How do mental health problems affect the likelihood of food security? This question is difficult to answer empirically for (at least) two main reasons:
- Endogeneity/Unobserved Factors. For example, personal, family, and neighborhood characteristics (e.g., family stability, access to health care, exposure to violence) can affect both mental health and the likelihood of food insecurity. Furthermore, the direction of causality is unclear, as mental health problems may reduce the likelihood of employment and thus food insecurity; Conversely, food insecurity can increase stress and increase the likelihood of mental illness.
- Measurement error. Many studies of mental illness rely on surveys and self-reported measures of mental illness. This can lead to significant measurement errors, especially because stigma leads to misinformation about mental health.
How can we address these dual issues simultaneously? This is what an article Jansen et al. (2023) attempts to solve (see also presentation here). A clear solution would be to use instrumental variables, but finding a valid instrument is problematic since most of the factors correlated with mental illness are also directly correlated with food insecurity. Furthermore, measurement error is more problematic when the key exposure variable (in this case the presence of mental illness) is binary.
The solution used by the authors is to use non-parametric partial identification methods developed in Kreider and Hill (2009) and Kreider et al. (2012). They apply these methods to data from the National Health Interview Survey (NHIS). They focus on patients who self-report “nonspecific psychological distress (NPD)” according to the Kessler scale (K-6).
In the standard OLS regression model (see below), there may be endogeneity as “treatment” (mental illness) may be correlated with the error term. Furthermore, mental health status (D) is measured with uncertainty. For example, let D* is equal to 1 if the individual is truly in mental distress and 0 otherwise. However, researchers only look at dwhich is self-reported distress.
The key way researchers solve this is through the partial identification method. The objective is to estimate the following average treatment effect (ATE):
In this equation, Y(D* = 1) represents the possible food safety outcome if an adult were in danger; Y(D* = 0) represents the food security outcome if adults were not in danger.
Estimating this equation is problematic. To see why, let’s decompose these values. Let’s suppose P(Y=1|D*=1)=P(Y(1)=1|D*=1)*P(D*=1). If the true probability of suffering mental distress…P(D*=1)–if they were known, this amount could be estimated. However, the term P[Y(1)=1|D*=0]because it estimates a counterfactual not observed in the data (i.e., the level of food security that people without mental illness would have had if they had suffered from it).
The second issue is that we do not actually observe D*, so the first term is not estimable. The authors decompose this term into something estimable. [i.e., P(Y=1,D=1)] and measurement error terms. Because there is often a sigma surrounding mental illness, mental illness is likely to be underdiagnosed rather than overdiagnosed. The authors state that once it can be assumed that there are no false positives so the θ1+=θ0+=0. The authors also assume that the ratio between true and observed non-specific mental illnesses is proportionally the same as that reported for all types of mental illnesses. To do this, they use data reported by SAMHSA.
They also impose 3 different types of assumptions:
- Monotonic Treatment Selection (MTS). This means that people who truly have a mental illness are (weakly) less likely to be food secure than those who truly do not have a mental illness.
- Monotonic instrumental variable (MIV). Here they assume that people living in areas with fewer food stores would be (weakly) less likely to be food secure.
- Monotonic treatment response (MTR). Psychological distress would not improve food security on average.
Using these approaches, the author finds that:
Applying relatively weak monotonicity assumptions on the latent food security outcomes, we find that alleviating the SMI would improve the food security rate by at least 9.5 percentage points, or 15%.
You can read the full article. here and there’s a helpful summary slide deck (which I borrowed heavily from) here.
