Table 2.

Results of the simulation study under correct selection of γ and h. Each simulation scenario is described by μ_A (instrument strength, given by average level of engagement) and γ₀ (extent of departure from exclusion restriction); further, results are shown under two different sample sizes (N =50 and N =200). Provided in the table for reference is the implied intention-to-treat effect, Δ_ITT. Depicted are the average point estimates, empirical standard error (ESE), the average large-sample-theory (LST) standard error for ${\widehat{\Delta }}_{\gamma }(1)$, the coverage probability, and power. Note that in all cases, Δγ (1) = −0.80.

			N = 50					N = 200
μ A	γ 0	ΔITT	Est.	ESE	$\widehat{\text{SE}}$	CP	Power	Est.	ESE	$\widehat{\text{SE}}$	CP	Power
0.25	0.00	−0.20	−0.858	1.223	1.155	0.968	0.063	−0.803	0.513	0.518	0.961	0.342
0.25	0.25	−0.35	−0.819	0.589	0.573	0.944	0.300	−0.803	0.286	0.285	0.946	0.815
0.25	0.50	−0.50	−0.803	0.411	0.390	0.933	0.536	−0.803	0.200	0.197	0.943	0.982
0.25	0.75	−0.65	−0.796	0.316	0.298	0.931	0.745	−0.798	0.154	0.151	0.945	1.000
0.25	1.00	−0.80	−0.806	0.252	0.245	0.939	0.900	−0.802	0.125	0.124	0.944	1.000
0.50	0.00	−0.40	−0.818	0.523	0.506	0.948	0.371	−0.802	0.252	0.249	0.95	0.899
0.50	0.25	−0.50	−0.808	0.397	0.390	0.944	0.545	−0.799	0.199	0.196	0.947	0.983
0.50	0.50	−0.60	−0.802	0.343	0.320	0.931	0.694	−0.801	0.167	0.162	0.943	0.998
0.50	0.75	−0.70	−0.803	0.288	0.275	0.937	0.817	−0.798	0.143	0.139	0.941	1.000
0.50	1.00	−0.80	−0.798	0.252	0.245	0.937	0.894	−0.801	0.124	0.124	0.948	1.000
0.75	0.00	−0.60	−0.800	0.344	0.338	0.943	0.663	−0.800	0.167	0.169	0.953	0.999
0.75	0.25	−0.65	−0.801	0.312	0.303	0.940	0.754	−0.801	0.154	0.153	0.95	1.000
0.75	0.50	−0.70	−0.804	0.288	0.276	0.936	0.822	−0.798	0.142	0.140	0.948	1.000
0.75	0.75	−0.75	−0.801	0.270	0.257	0.930	0.864	−0.796	0.132	0.130	0.949	1.000
0.75	1.00	−0.80	−0.800	0.252	0.244	0.941	0.898	−0.799	0.126	0.124	0.942	1.000