The Effect of SNAP Participation on Mental Health: Using Marginal Effects to Bound Average Effects

This study introduces a novel nonparametric approach to partially identify the causal average treatment effect (ATE) of SNAP participation on mental health, such as nonspecific psychological distress (NPD). In our application, the ATE reveals how the fraction of low-income adults in good mental health would differ if all participated in SNAP versus all not participating. Point-identifying the ATE requires strong, and arguably untenable, assumptions about the data, how participants behave, and the factors leading to SNAP participation. Most importantly, respondents are not randomly assigned into the program. A selection problem arises because the choice to participate depends on unobserved factors such as financial stability, human capital characteristics, disability, and motivation toward work, all thought to be jointly related to SNAP participation and mental health outcomes. Instead of attempting to point-identify the ATE, we establish bounds on this quantity by leveraging state-level variation in SNAP program eligibility rules. These rules, which affect the difficulty in joining the program, plausibly affect participation without otherwise affecting mental health status. Our approach partially identifies the ATE by extrapolating from the population of SNAP compliers – i.e., those who respond to the variation in eligibility rules. Partial identification in this setting relies on two assumptions: (i) costs associated with receiving SNAP – such as stigma or administrative burdens – are monotonically related to psychological distress, and (ii) SNAP participation does not, on average, exacerbate psychological distress.