Partial identification of nonlinear peer effects models with missing data

Swiss Journal of Economics and Statistics

Table 3 Bias, standard deviation and mean absolute deviation of the estimates for the endogenous effects coefficient (J) of the logit endogenous social interactions model

Group size	No. of groups	Bias: \({\bar{\theta }}-\theta (\bar{\theta }=\frac{ {\textstyle \sum _{s}} {\hat{\theta }}_{s}}{S})\)				STD: \(\sqrt{\frac{ {\textstyle \sum _{s}} ({\hat{\theta }}_{s}-{\bar{\theta }})^{2}}{S-1}}\)				MAD: \(\frac{ {\textstyle \sum _{s}} \left\| {\hat{\theta }}_{s}-\theta \right\| }{S}\)
Group size	No. of groups	M1	M2	M3	M4	M1	M2	M3	M4	M1	M2	M3	M4
5	50	\(-\)0.32	6.68	\(-\)0.63	10.19	1.29	0.75	2.19	1.90	0.91	6.68	1.80	10.19
5	100	\(-\)0.10	6.72	0.04	9.52	0.84	0.60	1.55	1.39	0.60	6.72	1.22	9.52
5	200	0.01	6.70	\(-\)0.20	9.62	0.54	0.41	1.16	0.85	0.41	6.70	0.95	9.62
5	500	0.09	6.72	0.01	9.62	0.40	0.19	0.55	0.46	0.29	6.72	0.42	9.62
5	1000	0.10	6.67	\(-\)0.01	9.62	0.21	0.17	0.42	0.39	0.18	6.67	0.34	9.62
5	2500	0.11	6.67	0.07	9.66	0.14	0.12	0.28	0.27	0.15	6.67	0.23	9.66
10	50	\(-\)0.15	6.47	\(-\)0.51	7.67	1.23	0.88	2.35	1.53	0.95	6.47	1.90	7.67
10	100	0.03	6.52	\(-\)0.13	8.11	0.92	0.57	1.19	1.14	0.75	6.52	0.99	8.11
10	200	0.16	6.31	\(-\)0.01	8.05	0.62	0.40	1.07	0.78	0.54	6.31	0.83	8.05
10	500	0.19	6.26	0.03	8.09	0.36	0.25	0.62	0.45	0.32	6.26	0.48	8.09
10	1000	0.23	6.30	0.14	8.18	0.26	0.15	0.37	0.29	0.29	6.30	0.31	8.18
10	2500	0.30	6.30	0.22	8.15	0.14	0.09	0.25	0.23	0.31	6.30	0.27	8.15
25	50	\(-\)0.17	6.20	\(-\)0.02	5.27	1.28	0.80	1.54	1.27	1.05	6.20	1.28	5.27
25	100	0.15	6.12	\(-\)0.12	5.19	0.83	0.53	0.93	1.00	0.67	6.12	0.74	5.19
25	200	0.44	6.18	0.17	5.19	0.50	0.35	0.83	0.56	0.53	6.18	0.69	5.19
25	500	0.33	6.08	0.02	5.29	0.35	0.18	0.41	0.36	0.41	6.08	0.33	5.29
25	1000	0.35	6.09	0.27	5.23	0.27	0.13	0.26	0.35	0.38	6.09	0.31	5.23
25	2500	0.36	6.09	0.14	5.26	0.18	0.08	0.19	0.19	0.37	6.09	0.18	5.26

Model 1: Closed groups, with individuals excluded from their own peer group. Model 2: Closed groups, with individuals as part of their own peer group. Model 3: Non-closed groups, with individuals excluded from their own peer group. Model 4: Non-closed groups, with individuals as part of their own peer group. 50 Monte Carlo simulations