Table 7. Operating characteristics of the Bayesian estimator (posterior mean) of the treatment effect (ψ) as a function of the strength of the IV (λ).

Sample size (n)	True correlation (ρGEN)	Treatment effect (true ψ= -.5)	IV effect (λ)
			0	.5	1.0	2.0
1000	0	Bias	.043	.021	-.025	.002
		$\sqrt{\text{MSE}}$	.692	.549	.347	.176
		Coverage (%)	93	92	92	93
	.2	Bias	.293	.060	-.005	.015
		$\sqrt{\text{MSE}}$	.750	.546	.304	.161
		Coverage (%)	91	98	97	97
	.5	Bias	.426	.142	.012	-.030
		$\sqrt{\text{MSE}}$	.762	.493	.260	.163
		Coverage (%)	93	97	96	96
5000	0	Bias	.050	-.011	-.015	.003
		$\sqrt{\text{MSE}}$	.483	.316	.148	.074
		Coverage (%)	87	84	93	95
	.2	Bias	.338	.011	.012	-.005
		$\sqrt{\text{MSE}}$	.599	.261	.140	.073
		Coverage (%)	77	94	95	99
	.5	Bias	.386	.020	.001	-.014
		$\sqrt{\text{MSE}}$	.609	.211	.125	.077
		Coverage (%)	78	95	93	94

Note: The vague prior for ρ with E[ρ] = 0 and Var[ρ] = .33 is used.