Variation in mental illness and provision of public mental health services

Abstract

By providing affordable healthcare to many Americans for the first time, the Affordable Care Act increases demand for public mental health services. It is, however, unclear if states’ provision standards for supply of mental health services will be able to accommodate this demand increase. Both the demand and supply of public mental health services vary within states; it is necessary to measure both locally. In this paper, we estimate the prevalence of mental illness within 30 geographical regions in the state of Virginia, a representative example of how many states organize their public mental health systems and how mental illness prevalence can be measured locally. Our methodology extends the analysis in Stern (Health Serv. Outcomes Res. Methods 14:109–155, 2014) by covering an entire state and accounting for peoples’ insurance status. The latter allows us to compare estimates of demand for public mental health services among those 30 geographical regions. We find that over 66,000 uninsured and Medicaid-insured individuals in Virginia are not provided with public mental health services. The deficit varies locally, with several regions having no deficit and others having 5000 or more untreated people. We also estimate that a large portion of the unserved people with mental illness are uninsured but would be insured for mental health services through Medicaid if Virginia were to accept the Medicaid expansion associated with the Affordable Care Act. These results provide evidence that there is significant variation in the demand for and public health systems’ ability to supply mental health services within states. This implies states can better serve populations relying on mental health care by allocating scarce public mental health dollars to localities reflecting their need.

Appendix 1

This appendix explains how to interpret the probit estimates in Table 1 in terms of a simpler example. Consider a model,

$$ y_{i}^{*} = X_{i} \beta + \alpha e_{i} + u_{i} ; $$

(2)

$$ e_{i} = Z_{i} \gamma + \delta y_{i}^{*} + \varepsilon_{i} ; $$

$$ y_{i} = 1\left( {y_{i}^{*} > 0} \right) ; $$

$$ \left( { \begin{array}{*{20}c} {u_{i} } \\ {\varepsilon_{i} } \\ \end{array} } \right) \sim iidN\left[ {0,\Omega } \right] ; $$

$$ \Omega = \left( { \begin{array}{*{20}c} 1 & {\rho \sigma_{\varepsilon } } \\ {\rho \sigma_{\varepsilon } } & {\sigma_{\varepsilon }^{2} } \\ \end{array} } \right) . $$

We can write Eq. (2) as

$$ \begin{aligned} y_{i}^{*} & = X_{i} \beta + \alpha e_{i} + u_{i} \\ & = X_{i} \beta + \alpha e_{i} + E\left( {u_{i} | e_{i} ,X_{i} } \right) + u_{i} - E\left( {u_{i} | e_{i} ,X_{i} } \right) \\ & = X_{i} \tilde{\beta } + \tilde{\alpha }e_{i} + \hat{u}_{i} \\ \end{aligned} $$

where

$$ \tilde{\beta } = \beta + \frac{{\partial E\left( {u_{i} | e_{i} ,X_{i} } \right)}}{{\partial X_{i} }} , $$

$$ \tilde{\alpha } = \alpha + \frac{{\partial E\left( {u_{i} | e_{i} ,X_{i} } \right)}}{{\partial e_{i} }} , $$

$$ \tilde{u}_{i} = u_{i} - E\left( {u_{i} | e_{i} ,X_{i} } \right) . $$

Obviously, endogeneity leads to asymptotically biased estimates of (β, α). But, if one is comfortable assuming that $\tilde{u}_{i} \sim iidN\left( {0,1} \right)$, then the (biased) probit estimator still provides a good estimator of $E\left( {y_{i} | e_{i} ,X_{i} } \right)$. Stern (1992a, 1992b), among others, provides suggestive evidence that binary discrete choice models are somewhat robust to distributional assumptions.

1.1 Appendix 2

The map in Fig. 8 was taken from http://www.dbhds.virginia.gov/individuals-and-families/community-services-boards.

Fig. 8

Virginia’s community services boards