Table 1 Results for setting A (fully linear in \({{\,\mathrm{\textrm{ilr}}\,}}(X)\)). Bold values indicate the lowest OOS MSE resp. β-MSE in the corresponding dimension scenario.
From: Instrumental variable estimation for compositional treatments
Setting A, Equation (5) | |||||
|---|---|---|---|---|---|
Dim. | Method | OOS MSE | \(\beta\)-MSE | FZ | FNZ |
\(p=3\) \(q=2\) | DIR+LC | \(0.58\) \(\pm 0.08\) | \(1.6\) \(\pm 0.17\) | 0.0 | 0.0 |
ILR+LC\(^{\dagger }\) | \(\varvec{0.37}\) \(\pm 0.07\) | \(\mathbf {1.1}\) \(\pm 0.15\) | 0.0 | 0.0 | |
KIVILR | \(\varvec{0.37}\) \(\pm 0.07\) | – | – | – | |
Only LC | \(15.03\) \(\pm 0.20\) | \(32.6\) \(\pm 0.14\) | 0.0 | 0.0 | |
2SLS | \(>200\) | \(>5\)k | 0.0 | 0.0 | |
\(p=30\) \(q=10\) | ILR+LC | \(\varvec{0.42}\) \(\pm 0.08\) | \(\varvec{0.22}\) \(\pm 0.01\) | 0.0 | 12.0 |
KIVILR | \(240.6\) \(\pm 35.7\) | – | – | – | |
Only LC | \(24.4\) \(\pm 0.37\) | \(1.9\) \(\pm 0.00\) | 0.0 | 12.3 | |
\(p=250\) \(q=10\) | ILR+LC | \(\varvec{0.67}\) \(\pm 0.14\) | \(\varvec{0.22}\) \(\pm 0.02\) | 0.0 | 0.0 |
KIVILR | \(5060.5\) \(\pm 1196.2\) | – | – | – | |
Only LC | \(30.8\) \(\pm 0.48\) | \(143.3\) \(\pm 0.27\) | 3.0 | 1.0 | |
