Table 3.
Simulation results for Case 2B: the instrumental variable estimators of Cases
2B and 1A and the naïve rank estimator; all values have been multiplied by
|
|
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|
|
Method | Parameter | Bias | ESE | ASE | ECR | Bias | ESE | ASE | ECR |
| 800 | Case 2B IV |
|
–3.5 | 25.7 | 25.2 | 96.2 | –1.3 | 12.4 | 12.1 | 94.8 |
|
0.2 | 5.4 | 5.5 | 96.2 | –0.2 | 4.8 | 4.9 | 95.2 | ||
| Case 1A IV |
|
–15.2 | 26.4 | 26.1 | 92.0 | –2.4 | 14.3 | 13.8 | 92.6 | |
|
0.3 | 5.6 | 5.6 | 96.6 | –0.1 | 5.1 | 5.3 | 95.8 | ||
| Naïve |
|
28.8 | 5.7 | 5.9 | 0.2 | 23.4 | 5.3 | 5.3 | 0.6 | |
|
–2.7 | 4.4 | 4.6 | 90.6 | –2.3 | 4.4 | 4.6 | 92.6 | ||
| 1600 | Case 2B IV |
|
–1.0 | 17.7 | 17.3 | 94.9 | –0.4 | 8.7 | 8.5 | 93.6 |
|
0.1 | 3.8 | 3.8 | 94.7 | 0.0 | 3.4 | 3.5 | 95.9 | ||
| Case 1A IV |
|
–13.4 | 18.4 | 18.2 | 89.6 | –1.4 | 9.8 | 9.7 | 94.2 | |
|
0.2 | 3.8 | 3.9 | 95.2 | 0.0 | 3.6 | 3.7 | 96.4 | ||
| Naïve |
|
29.2 | 3.9 | 4.2 | 0.0 | 23.3 | 3.7 | 3.7 | 0.0 | |
|
–2.8 | 3.2 | 3.2 | 85.2 | –2.1 | 3.1 | 3.2 | 90.2 | ||
Bias, average bias; ESE, empirical standard error; ASE, average of the estimated standard errors; ECR, empirical coverage rate of the 95% Wald confidence intervals; Case 2B IV, instrumental variable method of Case 2B; Case 1A IV, instrumental variable method of Case 1A.