Conceptual Model

Acute medical care is one service of many on which people are able to spend their time or money, and they will select a utility maximizing number of ER visits, subject to a budget constraint. I assume that ER visits do not provide any utility in and of themselves, but rather, going to the ER restores utility by alleviating or eliminating disutility that is caused by an injury or illness. To consume an ER visit, individuals incur a cost (e.g., time and money), and so only visit the ER when the utility restored by doing so exceeds the utility that could be purchased by using the same resources (e.g., time and money) on other goods or services.¹⁴ Therefore, demand for ER visits depends on the amount of utility that would be gained by going to the ER and the amount of utility that would be foregone by going.

Consistent with French et al. (2011), I assume that individuals have a latent probability of negative health shocks determined by H(X_o, ,M(X_o,X_u),D(X_o,X_u), X_u, μ), where Xo is a vector of observable individual demographic and socioeconomic

characteristics, M is a binary variable representing MUD, D is set of binary variables representing alcohol, nicotine, and/or hard drugs use disorders, Xu represents unobserved heterogeneity that may be jointly correlated with MUD and the probability of a negative

14 The monetary cost of visiting the ER is capped at $3.90 for Medicaid recipients, so time costs and

“psychic” costs of going to the ER will be the primary costs associated with ER visits.

health shock (e.g., future discount rate, health knowledge), and μ is a stochastic error term capturing factors that may affect health but are assumed to be exogenous to substance use disorders.

The probability of negative health shocks may be increased by MUD through illness (e.g., respiratory issues among marijuana smokers, or reduced time and money for investment in health stock), or through an increased probability of injury (e.g., driving while under the influence). On the other hand, the probability of health events may be decreased if, for example, individuals with MUD are less likely to participate in activities that can result in injury (e.g., less time driving, less time pursuing outdoor activities). If those with MUD are more likely to suffer adverse health events, then the expected benefit of going to the ER should be higher than among non-dependents, and ceteris paribus marijuana dependents should visit the ER more often. Conversely, if those with MUD are less likely to suffer adverse health events then their expected benefit of going to the ER should be lower, and we should see fewer visits to the ER.

While the demand for ER visits (ER) will partly (or even primarily) be determined by H, other inputs such as M, D, factors contained in Xo (e.g., relative income) or X_u (e.g., future discount rate) will also influence demand by determining the tradeoff in utility between the consumption of ER visits and the consumption of other goods (including marijuana), conditional on H.¹⁵ The full demand equation for acute medical care may thus be expressed as

15 Since data are not available on the price of acute medical care or marijuana, these factors are also contained in X_u.

ER = f(H(Xo, Xu, M, D, μ), Xo, Xu, M, D). (Eq. 1)

Since H is unobserved, the goal of the empirical model is to estimate the reduced-form equation

ER = f(Xo, Xu, M , D). (Eq. 2)

The effect of MUD is considered independently of other illicit drugs for several reasons.

First, marijuana is the most commonly used illicit drug in the United States: in 2012 roughly 7% of Americans twelve and older had used marijuana at least once in the past month (National Institute on Drug Abuse, 2014). Although the risk of dependence is estimated to be less than for other substances such as nicotine, alcohol, or other drugs, roughly one in ten individuals who ever try marijuana will at some point develop

dependence: a risk that rises to one in two among daily users (Copeland & Swift, 2009).

Second, marijuana is policy-relevant in isolation given the current political climate where the need to assess the potential costs of expanded marijuana use, and the subsequent potential for increased levels of marijuana use disorder, is a pressing issue at the state and federal level. Finally, there is reason to believe that the effect of marijuana on demand for acute medical care may differ to that of other illicit drugs. In general, marijuana is substantially cheaper in monetary terms than many other illicit drugs (Fries, Anthony, Cseko, Gaither, & Sculman, 2008) and due to the relative prevalence of marijuana is also likely cheaper in time costs to obtain. Moreover, consumption methods for marijuana are generally less prone to directly cause disease (e.g., infection), or to result in direct health

shocks from accidental overdose or substance adulteration (Ashton, 2001; British Medical Association, 2013).

One remaining identification issue is that Xu is not observed. Since M is a function of X_u, failure to condition on these unobservable factors will produce estimates that are confounded by the joint relationship of Y and M to Xu. To account for this, I utilize a nonlinear instrumental variables method introduced by Terza (1998, 2009). By assuming that X_u is continuous and standard normally distributed conditional on

observable covariates (and with at least one valid instrument that is correlated with M and independent of Y conditional on X_o), I am able to condition on X_u, which renders M exogenous to Y. This approach will be addressed further in the empirical section.

5. Data and Variables