Table 1.
Mean treatment effects
| Treatment effects | With age omitted | With age observed |
|---|---|---|
| Mean (se) | Mean (se) | |
| Naive estimate | 0.05 (0.012) | 0.03 (0.01) |
| IV estimate | −0.07 (0.13) | −0.14 (0.11) |
| LIV-based estimates | ||
| IV effecta | −0.10 (0.10) | −0.17 (0.13) |
| Empirical ATE | −0.15 (0.09) | −0.17 (0.13) |
| TT | −0.12 (0.09) | −0.15 (0.13) |
a
This is the reconstructed IV estimator based on the estimated distribution of MTEs and the IV weights [23]. It is used to show that a certain combination of MTEs can be used to explain the traditional IV results