Adjusting for selection bias in longitudinal analyses using simultaneous equations modeling

Background: Effects of labor force participation on mental health can be difficult to discern due to the possibility of selection bias. Previous research typically adjusts for direct selection (reverse causality) but ignores indirect selection (unmeasured confounders). Methods: We investigate the relationship between men’s employment transitions and mental health using a dynamic simultaneous equations model applied to data from the British Household Panel Survey (1991–2009). Outcome is self-reported distress and anxiety as summed on a 12-point scale. We allow for direct selection by allowing prior mental health to affect both subsequent mental health and employment transitions in the joint model. We adjust for indirect selection by allowing for residual correlation between mental health and employment. Results: Moving from unemployment to employment was strongly associated with an improvement in mental health, whereas becoming unemployed was detrimental. However, these associations were attenuated by unmeasured confounders. After adjustment for indirect selection, the increased distress and anxiety associated with becoming unemployed decreased from 2.5 (95% confidence interval = 2.2 to 2.7) to 2.2 (2.0 to 2.5). (A change of 2.5 equates to half a standard deviation on the 12-point scale.) The improvement with moving from unemployment to employment was also weakened slightly (from -2.1 [-2.4 to -1.7] to -1.8 [-2.1 to -1.5]). Conclusions: There was strong evidence of indirect selection, but less support for direct selection. Nevertheless, the effects on psychological health of transitions between employment and unemployment, and between employment and economic inactivity, remained substantial after adjusting for selection