Table 2.

Simulation results for Case 2A: the two-stage instrumental variable estimator and the naïve rank estimator; all values have been multiplied by

	Method	Parameter	Bias	ESE	ASE	ECR
100	Two-stage		–2.5	24.5	25.4	94.6
			0.2	30.4	29.8	95.4
	Naïve		28.9	10.1	10.1	18.6
			–28.8	18.1	17.6	62.2
200	Two-stage		–2.5	17.7	17.4	91.7
			0.6	20.8	20.3	93.3
	Naïve		28.5	6.8	7.1	1.2
			–28.1	12.3	12.3	37.8
400	Two-stage		–0.3	11.7	12.3	95.8
			–0.5	13.7	14.2	97.0
	Naïve		27.9	4.7	5.0	0.0
			–27.7	8.8	8.6	13.0

Bias, average bias; ESE, empirical standard error; ASE, average of the estimated standard errors; ECR, empirical coverage rate of the 95% Wald confidence intervals.