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Losing insurance and psychiatric hospitalizations

We study the effect of losing insurance on psychiatric – mental health disorder (MHD) and substance use disorder (SUD) – hospital-based care. Psychiatric disorders cost the U.S. over $ 1T each year and hospitalizations provide important and valuable care for patients with these disorders. We use variation in public insurance coverage (Medicaid) eligibility offered by a large-scale and unexpected disenrollment in the state of Tennessee in 2005 that lead to 190,000 individuals losing their insurance. Medicaid enrollees are at elevated risk for psychiatric disorders. Following the disenrollment, hospitalizations for SUDs declined by 15.4%. Findings suggest that MHD hospitalizations declined by 4.2%, but the coefficient estimate is imprecise. The expected financing of hospital care received also changed, with the probability that Medicaid was listed as the expected payer for MHD and SUD hospitalizations declining by 27.5% and 30.8% respectively post-disenrollment. We provide suggestive evidence that psychiatric health declined post-disenrollment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. All authors contributed equally to this study. HCUP data were obtained by Sebastian Tello-Trillo under the purview of the University of Virginia licenses. The remaining co-authors did not have any unau-thorized access to these data while working on


Introduction
In this study we provide the first causal evidence on the effect of losing insurance on psychiatric disorder hospitalizations. Psychiatric disorders − mental health disorders (MHD) and substance use disorders (SUD) − are important to consider as these conditions are common and costly, but are also effectively treated. Each year these disorders cost the United States over $1T (Insel, 2008;Caulkins et al., 2014) and 47.6M and 20.3M Americans have a MHD and SUD respectively (Substance Abuse and Mental Health Services Administration, 2021), with millions more experiencing poor mental health and problematic patterns of substance use and misuse. As a specific example, the U.S. is currently in the middle of an opioid epidemic that has claimed well over 500,000 lives since 1999 (Centers for Disease Control and Prevention, 2022a).
We exploit exogenous variation in public insurance coverage eligibility generated by one of the largest disenrollments in the history of the Medicaid program: an August 2005 disenrollment in the state of Tennessee. Medicaid is a public insurance program for low-income people in the U.S. that covers approximately one in five Americans (Kaiser Family Foundation, 2022) and Medicaid enrollees have elevated rates of psychiatric disorders, leading to Medicaid being the single largest payer for associated services in the country (Medicaid and CHIP Payment and Access Commission, 2015). The disenrollment we study resulted in 190,000 enrollees -10% of those enrolled in Medicaid in the state of Tennessee and 3% of the total state population (Chang and Steinberg, 2009)unexpectedly losing Medicaid (referred to as 'TennCare'). The disenrollees were predominantly nondisabled, nonelderly, and childless adults. 24% of this population had serious psychological distress and 12% had an SUD in 2004 (the year prior to the disenrollment).
Many more disenrollees likely had less severe psychiatric conditions that could benefit from treatment previously available through TennCare coverage. 1 TennCare generously covers a wide range of efficacious psychiatric healthcare services including hospitalizations, medications, counseling services, and standalone inpatient and outpatient treatment. Additionally, access to primary care, also covered by TennCare, can have important and positive spillover benefits for psychiatric disorders  2 and primary care providers deliver substantial psychiatric care, one recent study found that that over the period 2016-2018, primary care physicians provided most of the care for depression, anxiety, and any mental illness in the U.S. (Jetty et al., 2021) and, for some patients, primary care providers can treat psychiatric health as well as specialists (Gaynes et al., 2009). The disenrollment reduced access to affordable treatment for many low-income individuals who had limited access to other forms of insurance (Farrar et al., 2007). We examine administrative data on psychiatric hospitalizations coupled with difference-in-differences methods to study TennCare effects.
Findings from the TennCare experience are useful to both economists and policymakers. Demand theory predicts that insurance, by reducing the out-of-pocket price faced by consumers, should increase the quantity of healthcare demanded (Grossman, 1972). To date, the literature has explored the effect of gaining insurance on psychiatric healthcare use due to available sources of experimental and quasi-experimental variation (Golberstein and Gonzales, 2015;Wen et al., 2015;Baicker et al., 2017;Wen et al., 2017;Meinhofer and Witman, 2018;Grooms and Ortega, 2019;Maclean and Saloner, 2019). While there are exceptions, public insurance expansions appear to increase psychiatric healthcare use and shift financing away from patients and tounderstates the actual number disenrolled individuals who could benefit from the psychiatric healthcare services offered by TennCare coverage as we consider only serious conditions. For instance, 92% had some level of psychological distress and 20% reported past year illicit drug use (illicit drug use tends to be under-reported in survey settings, suggesting that this is a lower bound on such use). Further, the financial strain and general shock associated with unexpectedly losing insurance (and therefore access to treatment and providers) could potentially exacerbate psychiatric disorders (Maclean et al., 2015), pushing a less serious condition to a serious one. 2 Medicaid enrollees have high rates of both physical health conditions and psychiatric disorders. Treating physical health conditions (e.g., diabetes, heart disease) can improve psychiatric disorders through reduced stress and simply improved health overall. wards insurance. 3 No study has estimated the impact of losing insurance on psychiatric healthcare or health and this is the contribution of our study.
The effects of insurance gains and losses need not be symmetric. Previous work has noted this possibility within the context of physical health and healthcare (Ghosh and Simon, 2015;Tello-Trillo, 2021). For instance, a person who loses insurance can retain accumulated 'patient education,' which includes information on one's health stock, how to manage chronic conditions, how to interact with the healthcare system, and so forth.
This education may allow a patient to continue to maintain health after a coverage loss more effectively than a patient with no insurance experience.
The nature of psychiatric disorders, patients who receive care, healthcare professionals who deliver care, and the structure of the U.S. healthcare delivery system generally suggests additional reasons to suspect asymmetry. First, a substantial fraction of psychiatric care is provided for free and/or at a heavy discount, with insurance playing a relatively modest role in the financing of such treatment; this is particularly true for SUD care (Buck, 2011). Charity care may act as a substitute for paid care, thereby muting the effect of any insurance loss. Second, many U.S. healthcare professionals will not accept public insurance patients − in particular Medicaid which offers low reimbursement rates relative to other payers (Decker, 2012), and this practice is particularly common within psychiatric care (Wen et al., 2019). 4 Losing insurance that cannot be used to pay for treatment may not lead to substantial reductions in use or shifts in payment source.
Finally, there are established psychiatric provider shortages in the U.S. (Buck, 2011;3 We note that Golberstein and Gonzales (2015) document no change in MHD treatment use following a Medicaid expansion. The authors rely on a simulated instrument approach while other studies cited here enter Medicaid policies directly into the regression. This difference in methodology may lead to discordant findings. See Hamersma and Kim (2013) for a thoughtful discussion of alternative approaches to modelling Medicaid generosity. Further, many studies in this literature examine the effects of expansions to non-traditional populations (e.g., low-income childless and non-disabled adults) while Golberstein and Gonzales (2015) examine increases in income generosity for traditional populations (e.g., the disabled and low-income adults with children, often mothers). Differences across studies may be driven by differences in the marginal enrollee who gains coverage following an expansion.
4 Nearly 50% of standalone SUD treatment providers did not accept Medicaid in 2004 (authors' calculations based on the 2004 National Survey of Substance Abuse Treatment Services). Bishop et al., 2014); e.g., 77% of U.S. counties do not have a sufficient mental healthcare workforce to meet local patient demand. If losing insurance curtails a patient's access to their provider, the patient may be unable to locate alternative care.
We have several findings. Psychiatric hospitalizations declined post-disenrollment in Tennessee relative to a comparison group of geographically similar U.S. states, with some suggestive evidence of heterogeneity in effect size across disorders, although coefficient estimates are only precise for SUD hospitalizations. MHD hospitalizations declined by 4.2% and SUD hospitalizations declined by 15.4%. The expected financing of care was also altered, with the probability that Medicaid was the expected payer for hospital care declining 27.5% for MHD and 30.8% for SUD hospitalizations post-disenrollment.
MHD disorder hospitalizations were more likely to have private insurance (7.7%) or Medicare (5.8%) as the expected payer post-disenrollment, but there was no change in the probability of either of these insurance forms as the expected payer for SUD hospitalizations. For both types of hospitalizations, the probability that the patient was listed as the expected payer increased, although effect sizes were somewhat larger for SUD than for MHD hospitalizations (60.7% and 42.5% respectively). In an extension to the main analysis, we offer suggestive evidence that the severity of psychiatric disorders may have worsened post-disenrollment, potentially through both reduced care and potentially increased financial burden associated with care received.
The paper is structured as follows. Section 2 provides background details on psychiatric disorders and associated care, the TennCare disenrollment we exploit, and related literature. Data and methods are described in Section 3. We present our main results in Section 4 and report robustness checking in Section 5. Finally, Section 6 offers a discussion and conclusion.
2 Background and prior research 2.1 Psychiatric disorders and associated healthcare The American Psychiatric Association (APA) defines MHDs as '. . . conditions involving changes in thinking, emotion, or behavior (or a combination of these)' (American Psychiatric Association, 2018). Further, the APA defines SUDs as conditions that occur '. . . when the recurrent use of alcohol and/or drugs causes clinically and functionally significant impairment, such as health problems, disability, and failure to meet major responsibilities at work, school, or home' (American Psychiatric Association, 2013). These conditions impose substantial burden on affected individuals, families, and communities.
Psychiatric disorders are common. In the U.S. 19.1% (47.6M) and 7.4% (20.3M) of adults met diagnostic criteria for a MHD and an SUD in 2020 (Substance Abuse and Mental Health Services Administration, 2021). The U.S. is in the midst of an unprecedented fatal drug overdose epidemic, largely related to opioids, with 93,398 fatal drug overdoses in 2020 (Ahmad et al., 2021). There are over 207 fatal opioid overdoses each day (Centers for Disease Control and Prevention, 2021b) and deaths related to stimulants such as cocaine are rising rapidly (Maclean et al., 2021). In 2020, 45,979 U.S. residents died by suicide (Centers for Disease Control and Prevention, 2022b) and the misuse of alcohol is associated with over 88,000 deaths annually (Centers for Disease Control and Prevention, 2021a). In 2021, MHDs and SUDs cost the U.S. over $1T in healthcare expenditures, disability payments, crime and violence, a less productive work force, and so forth (Insel, 2008;Caulkins et al., 2014). 5 While disadvantaged populations (e.g., those with lower income) are at elevated risk for psychiatric disorders (Substance Abuse and Mental Health Services Administration, 2021), no population is immune to these disorders and society as a whole pays the associated costs (financial and otherwise).
While they are costly, there are numerous effective treatment options for psychi-5 The original estimates are inflated by the authors to 2021 dollars using the Consumer Price Index. atric disorders, both care provided by specialists and primary care providers (Lu and McGuire, 2002;American Psychiatric Association, 2006;Hunot et al., 2007;Scott et al., 2007;Gaynes et al., 2009;Cuijpers et al., 2011;Popovici and French, 2013;Murphy and Polsky, 2016;Olfson, 2016;Kisely et al., 2017;Krebs et al., 2018; National Institute on Drug Abuse, 2018). For example, individuals with a psychiatric disorder can be prescribed medications or receive therapy from primary care physicians or psychiatrists. Patients can obtain treatment in standalone outpatient and residential facilities, or hospital (community or psychiatric) settings from psychologists, psychiatrists, social workers, counsellors, and other healthcare professionals.
Despite effective treatment options, many individuals do not receive psychiatric care -any care or adequate care, where adequate care is care that is of reasonable duration and is matched to patient need (National Institute on Drug Abuse, 2018). In 2020, less than half of U.S. adults who could benefit from mental healthcare did not receive any treatment while approximately one in ten adults meeting diagnostic criteria for an SUD received any care (Substance Abuse and Mental Health Services Administration, 2021).
Commonly reported barriers to treatment receipt are inability to pay and lack of insurance coverage (Rowan et al., 2013;Substance Abuse and Mental Health Services Administration, 2021;Federal Reserve Board of Governors, 2022). For example, among adults who needed, but did not receive mental healthcare, in 2020 the most commonly stated reason for failure to receive care was inability to pay (44.9%). Treatment is likely unaffordable for many low-income and uninsured individuals. The reimbursement rates for a single in-network session with a psychiatrist can cost up to $77 (CPT code 99213) to $106 (CPT code 99214) and such treatment typically involves a series of visits (Mark et al., 2018). Food and Drug Administration-approved medications used to treat opioid use disorder (buprenorphine, methadone, and naltrexone) cost up to $16,470 per year (National Institute on Drug Abuse, 2021). 6 For comparison, in 2021 the median maximum income at which a single adult was eligible for Medicaid in the U.S. was $17,774 (Kaiser Family Foundation, 2022). Finally, there is evidence that delays in receiving care, which could occur following an insurance loss, can have negative effects on psychiatric health (Penttilä et al., 2014;Reichert and Jacobs, 2018). In particular, insurance lossinduced treatment discontinuation can be fatal for those with an SUD (Sordo et al., 2017;Connery and Weiss, 2020;Krawczyk et al., 2020).
One policy approach to addressing unmet need (quantity and/or quality) for psychiatric healthcare services is the provision of affordable insurance that covers a range of treatment options. TennCare provided such insurance to low-income and uninsurable Tennessee residents. Thus, removing this coverage from 190,000 people with elevated risk for a psychiatric disorders could have lead to a substantial reduction in access to valuable care for chronic conditions. We study the effects of losing TennCare on hospital-based psychiatric treatment.
While hospitalizations represent a single modality, they are an important one to consider for several reasons. First, in the U.S., hospitalizations comprise 18% of overall psychiatric healthcare service expenditures and 25% of total payments to providers and are therefore important from a cost perspective (Substance Abuse and Mental Health Services Administration, 2014). In 2004 (the year prior to the TennCare disenrollment), one in four community adult hospitalizations (or 7.6M hospitalizations) involved a psychiatric disorder (Owens et al., 2007). Thus, due to their costs and use by patients, hospitalizations are central in discussions related to containing overall expenditures on healthcare. Second, and perhaps more practically, despite growth in ambulatory facilities and primary care for psychiatric treatment, community hospitals remain a critical facet of treatment for the thousands of Americans with psychiatric disorders (Stensland et al., 2012). Community hospitals provide patient stabilization services, complex drug therapies, coordinated psychotherapy, short-term detoxification, intense observation, and crisis care to psychiatric patients each year. Third, and related to the previous point, hospitalizations are important components of evidence-based psychiatric care: this modality is included in the Addiction Medicine Society of America's continuum of care and is used to treat patients with relatively severe episodes (Mee-Lee et al., 2013).
Fourth, hospitalizations are often an entry point to the healthcare system for individuals with a psychiatric disorder and can lead patients to receipt of a broader set of services (O'Toole et al., 2002;Houry et al., 2018). Finally, through the federal The Emergency Medical Treatment and Labor Act (EMTALA), in the U.S. all emergency departments must accept patients regardless of ability to pay, suggesting that hospitals may be particularly exposed to patients needing care following an insurance loss.

A brief overview of TennCare
Tennessee originally offered a fee-for-service Medicaid program. Due to high costs, the state transitioned to a managed care program in 1994, making Tennessee the first state in the U.S. to adopt managed care within Medicaid. 7 State legislators anticipated that the transition would reduce overall program costs. The expected savings were allocated to support a large-scale increase in Medicaid eligibility to low-income, non-disabled childless adults and uninsurable adults, defined as adults with pre-existing conditions that lead to prohibitively high premiums (Farrar et al., 2007). This population has historically had limited access to insurance in the U.S. The program was popular and TennCare covered 22% of the state's population by 2004. The TennCare program, which used a psychiatric healthcare carve out 8 throughout our study period, generously covered a wide range of efficacious psychiatric services (e.g., medications, assessment and evaluation services, and counseling) at low cost-sharing with limited application of utilization management; e.g., prior authorization (Farrar et al., 2007;Chang and Steinberg, 2009;Kaiser Family Foundation, 2021). TennCare coverage for physical health conditions was similarly generous and, through positive spillovers attributable to well-managed co-morbidities (e.g, diabetes, heart disease), psychiatric care delivered by primary care providers (Gaynes et al., 2009;Jetty et al., 2021), and overall improvements in well-being, likely enhanced psychiatric health among enrollees .
By 2004 the program accounted for one-third of the state's budget (Farrar et al., 2007). ). 9 Importantly for our design, the disenrollment was essentially unexpected by disenrollees (Farrar et al., 2007).

TennCare disenrollment literature
There is a small literature examining the health insurance, service use, and outcome effects of the TennCare disenrollment using quasi-experimental methods. To date, the literature has focused on general populations and physical health. No studies have examined psychiatric health or healthcare outcomes or insurance among patients with psychiatric disorders. Examining these outcomes is our contribution to this literature.
We contend that separate consideration of psychiatric disorders is warranted, which motivates our study. In addition to features of psychiatric disorders and associated care noted in Section, 1, important differences between psychiatric and physical health and healthcare have been highlighted by economists for decades (Frank and McGuire, 2000).
As noted by Frank and McGuire (2000) in the context of mental vs. physical healthcare: 'Uncertainty and variation in treatments are greater; the assumption of patient selfinterested behavior is more dubious; response to financial incentives such as insurance is exacerbated; the social consequences and external costs of illness are formidable.' Further, the risk of an overdose is elevated after periods of abstinence among those with SUDs (Merrall et al., 2010). An abrupt termination in access to treatment or the associated loss of financial resources conferred by insurance (Maclean et al., 2015) could be especially relevant for patients with SUDs.

Coverage effects
The TennCare disenrollment reduced Medicaid and overall insurance coverage with some private insurance substitution (Garthwaite et al., 2014;Tarazi et al., 2017;DeLeire, 2019;Tello-Trillo, 2021). For instance, using the Current Population Survey, Garthwaite et al. (2014) find that, post-disenrollment, the probability of having Medicaid declined by 33% among low-income, childless, and non-disabled adults. 10

Healthcare service use and health outcome effects
Several studies have examined the effect of the disenrollment on healthcare and health outcomes. Findings from the TennCare literature on physical healthcare suggest that losing insurance reduced service use, increased unmet need, and increased patient financial burden and hospital provision of uncompensated care, although there is some heterogeneity in estimated effects across studies.
Tello-Trillo (2021) leverages survey data from the National Health Interview Survey and Behavioral Risk Factor Surveillance Survey (BRFSS). The author finds that the reform lead to a 4% -5% reduction in mammograms and breast exams, and an increase of 20% in number of days with limited by one's health and no strong evidence of changes 10 There is also work on labor market effects (Garthwaite et al., 2014;Ham and Ueda, 2017). in emergency department visits. Tarazi et al. (2017) use the BRFSS and show that the disenrollment increased cost-related barriers to seeing a doctor but did not change the probability of having a personal doctor. DeLeire (2019) uses the Survey of Income and Program Participation and finds reports of unmet healthcare need and reliance on charity care increased and doctor visits and self-reported health declined post-disenrollment. Garthwaite et al. (2018) use American Hospital Association data and document that uncompensated care increased in Tennessee post-disenrollment. Finally, in a working paper, Ghosh and Simon (2015) use the National Inpatient Sample (NIS) and show that, post disenrollment, the share of total non-elderly adult hospitalizations with Medicaid as the expected payer decreased by 21% and hospitalizations with patients as the expected payer increased in Tennessee relative to a comparison group. There was no change in the number of hospitalizations.

Hospitalization data
Our primary dataset is the NIS, an administrative database compiled by the Healthcare Cost and Utilization Project (HCUP). 11 These data allow us to study hospitalizations and are the largest publicly available U.S. all-payer inpatient healthcare database.
The NIS are regularly used by economists to study psychiatric healthcare (Antwi et al., 2015;. The sample reflects a 20% stratified sample of U.S. hospitals, with five to eight million hospitalizations occurring at over 1,000 hospitals each year. Hospitals are sampled on region, ownership status, and bed size. In 2007 (the last year of our study) the weighted NIS sample covered 90% of the universe of hospitalizations and 78% of all hospitals (Barrett et al., 2010 (Ruhm, 2015;Carpenter et al., 2017;Hollingsworth et al., 2017), and psychiatric healthcare use (Bradford and Lastrapes, 2014;Maclean et al., 2020). 13 The NIS is not designed to be state representative. Instead these data (over our study period) are designed to be representative at the level of the region. 14 We are concerned that using the NIS data for Tennessee, which is a state with 5.9M residents (2% of the total U.S. population) in 2004 (University of Kentucky Center for Poverty Research, 2020), could lead to reliance on an unrepresentative sample of hospitals. 15 Given the structure of the NIS and our focus on a policy occurring in Tennessee, we propose an alternative empirical approach. We use state-representative data for Tennessee (from administrative sources) instead of the Tennessee observations included in the NIS, and then use the other Southern states (i.e., the comparison group) from NIS. Since we are combining data sets, we perform a simulation to test if our proposed strategy will allow us to estimate more accurate disenrollment effects. The results from this exercise are included in the Data Appendix (Section 8). Our analysis suggests that combining data in this manner allows us to more accurately estimate treatment effects. 12 We considered using elderly adults as a within-state comparison group in a triple difference estimator. The elderly have very different trends in psychiatric outcomes than the non-elderly. For example, 8% of adults 18 years and older met diagnostic criteria for an SUD while the share was 2% for elderly adults in 2020 (Substance Abuse and Mental Health Services Administration, 2021). 13 Further, there was a major re-certification of all Medicaid enrollees in Tennessee in 2002 (Division of TennCare, ND) and we do not want to confound effects by including data before and after this event.
14 In more recent years, the NIS is representative at the level of the nation. 15 We are less concerned with this issue in our comparison group as the NIS is designed to be representative at the regional level over our study period and our comparison group covers all other states in the South region. We have confirmed this assumption with an economist at the Agency for Healthcare Quality and Research, the agency that administers the HCUP. Further, we establish this point in a Monte Carlo simulation. Details available on request.
We also report results using NIS for Tennessee as a robustness check (see Section 5).
We analyze two sets of outcomes to study disenrollment effects. First, we consider the quarterly number of MHD and SUD hospitalizations per hospital (technically, we measure hospital discharges, but we refer to them as hospitalizations for simplicity). We separately classify MHD and SUD hospitalizations based on ICD-9 codes available on the discharge record (Stranges et al., 2011;Heslin et al., 2015). Second, we examine indicators for expected (not actual) payment source: Medicaid, any insurance, private insurance, Medicare, and self-pay (which plausibly includes uninsured patients). We have information on up to two expected payers per hospitalization listed by the hospital and code these variables one if the payer is listed as primary or secondary payer, and zero otherwise. Importantly, self-payment patients are often uninsured and do not necessarily pay the costs of hospitalization themselves, instead these costs are often borne by the hospitals who treat these patients. We are not able to study who eventually paid for the services as we have only expected payer information, which is a limitation of the study.

Empirical model
We estimate the difference-in-differences (DID) model outlined in Equation 1: where Y h,s,q,t represents a hospitalization or insurance outcome for hospital h in state s and in quarter q in year t. DID s,q,t is an indicator variable that takes on a value of one in Tennessee after the disenrollment and zero otherwise. pop s,t is the annual state population (University of Kentucky Center for Poverty Research, 2020), we include this variable to capture differences in demand for hospitalizations across states. α h is a vector of hospital fixed-effects (which subsume state fixed-effects), and α q and α t are vectors of quarter and year fixed-effects respectively. ϵ h,s,q,t is the error term. We apply NIS weights to the (non-Tennessee) NIS data and weight the Tennessee data equally.
A necessary assumption for canonical DID models to recover causal estimates is that the treatment and comparison group would have followed the same trends in outcomes had the treatment group not received treatment (i.e., 'parallel trends'). The assumption is untestable as the treatment group is treated in the post-period. We provide suggestive evidence on parallel trends through estimation of an event-study.
Quarterly hospital-level summary statistics using data from the pre-disenrollment period in Tennessee and other Southern states are reported in Table 1. Unadjusted trends 16 In our main specifications, we do not include time-varying covariates, beyond the state population which we believe is important to capture demand for services, as recent work suggests that estimation of a DID method using two-way fixed-effects, as we do here, with time-varying controls can lead to inaccurate estimates of average treatment effects on the treated (Caetano et al., 2022). We report results based on regressions that control for a range of time-varying covariates in a robustness check.
in MHD and SUD hospitalizations and expected payment sources for the treatment and comparison groups are reported in Figure 1. While there are some level differences across the two groups of states, trends in outcomes (pre-disenrollment) appear to move in parallel, post-disenrollment there are some differences in trends. 17

DID analysis of hospitalizations and expected payment sources
Our main DID results for hospitalizations are reported in Table 2. Following the disenrollment, quarterly MHD and SUD hospitalizations declined by 4.9 and 5.8 per hospital operating in Tennessee, although the coefficient estimate in the MHD hospitalizations regression is not precise. Comparing these coefficient estimates to the means in Tennessee pre-disenrollment, our findings suggest a 4.2% reduction in MHD hospitalization (baseline mean = 115.0) and 15.4% in SUD hospitalizations (baseline mean = 37.4).
Thus, the disenrollment arguably lead to meaningful reductions in hospitalization care for psychiatric disorders among Tennessee Medicaid enrollees.
In Tables 3 and 4 we report the estimated impacts on expected payment sources for MHD and SUD hospitalizations. We note that we interpret these findings cautiously as they are based on samples of patients receiving hospital care for psychiatric conditions, which appear to be impacted by the policy (see Table 2), and hence findings are potentially subject to conditional-on-positive bias. With this caveat in mind, we show that the probability that Medicaid was the expected payer for psychiatric treatment declined by 9.5 percentage points ('ppts') and 12.0 ppts for MHD and SUD hospitalizations respectively. Compared to the proportions of hospitalizations expected to be financed by Medicaid in Tennessee pre-disenrollment (34.6% for MHD and 39.0% for SUD), these coefficient estimates imply that expected Medicaid financing was reduced by 27.5% for MHD hospitalizations and 30.8% for SUD hospitalizations. The probability that any insurance was the expected source of payment for treatment declined more modestly for MHD hospitalizations (3.2 ppts or 3.3%). The decline in any insurance as the expected payer for SUD hospitalizations was nearly as large as the Medicaid decline (10.4 ppts or 12.1%). MHD patients were able to partially offset the insurance loss with private and Medicare coverage (for which expected payment increased by 2.2 ppts or 7.7% and 1.9 or 5.8% respectively), but SUD patients were not able to substitute expected forms of payment in this matter. Expected self-financing increased for both MHD and SUD: 1.7 ppts and 8.2 ppts respectively, which correspond to 42.5% and 60.7% rises.
Thus, while the reductions in the expected use of Medicaid to pay for care were similar for MHD and SUD patients, the 'substitute' expected payment forms were potentially somewhat different, with SUD patients more likely to shoulder the expected costs of care to a larger extent than MHD patients. Given that the average charge for a community hospitalization for psychiatric conditions ranged from $6,432 to $26,986 for an uninsured patient in 2006 (Stensland et al., 2012), this shift in expected financing from Medicaid to patients (in particular SUD patients) was arguably non-trivial. Further, many expected self-pay hospitalizations result in the facility absorbing the cost as patients, ultimately, are not able to (at least fully) pay for treatment (Garthwaite et al., 2018).

Internal validity
We estimate an event study to provide suggestive evidence as to whether our treatment and comparison groups would have followed parallel trends in psychiatric hospitalizations and payment sources post-disenrollment after adjusting for fixed-effects. More specifically, we decompose DID s,q,t in Equation 1 into a series of interactions between an indicator for Tennessee and time leads and lags reflecting periods around the disenrollment. To smooth the data, we use six-month bins to define periods. The omitted category is the six-month period prior to the disenrollment. Event study results are reported graphically in Figures 2 (hospitalizations) and 3 (expected payment source).
There are two key findings from the event studies. First, we do not observe substantial evidence of differential pre-trends in our outcomes between Tennessee and comparison states. Coefficient estimates are small and not statistically distinguishable from zero for the policy lead indicators. Second, examination of the policy lag indicators largely supports our DID findings.

DID analysis of psychiatric health
Next, we explore the impact of the disenrollment on MHD and SUD proxies: deaths by suicide, and fatal alcohol poisoning and drug overdoses. We use the Centers for

Disease Control and Prevention's National Vital Statistics System (NVSS) Underlying
Cause of Death public use files. These data record the universe of deaths in the U.S. and classify deaths by cause. We select all related deaths for adults 21 to 64 in each quarter 2002 to 2007 for Tennessee and other Southern states. We report results based on all states but results based on only state/year pairs in the NIS data are available on request and are similar. Deaths are expressed as a quarterly rate per 100,000 adults 21 to 64 and data are weighted by that population. 18 We modify Equation 1 to account for the fact that the NVSS data are at the state rather than hospital level, in particular hospital fixed-effects are replaced with state fixed-effects.
Results are reported in Table 5. Rates of deaths by suicides increased by 0.479 per 100,000 state non-elderly adult residents or 11.2% relative to the mean in Tennessee predisenrollment. Rates of fatal alcohol and drug poisonings increased by 0.765 or 24.4%.
These findings suggest that losing insurance, through reduced service use or increased financial burden associated with healthcare, may lead to worse psychiatric health. 19 18 All state-month cells in the public use NVSS with less than ten suicides are suppressed for confidentiality reasons. We impute these cells with a value of five. Results are not sensitive to imputing a value of zero (the smallest possible value) or nine (the largest possible value). 19 As noted by Black et al. (2019), we could be under-powered to detect effects. To speak to this issue, Effects appear to be larger for alcohol poisonings and drug overdoses. This finding is in line with previous research suggests that unexpected treatment discontinuation can be fatal for those with an SUD (Sordo et al., 2017;Connery and Weiss, 2020;Krawczyk et al., 2020).

Robustness checks
We report a serious of robustness checks. Reassuringly, our findings are stable. For brevity, we report robustness checking for hospitalization outcomes. Results for payment sources are similarly stable and are available on request.

Alternative specifications, samples, and periods
We re-estimate Equation 1 using alternative time periods, comparison groups, and specifications. More specifically, we: (i) include time-varying state-level covariates (see Table 1, demographics from the CPS (Flood et al., 2021) and population from the Census); 20 (ii) aggregate to the state-year level; (iii) estimate unweighted regression; (iv) use the NIS data for Tennessee; 21 (v) exclude Texas and Georgia from the comparison group -we exclude these states as their Medicaid programs appear, based on available evidence, to potentially cover psychiatric healthcare services less generously than Tennessee over our study period ( we have attempted to assess statistical power in our study. In unreported analyses, we conducted a post-hoc power analysis. Results, available on request, suggest that we are able to detect effect sizes of the magnitudes that we estimate with approximately 80% power. 20 In earlier versions of this manuscript, we included time-varying covariates in our main specifications, reporting regressions without these controls as a robustness check. We have elected to change our presentation to emphasize the more parsimonious specifications (i.e., not including the time-varying state-level covariates beyond the state population which we view as important as this variable allows us to account for demand for hospital services within states) based on recent research suggesting that DID regressions are vulnerable to bias from such controls. See Caetano et al. (2022) for a helpful discussion of this issue. 21 We apply the NIS-provided weights to both Tennessee and other Southern States in this regression.
Overall, our findings − while not identical across all specifications − appear to be broadly stable. Findings are less precise when we include time-varying covariates, this change may be attributable to the vulnerabilities of two-way fixed-effects DID regressions with such controls included (Caetano et al., 2022).

Program-induced migration
An empirical concern in policy analysis is that the policy under study may have induced individuals to migrate away from or towards the affected locality leading to biased estimates of regression coefficients due to violation of STUVA (Moffitt, 1992 as outlined in Section 4.3, although due to the structure of the ASEC, we have annual not quarterly data and thus we cannot include quarter fixed-effects in the regression.
We find no evidence that the disenrollment lead to changes in the propensity to move towards or away from Tennessee among non-elderly adults of lower income levels. The coefficient estimate is small in size and not statistically distinguishable from zero. 22 We do not control for the state population as we do in other regressions given the close connection between migration and population, e.g., out-migration all else equal will mechanically lower population. However, we have included this covaraite in the regression in unreported analyses and the results are very similar and available on request.

Discussion
We provide the first evidence on the effect of losing public insurance on psychiatric hospitalizations. Our findings are relevant from both an economic and a policy perspective. First, we extend the economic literature that has estimated the insurance-elasticity of demand for psychiatric healthcare by leveraging plausibly exogenous variation offered by a large and unexpected Medicaid disenrollment. We are the first study to document this elasticity. Second, many countries grapple with providing quality healthcare to individuals and curtailing high healthcare costs to governments, which are in turn borne by taxpayers. For example, in the United States there have been recent policy debates regarding repealing or re-designing the Affordable Care Act (ACA) -a massive transformation of the U.S. healthcare system which substantially increased both public and private coverage and required insurers to cover psychiatric healthcare services. These findings speak to the insurance elasticity of demand for psychiatric healthcare services and can inform policy decisions how best to provide coverage for such care.
Our findings suggest that the disenrollment reduced MHD hospitalizations by 4.2% and SUD hospitalizations by 15.4%, although findings for MHD hospitalizations are not precise. In additional, the expected financing of psychiatric care changed, MHD hospitalization expected financing was partially shifted to private and Medicare insurance while SUD expected financing was transferred entirely to patients. These findings suggest that losing insurance reduces access to valuable psychiatric care and likely imposes financial burden on patients. Given that self-payments by patients often translates into bad debt to hospitals (Garthwaite et al., 2018), this shift in financing may also spillover to healthcare providers who treat patients with psychiatric disorders. Further, while both MHD and SUD patients were arguably negatively impacted by the disenrollment, effects were disproportionately larger for those with SUDs.
While we lack the data to fully explore why findings differed for MHD and SUD patients, we can propose some hypotheses. SUD patients may be more disadvantaged than MHD patients. This disadvantage may manifest in being less able to secure employment that offers insurance, and insurance that covers SUD treatment, following a large-scale disenrollment. That is, patients with MHD may be able to find a job that will offer coverage for MHD or offer sufficient income so that these patients can purchase coverage individually post-disenrollment. Over our study period, while private coverage for MHD and SUD services was limited, more states required private plans to cover MHD than did SUD services, thus obtaining private coverage that included services was likely less difficult for MHD than SUD patients. Providers may have been less willing to treat patients with SUDs in the hospital due to stigma, misunderstanding of addiction, and so forth. For example, an SUD patient appearing in the emergency department may have been allowed to detox in the emergency department and then discharged, while a patient with a MHD appearing in the emergency department may have been admitted to the hospital. Patients with MHDs were potentially better able to secure other forms of public coverage than patients with SUDs following the disenrollment. For example, MHDs are a qualifying condition for Supplemental Security Income (SSI), but SUD was removed as a qualifying condition for this program in the 1990s, thus those with SUD may be less able to qualify for other forms of public insurance. We note that our explanations are not likely fully satisfactory and we encourage more work on understanding how those with SUDs and MHDs are able to respond to policy shocks such as a large-scale insurance disenrollment and associated loss of coverage.
We can compare our findings to studies that have examined the effect of pre-and post-ACA state Medicaid expansions to 'non-traditional' populations similar to the population impacted by the TennCare disenrollment (Wen et al., 2015(Wen et al., , 2017Meinhofer and Witman, 2018;Cher et al., 2019;Ghosh et al., 2019;Grooms and Ortega, 2019;Maclean and Saloner, 2019;Saloner and Maclean, 2020) and the Oregon Medicaid experiment (Baicker et al., 2017). Non-traditional populations are low-income non-disabled childless adults that historically been categorically ineligible for Medicaid coverage. To date, this literature has examined the effect of insurance gains attributable to Medicaid expansions. We examine insurance losses following the TennCare disenrollment. While there are numerous reasons to expect asymmetry in the effects of insurance gains and losses on psychiatric healthcare, we do not find that to be the case. We observe suggestive evidence that psychiatric health may worsen following an insurance loss but there is less of improvements in this health metric following an insurance gain (Abouk et al., 2019;Averett et al., 2019), although Wettstein (2019) shows that private insurance gains among young adults appear to improve psychiatric health.
Our findings depart from the TennCare literature on all-cause hospitalizations. Ghosh and Simon (2015) show that there was no change in the number of total hospitalizations post-disenrollment. These differing findings may imply differences in the insuranceelasticity of demand across services. Previous work demonstrates differences in the priceelasticity of demand for healthcare services (Ellis et al., 2017). However, findings for shifts in the expected financing of hospitalizations post-disenrollment across total and psychiatric hospitalizations: for example Ghosh and Simon (2015) find a 21% reduction in the expected use of Medicaid to pay for hospitalizations while we document a 27.5% and 30.8% reduction for MHD and SUD hospitalizations respectively.
In sum, we provide the first evidence on the impact of losing insurance on psychiatric hospitalizations and financing, and measures of psychiatric health. Given the ongoing opioid and mental illness crisis in the U.S. (Maclean et al., 2021), alongside an emerging stimulant crisis, understanding how insurance impacts these outcomes is critical. Establishing and understanding differences in responsiveness to policy changes across services is critical to optimal insurance design. Our findings shed light on these questions.          Garthwaite et al. (2014) and are reported in parentheses. ***, **, & * = statistically different from zero at the 1%, 5%, and 10% level of confidence.  Garthwaite et al. (2014) and are reported in parentheses. ***, **, & * = statistically different from zero at the 1%, 5%, and 10% level of confidence.    Regressions are estimated with least squares and control for hospital, quarter, and year fixed-effects and state population as a coviarate unless otherwise noted. 95% confidence intervals are estimated with a modified block-bootstrap procedure following Garthwaite et al. (2014) and are reported with vertical lines.

Data appendix
The NIS is not designed to be state representative. Instead, the dataset is representative at the national and regional level over our study period. HCUP administrators strongly advise researchers against using the NIS for single-state estimates. 23 We study a subset of the population (ages 21 to 64) and specific types of hospitalizations (i.e, psychiatric  (2), and the value of our proposed combination of NIS and other administrative data which we describe in more detail later (3). We then estimate a DID specification in each sampling scheme across 1,000 simulated populations. Full details are available on request.
The simulation results are reported in Data Appendix Figure A1, and the implications of reliance on the NIS are immediately apparent. First, all distributions of beta hat are centered on the true parameter value (constructed to have a value of two). However, the sampling framework employed has consequential implications for the likelihood that the estimated DID parameter will be significantly over-or under-estimated. The difference between region-and state-representativeness matters in a DID context, particularly one in which only a single state is treated. In a regionally representative dataset such as the NIS, a state like Tennessee may contribute a very small number of observations within any given conditional cell (e.g., ownership, bed size, and year). Intuitively, when the identifying variation is small number of observations which by design are not necessarily representative of the treatment group, the variability in coefficient estimates increases substantially.
Using the 100% sample, the distribution of beta hats is tightly centered around the true value, as we would expect. The 20% sample with exclusions required to form our analysis sample produces a very wide distribution of estimates, with many estimates differing substantially from the true treatment effect. Using a combination of the universe of Tennessee hospitals and a 20% sample of hospitals in other Southern states, while not fully alleviating the increase in distribution spread, substantially tightens the distribution of beta hats and nearly offsets the increase in the width of the distribution induced by sampling. In sum, this simulation exercise implies that sampling used to construct the NIS, while not leading to bias, substantially increases the chance that the researcher will have an unrepresentative sample which can lead to inaccurate estimates of treatment effects. This outcome is what NIS administrators state will occur when the NIS is used for state-level analyses, but researchers (including ourselves in previous work) often ignore this caution.
A high-variance estimator, like the one arising from the typical state-level analysis administrators warn researchers against applying when using the NIS data, is underpowered to detect small and modest effect sizes. When using an underpowered estimator, the distribution of statistically significant coefficient estimates will be biased away from zero. This situation illustrates the real danger of using such estimators: researchers who find statistically significant evidence are potentially overstating the true effect size.
Using the simulation evidence above to help us identify the best possible estimation strategy, we propose a combination of the NIS and administrative data for Tennessee. We replace the NIS Tennessee observations with the universe of hospitalizations at commu-nity hospitals for this state that we obtained from the Tennessee Department of Health ('DOH' data). 25 Of note, the NIS Tennessee is drawn from the DOH data that we use, thus the datasets are entirely compatible. Put differently, we are not introducing bias into the analysis attributable to using different data sources as the NIS uses a sub-set of the DOH data to form the Tennessee sample. This combination mimics (3) in our simulation and, we hypothesize, will allow more accurate estimates of treatment effects than reliance on the NIS data alone. 26 We further investigate the value of our combined dataset by comparing NIS and DOH data for Tennessee over our study period. We exclude non-community hospitals from the DOH data to match the NIS sample frame; we confirmed our definition of community hospitals with administrators at the Tennessee DOH (details available on request). We plot trends in the average number of hospitalizations among non-elderly adults per hospital in each quarter of our study period in Tennessee in the NIS and the DOH data. Trends in MHD, SUD, and total hospitalizations (Data Appendix Figure   A2) display more period-to-period variation in the NIS data than the DOH data, and the variation in the NIS occurs around the disenrollment period. Differences in trend between NIS hospitals and the universe of hospitals in the DOH are arguably more pronounced for total hospitalizations. Of note, based on our analysis of the data, review of Tennessee DOH hospital directories, and discussions with DOH staff, the deviations apparent in the NIS data for Tennessee do indeed reflect the unrepresentative nature of the hospitals sampled for the NIS, which further underscores our concern that reliance on the NIS for a single-state analysis may be problematic. The correlations between the DOH and NIS time series are 0.46 (MHD), 0.56 (SUD), and 0.39 (total). Thus, while the 25 Because the Tennessee NIS data is drawn from the DOH data the measures, we use in our analysis are standardized across the two datasets (i.e., NIS Tennessee sample and DOH). However, we note that the parameters of our data use agreement with the Tennessee Department of Health do not permit us to link data in the DOH to the Tennessee NIS data to compare hospitals. Full details available on request.
26 The State Inpatient Database or the State Emergency Department Database for Tennessee are not available to the public (https://www.hcup-us.ahrq.gov/db/availability_public.jsp; last accessed September 8th, 2021). DOH and NIS time series generally follow similar trends, there are clear and non-trivial differences, in particular at pivotal periods relative to the TennCare disenrollment.
Data Appendix Tables A1 and A2 report the shares of MHD and SUD hospitalizations, and total hospitalizations respectively that appear in the NIS in each year of our study period. We include only hospitals that have positive MHD or SUD hospitalizations in at least one quarter during our study period in our calculations. 27 There are substantial differences across the DOH and the NIS data suggesting that the NIS data are not representative of all community hospitals in Tennessee, which is perhaps not unexpected based on our simulation exercise and cautions from NIS administrators. For instance, in 2000 22% of all community hospitals in Tennessee appeared in the NIS while in 2004 the share had increased to 38%. In 2005 this share declined to 32%, and by 2007 the share fell to 20%. Changes in sample that are concurrent with the policy under study can lead to inaccurate estimates.
We refer to the combined NIS (for non-Tennessee states) and DOH (for Tennessee) dataset as the 'hospitalizations dataset. ' We view our large sample size for Tennessee, we have the universe of community hospitals, as an advantage over previous TennCare studies that have relied on smaller, non-state representative datasets for Tennessee. Other studies seeking to use NIS, or other datasets, to investigate single-state treatments may consider such a combination. Or, if data are not available, the potential limitation could be noted in the study.
27 Some hospitals have zero hospitalizations in a given year-quarter. When creating a percentage measure, we could not divide by zero as this value is undefined. Thus, to avoid losing these observations, we added a value of one to each hospital in our sample. The minimum for year-quarters is therefore one as opposed to zero. This change shifts the distribution but does not affect the coefficient estimates. We test whether the disenrollment influenced the probability that a hospital has any MHD or SUD hospitalizations using the empirical model outlined in Equation (1). The coefficient estimate and associated standard error for are -0.004 and 0.008. Thus, we observe no statistically significant evidence that the disenrollment influenced this probability.