Table 9.
Rosenbaum bounds sensitivity analysis by outcome variables (Kernel matching algorithm, bandwidth = 0.06).
| Outcome variable | ∗Gamma (hidden bias magnitude) | Significance level |
Hodges-Lehmann point estimate |
Confidence interval (95%) |
|||
|---|---|---|---|---|---|---|---|
| upper bound | lower bound | upper bound | lower bound | upper bound | lower bound | ||
| Wheat yield (kg ha-1) | 1 | 2.8e-15 | 2.8e-15 | 902.698 | 902.698 | 707.293 | 1093.13 |
| 2 | .000011 | 0 | 514.837 | 1279.24 | 312.152 | 1481.46 | |
| 3 | .007773 | 0 | 305.433 | 1487.9 | 67.3658 | 1714.46 | |
| 3.1 | .011389 | 0 | 287.815 | 1504.37 | 46.5598 | 1735.6 | |
| 3.2 | .016179 | 0 | 270.354 | 1521.32 | 26.3379 | 1755.55 | |
| 3.3 | .022348 | 0 | 253.181 | 1537.23 | 5.5909 | 1774.61 | |
| 3.4 | .030089 | 0 | 237.798 | 1553.08 | -10.8594 | 1792.03 | |
| 4 | .117203 | 0 | 152.366 | 1634.09 | -109.049 | 1887.92 | |
| 5 | .400121 | 0 | 32.4502 | 1749.65 | -227.191 | 2010.93 | |
| 5.1 | .432392 | 0 | 19.4553 | 1762.28 | -237.443 | 2021.96 | |
| 5.2 | .464475 | 0 | 9.72024 | 1770.81 | -249.618 | 2032.68 | |
| 5.3 | .496172 | 0 | 1.68402 | 1779.74 | -256.868 | 2043.54 | |
| 5.4 |
.5273 |
0 |
-9.33009 |
1788.98 |
-264.469 |
2051.62 |
|
| Wheat net income (in ‘000 birr ha-1 year-1) | 1 | 6.4e-08 | 6.4e-08 | 7.67643 | 7.67643 | 4.86032 | 10.374 |
| 1.1 | 1.1e-06 | 2.5e-09 | 6.89615 | 8.40895 | 4.05947 | 11.0665 | |
| 1.2 | .000012 | 9.2e-11 | 6.15835 | 9.14767 | 3.33205 | 11.8322 | |
| 1.3 | .000077 | 3.2e-12 | 5.47176 | 9.81392 | 2.72201 | 12.5079 | |
| 1.4 | .000371 | 1.1e-13 | 4.86988 | 10.3689 | 2.1226 | 13.0749 | |
| 1.5 | .001368 | 3.4e-15 | 4.32216 | 10.8397 | 1.57158 | 13.59 | |
| 1.6 | .004073 | 1.1e-16 | 3.78405 | 11.3686 | 1.04115 | 14.0718 | |
| 1.7 | .010181 | 0 | 3.30321 | 11.8597 | .539349 | 14.5796 | |
| 1.8 | .022011 | 0 | 2.91341 | 12.3542 | .07997 | 15.0423 | |
| 1.9 | .042154 | 0 | 2.47432 | 12.7514 | -.411635 | 15.4756 | |
| 2 | .072906 | 0 | 2.09184 | 13.1039 | -.83785 | 15.9194 | |
| 2.5 | .389293 | 0 | .387565 | 14.715 | -2.65621 | 17.8096 | |
| 2.6 | .469825 | 0 | .095027 | 15.0206 | -2.99061 | 18.1208 | |
| 2.7 |
.548534 |
0 |
-.186282 |
15.3175 |
-3.33203 |
18.4064 |
|
| Maize yield (kg ha-1) | 1 | .001326 | .001326 | 235.075 | 235.075 | 82.1905 | 392.101 |
| 1.05 | .003239 | .0005 | 214.555 | 256.627 | 61.804 | 417.21 | |
| 1.1 | .007059 | .000183 | 194.881 | 279.125 | 40.1629 | 438.779 | |
| 1.15 | .013934 | .000065 | 175.728 | 300.416 | 19.2788 | 460.093 | |
| 1.2 | .025238 | .000023 | 156.315 | 317.049 | -.360678 | 481.874 | |
| 1.25 | .042406 | 7.6e-06 | 137.816 | 336.222 | -19.7912 | 501.948 | |
| 1.3 | .066711 | 2.5e-06 | 119.767 | 355.656 | -36.9964 | 525.14 | |
| 1.4 | .139739 | 2.7e-07 | 83.6981 | 390.539 | -68.0076 | 567.959 | |
| 1.5 | .244305 | 2.6e-08 | 55.1584 | 423.765 | -97.0015 | 606.025 | |
| 1.6 | .370918 | 2.5e-09 | 25.6437 | 452.7 | -121.886 | 636.881 | |
| 1.7 |
.504524 |
2.3e-10 |
-.955894 |
482.527 |
-146.854 |
668.765 |
|
| Maize net income (in ‘000 birr ha-1 year-1) | 1 | .064087 | .064087 | .999053 | .999053 | -.290937 | 2.35105 |
| 1.01 | .071669 | .05714 | .958715 | 1.04427 | -.329796 | 2.3953 | |
| 1.1 | .166425 | .018866 | .603291 | 1.37935 | -.643468 | 2.76405 | |
| 1.2 | .320774 | .004802 | .289682 | 1.72051 | -1.01328 | 3.14615 | |
| 1.3 | .4985 | .001088 | .003831 | 2.01882 | -1.3039 | 3.48846 | |
| 1.31 | .516128 | .000933 | -.028229 | 2.04707 | -1.32239 | 3.52099 | |
∗ - gamma (Г) - log odds of differential assignment due to unobserved factors.
Note: The lowest critical values of gamma for Hodges-Lehmann point estimate and 95% CI including zero are bolded.
Source: Stata output, 2020.