Table 6 Minimum and maximum bounds around the true coefficients of the Horowitz–Manski and Manski–Tamer estimators of the logit endogenous social interactions model with non-closed groups and individuals excluded from their own peer group
From: Partial identification of nonlinear peer effects models with missing data
Group size | No. of groups | HM | MT | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\({\bar{\theta }}_{\min }-\theta\) | \({\bar{\theta }}_{\max }-\theta\)Â Â | \(\bar{\theta }_{\min }-\theta\) | \({\bar{\theta }}_{\max }-\theta\) | ||||||||||||||
k | b | d | J | k | b | d | J | k | b | d | J | k | b | d | J | ||
5 | 50 | \(-\)0.12 | \(-\)0.29 | \(-\)0.16 | \(-\)2.51 | 0.63 | 0.09 | 0.17 | 1.03 | \(-\)0.22 | \(-\)0.29 | \(-\)0.16 | \(-\)2.51 | 0.63 | 0.09 | 0.17 | 1.20 |
5 | 100 | \(-\)0.12 | \(-\)0.13 | \(-\)0.11 | \(-\)0.94 | 0.29 | 0.05 | 0.03 | 0.93 | \(-\)0.12 | \(-\)0.13 | \(-\)0.11 | \(-\)0.94 | 0.29 | 0.05 | 0.03 | 0.93 |
5 | 200 | \(-\)0.03 | \(-\)0.05 | \(-\)0.05 | \(-\)0.60 | 0.16 | 0.04 | 0.03 | 0.34 | \(-\)0.03 | \(-\)0.05 | \(-\)0.05 | \(-\)0.60 | 0.16 | 0.04 | 0.03 | 0.34 |
5 | 500 | 0.00 | \(-\)0.02 | \(-\)0.03 | \(-\)0.25 | 0.08 | 0.01 | 0.00 | 0.12 | 0.00 | \(-\)0.02 | \(-\)0.03 | \(-\)0.25 | 0.08 | 0.01 | 0.00 | 0.21 |
5 | 1000 | \(-\)0.01 | \(-\)0.01 | \(-\)0.01 | 0.00 | 0.03 | 0.01 | 0.01 | 0.19 | \(-\)0.01 | \(-\)0.01 | \(-\)0.01 | 0.00 | 0.03 | 0.01 | 0.01 | 0.19 |
5 | 2500 | 0.02 | 0.00 | \(-\)0.01 | 0.00 | 0.03 | 0.01 | 0.00 | 0.07 | 0.02 | \(-\)0.01 | \(-\)0.01 | 0.00 | 0.03 | 0.01 | 0.00 | 0.08 |
10 | 50 | \(-\)0.03 | \(-\)0.14 | \(-\)0.08 | \(-\)1.83 | 0.44 | 0.04 | 0.09 | 0.55 | \(-\)0.03 | \(-\)0.14 | \(-\)0.08 | \(-\)1.83 | 0.44 | 0.05 | 0.09 | 0.55 |
10 | 100 | \(-\)0.05 | \(-\)0.09 | \(-\)0.05 | \(-\)0.58 | 0.18 | 0.01 | 0.03 | 0.58 | \(-\)0.05 | \(-\)0.09 | \(-\)0.05 | \(-\)0.58 | 0.19 | 0.01 | 0.03 | 0.58 |
10 | 200 | \(-\)0.05 | \(-\)0.03 | \(-\)0.04 | \(-\)0.13 | 0.06 | 0.01 | 0.00 | 0.46 | \(-\)0.05 | \(-\)0.04 | \(-\)0.04 | \(-\)0.13 | 0.06 | 0.01 | 0.01 | 0.46 |
10 | 500 | 0.00 | \(-\)0.02 | \(-\)0.02 | \(-\)0.07 | 0.05 | 0.00 | 0.00 | 0.17 | \(-\)0.01 | \(-\)0.02 | \(-\)0.02 | \(-\)0.07 | 0.05 | 0.00 | 0.00 | 0.19 |
10 | 1000 | \(-\)0.02 | \(-\)0.01 | \(-\)0.01 | 0.10 | 0.00 | 0.00 | \(-\)0.01 | 0.22 | \(-\)0.02 | \(-\)0.01 | \(-\)0.01 | 0.10 | 0.00 | 0.00 | \(-\)0.01 | 0.22 |
10 | 2500 | \(-\)0.02 | \(-\)0.01 | \(-\)0.01 | 0.18 | \(-\)0.01 | 0.00 | \(-\)0.01 | 0.23 | \(-\)0.03 | \(-\)0.01 | \(-\)0.01 | 0.18 | \(-\)0.01 | 0.00 | \(-\)0.01 | 0.23 |
25 | 50 | \(-\)0.05 | \(-\)0.08 | \(-\)0.04 | \(-\)0.78 | 0.17 | 0.00 | 0.03 | 0.40 | \(-\)0.05 | \(-\)0.08 | \(-\)0.04 | \(-\)0.78 | 0.17 | 0.01 | 0.03 | 0.40 |
25 | 100 | \(-\)0.03 | \(-\)0.03 | \(-\)0.03 | \(-\)0.25 | 0.07 | 0.01 | 0.00 | 0.30 | \(-\)0.03 | \(-\)0.03 | \(-\)0.03 | \(-\)0.25 | 0.07 | 0.01 | 0.01 | 0.30 |
25 | 200 | \(-\)0.04 | \(-\)0.02 | \(-\)0.01 | \(-\)0.05 | 0.02 | 0.00 | 0.01 | 0.24 | \(-\)0.04 | \(-\)0.02 | \(-\)0.01 | \(-\)0.09 | 0.03 | 0.01 | 0.01 | 0.24 |
25 | 500 | \(-\)0.02 | 0.00 | \(-\)0.01 | 0.04 | 0.00 | 0.00 | 0.00 | 0.15 | \(-\)0.02 | \(-\)0.02 | \(-\)0.01 | \(-\)0.05 | 0.02 | 0.00 | 0.00 | 0.15 |
25 | 1000 | \(-\)0.03 | 0.00 | \(-\)0.01 | 0.15 | \(-\)0.02 | 0.00 | \(-\)0.01 | 0.21 | \(-\)0.03 | 0.00 | \(-\)0.01 | 0.15 | \(-\)0.02 | 0.00 | 0.00 | 0.21 |
25 | 2500 | \(-\)0.02 | 0.00 | \(-\)0.01 | 0.16 | \(-\)0.02 | 0.00 | 0.00 | 0.18 | \(-\)0.02 | 0.00 | \(-\)0.01 | 0.13 | \(-\)0.02 | 0.00 | 0.00 | 0.18 |