)0.01 | \(-\)0.01 | 0.03 | 0.00 | 0.02 | 0.01 | \(-\)0.02 | \(-\)0.01 | \(-\)0.01 | \(-\)0.01 | 0.03 | 0.00 | 0.02 | 0.01 |
 10 | 500 | \(-\)0.01 | 0.00 | \(-\)0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | \(-\)0.01 | 0.00 | \(-\)0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 |
 25 | 50 | \(-\)0.03 | \(-\)0.01 | \(-\)0.04 | \(-\)0.02 | 0.07 | 0.00 | 0.01 | 0.01 | \(-\)0.03 | \(-\)0.01 | \(-\)0.04 | \(-\)0.02 | 0.07 | 0.00 | 0.01 | 0.01 |
 25 | 100 | 0.00 | 0.00 | \(-\)0.02 | \(-\)0.01 | 0.05 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | \(-\)0.02 | \(-\)0.01 | 0.05 | 0.00 | 0.01 | 0.00 |
 25 | 200 | \(-\)0.01 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.01 | 0.00 | \(-\)0.01 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.01 | 0.00 |
 25 | 500 | \(-\)0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | \(-\)0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |