Table 2.
Simulation results for as valid instrument (true effect=3)
| Method* | Estimate | Abs. Rel. Bias | Std. Error | ||
|---|---|---|---|---|---|
| U2 is not associated with A1 or A2. | R-IV | 16.60 | 443% | 727.30 | |
| S-IV | 4.68 | 56% | 2.63 | ||
| M-IV | 3.86 | 29% | 2.44 | ||
| Regression | 3.35 | 12% | 0.40 | ||
| U2 is only associated with A2. | Moderate Association | R-IV | −66.24 | 2308% | 2115 |
| S-IV | 4.31 | 44% | 2.48 | ||
| M-IV | 3.58 | 19% | 2.26 | ||
| Regression | 3.92 | 31% | 0.36 | ||
| Strong association | R-IV | 4.20 | 40% | 284.10 | |
| S-IV | 4.71 | 57% | 2.78 | ||
| M-IV | 3.73 | 24% | 2.47 | ||
| Regression | 4.53 | 51% | 0.38 | ||
| Very strong association | R-IV | 42.23 | 1308% | 940.69 | |
| S-IV | 4.81 | 60% | 3.63 | ||
| M-IV | 3.56 | 19% | 3.77 | ||
| Regression | 6.26 | 109% | 0.35 | ||
*
: R-IV for using randomization as the instrument, S-IV for using self-selection as the instrument, M-IV for matching enhanced IV estimation, and Regression for using the conventional linear regression model.