TABLE 1 Simulation results n = 600
| Mym | Mye | Mem | Munion | ||
|---|---|---|---|---|---|
| All correct | bias | 0.002 | 0.008 | 0.002 | 0.005 |
| MC s.e.* | 0.005 | 0.007 | 0.006 | 0.006 | |
| Y wrong | bias | -0.500 | -0.500 | 0.0001 | 0.004 |
| MC s.e. | 0.005 | 0.006 | 0.006 | 0.006 | |
| M wrong | bias | 0.038 | 0.008 | -0.054 | 0.003 |
| MC s.e. | 0.005 | 0.007 | 0.006 | 0.006 | |
| E wrong | bias | 0.003 | 0.027 | 0.059 | 0.004 |
| MC s.e. | 0.005 | 0.005 | 0.005 | 0.005 |
$M_{\text{ym}}: \hat{\theta}{0}^{\text{ym}} - \hat{\delta}{0}^{\text{doubly}}; M_{\text{ye}}: \hat{\theta}{0}^{\text{ye}} - \hat{\delta}{0}^{\text{doubly}}; M_{\text{em}}: \hat{\theta}{0}^{\text{em}} - \hat{\delta}{0}^{\text{doubly}}; M_{\text{union}}: \hat{\theta}{0}^{\text{triply}} - \hat{\delta}{0}^{\text{doubly}}$
*Monte Carlo standard error.
4. A data application. In this section, we illustrate the methods in a real world application from the psychology literature on mediation. We re-analyze data from The Job Search Intervention Study (JOBS II) also analyzed by Imai, Keele and Tingley (2010). JOBS II is a randomized field experiment that investigates the efficacy of a job training intervention on unemployed workers. The program is designed not only to increase reemployment among the unemployed but also to enhance the mental health of the job seekers. In the study, 1801 unemployed workers received a pre-screening questionnaire and were then randomly assigned to treatment and control groups. The treatment group with E = 1 participated in job skills workshops in which participants learned job search skills and coping strategies for dealing with setbacks in the job search process. The control group with E = 0 received a booklet describing job search tips. An analysis considers
TABLE 2 Simulation results n = 1000
| Mym | Mye | Mem | Munion | ||
|---|---|---|---|---|---|
| All correct | bias | 0.001 | 0.009 | 0.001 | 0.001 |
| MC s.e.* | 0.004 | 0.005 | 0.004 | 0.004 | |
| Y wrong | bias | -0.484 | -0.484 | 0.003 | 0.003 |
| MC s.e. | 0.004 | 0.004 | 0.004 | 0.004 | |
| M wrong | bias | 0.136 | -0.008 | 0.056 | 0.01 |
| MC s.e. | 0.004 | 0.05 | 0.004 | 0.01 | |
| E wrong | bias | 0.001 | -0.024 | -0.054 | 0.001 |
| MC s.e. | 0.004 | 0.004 | 0.004 | 0.004 |
$M_{\text{ym}}: \hat{\theta}{\theta}^{\text{ym}} - \hat{\delta}{\theta}^{\text{doubly}}; M_{\text{ye}}: \hat{\theta}{\theta}^{\text{ye}} - \hat{\delta}{\theta}^{\text{doubly}}; M_{\text{em}}: \hat{\theta}{\theta}^{\text{em}} - \hat{\delta}{\theta}^{\text{doubly}}; M_{\text{union}}: \hat{\theta}{\theta}^{\text{triply}} - \hat{\delta}{\theta}^{\text{doubly}}.$
*Monte Carlo standard error.