3–2. Two-stage least squares (2SLS)
The treatment effect (γ) of the sleep improvement program calculated in Since the estimation of In addition, note that only 58 people (approximately 40%) in the treatment group had higher posttreatment sleep satisfaction than preintervention, while 8 people (14%) in the control group reported improved sleep satisfaction. Since less than half of the treatment group also experienced improved sleep, it is necessary to determine the extent to which the intervention improved sleep and the extent to which productivity improved through that pathway. Even if the interventions did improve productivity, we do not know if all the improvement was realized through improved sleep health. For example, people may have become more conscious of their health and reviewed their dietary and exercise habits during the program, which in turn might have increased productivity through improved physical condition. It is also possible that the subjects’ assignment to the treatment group increased their loyalty to the company and raised their productivity as a result of working more diligently.If the ATT analysis includes effects through pathways other than sleep improvement, it is not possible to elucidate the extent to which sleep improvement contributed to the improvement in productivity. Therefore, we estimated the causal effect of sleep improvement by 2SLS as follows. Using the sleep health scores In what follows, we estimated the impact of the intervention on sleep health scores 