An Evaluation of

Prescription Drug Monitoring Programs

Ronald Simeone and Lynn Holland

Simeone Associates, Inc.

September 1, 20061

Abstract

This research examines the effects of Prescription Drug Monitoring

Programs (PDMPs) on the supply and abuse of prescription drugs. Information from the Automation of Reports and Consolidated Orders System

(ARCOS) is used to develop measures of supply, and information from

the Treatment Episode Data Set (TEDS) is used to develop measures of

abuse. Practical considerations lead us to focus on Schedule II pain

relievers and stimulants, and composite measures for these two classes

of drugs are developed. We estimate both aggregate and individual response models. The aggregate model suggests that PDMPs reduce the

per capita supply of prescription pain relievers and stimulants and in so

doing reduce the probability of abuse for these drugs. The evidence also

suggests that states which are proactive in their approach to regulation

are more effective in reducing the per capita supply of prescription pain

relievers and stimulants than states which are reactive in their approach

to regulation. The individual response model confirms these findings.

It is important to note that the probability of pain reliever abuse is actually higher in states that have PDMPs than in states that do not. But our

analysis demonstrates that in the absence of such programs the probability of abuse would be higher still.

Key words: drug abuse, multilevel model, binary response model.

1 We would like to thank Dr. Roger Vaughan, Department of Biostatistics, Columbia University for his review and comments. Please direct all correspondence to Dr. Ronald Simeone, Simeone Associates Inc.,

220 Lancaster Street, Albany, New York, 12210 (email ron@simeoneassociates.com). This project was sponsored by the United States Department of Justice, Office of Justice Programs, Bureau of Justice Assistance (No. 2005PMBXK189).
1 Introduction

Twenty states have implemented systems to monitor the prescription and sale of drugs identified as

controlled substances by the Drug Enforcement Administration (DEA). Another twenty-three states

are in the process of designing or planning to design such systems. This growth is fueled in part by

the Harold Rogers Prescription Drug Monitoring Program (PDMP). The competitive grant program,

managed by the Bureau of Justice Assistance (BJA) in the Office of Justice Programs (OJP), is

intended to support states wishing to enhance local capabilities to monitor the prescription and sale

of controlled substances.

States are eligible for these grants if they have in place, or have pending, an enabling statute or

regulation requiring the submission of prescription data on controlled substances to a central database.

States may also apply if they can introduce legislation or regulations for a prescription monitoring

program before the annual OJP Hal Rogers Program grant cycle begins. Prescription Drug Monitoring

Programs as they exist at the state level serve a variety of ends, but all are intended ultimately to

reduce the abuse of controlled pharmaceutical substances.

We focus on two possible channels by which a PDMP might affect the probability of prescription

drug abuse. The first is indirect, operating through the supply of controlled substances. If a PDMP

reduces the supply of prescription drugs, then this in turn may reduce the probability of abuse. The

second is direct: when supply is held constant, a PDMP may itself reduce the probability of abuse. The

former may be indicative principally of the effect that regulation has on prescribing behavior, whereas

the latter may be indicative principally of the effect that regulation has on dispensing behavior.

1
The purpose of this research is to provide a statistical basis for assessing these effects. To this

end, we propose a series of multilevel models for estimating the relationships among the presence of

a PDMP, supply, and abuse.

The specification of a two-equation multilevel model that makes use of repeated measurements of

state characteristics provides a starting point for our analysis, and allows both the supply and abuse

measures to be treated as endogenous to the PDMP measures. These relationships are examined

while controlling for other state-level characteristics that may be relevant to our task.

But individuals, not states, choose to abuse drugs. Hence, results based on aggregate data can

at best only suggest causality. At worst, they allow us to fall victim to the classic ecological fallacy

(Robinson [1]; for discussion of circumstances under which generalization from aggregate to individual

data is appropriate see Freedman et al. [2]; Greenland and Robins [3]; Freedman et al. [4]; Neeleman

and Lewis [5]). To address this problem, we propose another multilevel model that makes use of

repeated measurements made of individual characteristics that are likely to affect behavior.

Both our aggregate and our individual response models will allow relationships to be examined

over time. Therefore, it is necessary that we select a common period during which data from all of

our sources will be available for use in our analysis. This is the interval beginning January 1, 1997

and ending December 31, 2003.

We begin by discussing issues related to measurement in Section 2. An aggregate model involving

equations for supply and abuse is presented and estimated in Section 3. An individual response model

for abuse is presented and estimated in Section 4. Findings are discussed and directions for future

research are suggested in Section 5.

2
2 Measurement

The fundamental structure of our model, whether aggregate or individual response, involves three

sets of measures: those related to the PDMP, those related to supply, and those related to abuse.

Our ability to define these measures is constrained by data that are currently available for use in our

analysis. The actual choices that we make are guided by our desire to develop a parsimonious model

that avoids misspecification.

PDMP data. In support of our research the National Alliance for Model State Drug Laws

(NAMSDL) has assembled data that allow sources of variation in PDMP implementation to be examined over time. One of the most important of these is the manner in which cases are identified

and investigated. In some states the PDMP is "reactive" in nature, generating "solicited reports"

only in response to a specific inquiry made by a prescriber, dispenser, or other party with appropriate

authority. In other states the PDMP is "proactive" in nature, identifying and investigating cases, and

generating "unsolicited reports" when it deems that this is warranted. It is important to maintain

this distinction since program effects may vary by mode of implementation. Two measures of PDMP

status are therefore constructed for each state, for each year. The first involves coding the presence or

absence of any PDMP as 1 or 0 (respectively). The second involves coding the presence or absence

of a proactively monitoring PDMP in the same manner.

Prescription Drug Monitoring Programs also differ in their scope of coverage, at one extreme

including only Schedule II drugs, and at the other including Schedule II-V drugs. Coverage is

cumulative; any state that regulates the prescription and sale of Schedule III drugs also regulates

the prescription and sale of Schedule II drugs; any state that regulates the prescription and sale of

Schedule IV drugs also regulates the prescription and sale of Schedule II and III drugs, and so on.

3
Because we seek to examine whether the presence of a PDMP reduces supply it is reasonable

to define supply in a manner consistent with the scope of its influence. The most straightforward

way of accomplishing this is to limit elements of supply to Schedule II drugs. But the consequences

associated with excluding Schedule III-V drugs from our analysis warrants additional consideration.

Supply data. Our source of data on supply is the Automation of Reports and Consolidated Orders System (ARCOS) maintained by the DEA Office of Diversion Control (ODC). ARCOS includes

records on retail sales of twelve controlled substances (amphetamine, cocaine, codeine, fentanyl, hydrocodone, hydromorphone, methamphetamine, methylphenidate, meperidine, methadone, morphine,

and oxycodone). In support of our research the ODC has aggregated transactions for these drugs to

the zip-code and state level and provided data on the number of grams sold for each year during our

observation period.

Tables I-IV provide information on the relationship between drug schedule and four types of drugs:

"pain relievers", "tranquilizers", "stimulants" and "sedatives." This categorization scheme appears

often in drug abuse research and has been adopted as a convention by the National Survey on Drug Use

and Health (NSDUH) and other federal reporting systems. The tables were developed by Carnevale

Associates, LLC (CALLC) using the Centers for Disease Control (CDC) National Drug Code (NDC)

database. Generic drugs (shaded rows) and brand-name products are cross-classified by schedule for

pain relievers, tranquilizers, stimulants and sedatives.

Looking at the tables we see that the ARCOS drugs are principally Schedule II pain relievers

(opioid agonists including codeine, fentanyl, hydrocodone, hydromorphone, meperidine, methadone,

morphine, and oxycodone) and Schedule II stimulants (dopamine agonists and reuptake inhibitors

including amphetamine, cocaine, methamphetamine, and methylphenidate).

4
Table I: Pain Relievers

Drug Schedule II Schedule III Schedule IV Schedule V

buprenorphine x

Buprenex® x

codeine x

Tylenol with Codeine® x

dextropropoxyphene x

Darvocet® x

Darvon® x

fentanyl x

Actiq® x

Duragesic® x

Oralet® x

Sublimaze® x

hydrocodone x

Hycomine® x

Lorcet® x

Lortab® x

Lortab ASA® x

Vicodin® x

Vicoprofen® x

hydromorphone x

Dilaudid® x

Palladone® x

meperidine x

Demerol® x

Mepergan® x

methadone x

Dolophine® x

morphine x

Kadian® x

MS-Contin® x

MSIR® x

Oramorph SR® x

RMS® x

Roxanol® x

oxycodone x

OxyContin® x

OxyIR® x

Percocet® x

Percodan® x

Tylox® x

pentazocine x

Talacen® x

Talwin® x

Talwin Nx® x

5
Table II: Tranquilizers

Drug Schedule II Schedule III Schedule IV Schedule V

alprazolam x

Xanax® x

chlordiazepoxide x

Librium® x

Limbitrol® x

clonazepam x

Klonopin® x

clorazepate x

Tranxene® x

diazepam x

Valium® x

halazepam x

Paxipam® x

lorazepam x

Ativan® x

oxazepam x

Serax® x

prazepam x

Centrax® x

quazepam x

Doral® x

meprobamate x

Equanil® x

Miltown® x

Our research focuses on the indirect and direct effects of PDMPs on abuse. When assessing the

indirect effects we estimate the relationship between the presence of a PDMP and supply, and the

relationship between supply and abuse. It is therefore not unreasonable to limit our definition to

include only drugs that are subject to PDMP control and which have significant abuse potential.

Defining supply in terms of Schedule II drugs leads us to exclude codeine and hydrocodone since

they are Schedule II drugs only in their generic forms. The most common brand name products for

codeine (Tylenol with Codeine°R ) and hydrocodone (Lortab°R , Lorcet°R and Vicodin°R ) are regarded

as having less potential for abuse, thus their status as Schedule III drugs.

6
Table III: Stimulants

Drug Schedule II Schedule III Schedule IV Schedule V

amphetamine x

Adderall® x

Biphetamine® x

Dexedrine® x

Dextrostat® x

benzphetamine x

Didrex® x

diethylpropion x

Tenuate® x

Tepanil® x

mazindol x

Mazanor® x

Sanorex® x

methamphetamine x

Desoxyn® x

methylphenidate x

Concerta® x

Methylin® x

Ritalin® x

phendimetrazine x

Bontril® x

Plegine® x

Prelu-27® x

phentermine x

Adipex® x

Fastin® x

Ionamin® x

Lonamin® x

There may be another argument for limiting our analysis to include Schedule II pain relievers

and stimulants only. In examining the impact of PDMPs on supply we would ideally make use of

information on all sources of prescription drugs that might become candidates for abuse. Internet

sales therefore become a concern because they constitute an unmeasured component of supply in

each state. From a statistical perspective this problem would be less serious if the preponderance of

internet sales involved Schedule III-V rather than Schedule II drugs.

7
There is some limited evidence to suggest that this may be the case. As the result of a massive investigation (Cyber Chase) conducted by the Organized Crime Drug Enforcement Task Force

(OCDETF) a number of significant insights were gained into the operation of the Bansal organization, an India-based group that supplied controlled substances to rogue pharmacies operating Internet

Facilitation Centers (IFCs) in the United States.

The indictment (filed in the United States District Court for the Eastern District of Pennsylvania)

indicates that during the period from "August 2004...(to)...March 2005 the defendants and others

sold at least 400,000 dosage units of controlled substance pharmaceutical drugs in Schedule II, at

least 2,700,000 dosage units of controlled substance pharmaceutical drugs in Schedule III, and at least

12,287,000 dosage units of controlled substance pharmaceutical drugs in Schedule IV..." to IFCs.

In this case the preponderance of sales clearly involved Schedule III and IV drugs; and the majority

of Schedule II sales involved codeine liquid. If this portfolio were representative of all internet-based

trafficking activity, then our operational definition of supply would effectively eliminate at least one

confounding factor.

It is also important to differentiate drugs that are produced and distributed legally from drugs

that are produced and distributed illegally. Prescription Drug Monitoring Programs do not regulate

the production and distribution of illicit drugs. And this leads us to limit our definition of supply

further, excluding cocaine and methamphetamine from consideration.

The elements of supply thus become fentanyl, hydromorphone, meperidine, methadone, morphine

and oxycodone (which we define collectively as pain relievers in subsequent sections) and amphetamine

and methylphenidate (which we define collectively as stimulants in subsequent sections).

8
Table IV: Sedatives

Drug Schedule II Schedule III Schedule IV Schedule V

amobarbital x

Amytal® x

Tuinal® x

aprobarbital x

Alurate® x

butabarbital x

Butisol® x

butalbital x

Fiorina® x

chloral hydrate x

Aquachloral® x

Noctec® x

estazolam x

ProSom® x

flurazepam x

Dalmane® x

mephobarbital x

Mebaral® x

methohexital x

Brevital® x

pentobarbital x

Nembutal® x

phenobarbital x

Luminal® x

secobarbital x

Seconal® x

talbutal x

Lotusate® x

temazepam x

Restoril® x

thiamylal x

Surital® x

thiopental x

Pentothal® x

triazolam x

Halcion® x

zaleplon x

Sonata® x

zolpidem x

Ambien® x

9
Because states differ in population size it is necessary to establish some appropriate basis for

making comparisons among them. Thus, our measures of supply are defined as grams per capita

for fentanyl, hydromorphone, meperidine, methadone, morphine and oxycodone (pain relievers); and

amphetamine and methylphenidate (stimulants). These are calculated for each state, for each year.

The fact that there are a number of controlled substances under investigation and that each may

be regarded as endogenous relative to the presence of a PDMP causes us to consider whether there

are any methods that might be used to summarize our drug-specific per capita measures as one or

more composite measures.

Fentanyl, hydromorphone, meperidine, methadone, morphine and oxycodone are all opioid agonists

that have therapeutic utility because of their analgesic properties. The relative potency of these drugs

has been examined in some detail and therefore provides guidance to the construction of a general

measure of supply for pain relievers.

Findings from several surveys of studies that have attempted to establish equianalgesic dose ratios

for opioid agonists are presented in Table V (Gordon et al. [6]; Anderson et al. [7]; Pereira et al. [8]).

Since research in this area often involves substitution of one drug for another, the order of rotation is

regarded as important and therefore reported both in the literature and in our table.

All ratios presented are expressed by route of administration (PO = oral, SC = subcutaneous,

IV = intravenous) and relative to morphine. Therefore (reading across the first row entry in Table

V) when rotating between morphine and fentanyl 1 mg. fentanyl administered subcutaneously is

equivalent to 68 mg. morphine administered subcutaneously.

10
Table V: Equianalgesic Doses for Pain Relievers

Drug Rotation PO [ref] SC [ref] IV [ref]

Fentanyl Morphine-Fentanyl 68.00 [9]

Morphine-Fentanyl 84.50 [10]

Morphine-Fentanyl 70.00 [11]

(mean) 74.17 74.17

Hydromorphone Morphine-Hydromorphone 5.33 [12] 4.92 [13] 3.55 [14]

Morphine-Hydromorphone 5.71 [13]

Hydromorphone-Morphine 3.80 [12] 4.00 [13]

Hydromorphone-Morphine 3.45 [13]

(mean) 4.57 4.46 3.55

Meperidine N/A 0.10 [6] 0.13 [6]

(mean) 0.10 0.13

Methadone Morphine-Methadone 11.36 [15]

Morphine-Methadone 11.11 [16]

Morphine-Methadone 8.25 [15]

(mean) 10.24

Oxycodone N/A 0.71 [17]

Morphine-Oxycodone 1.33 [18] 0.70 [19]

Morphine-Oxycodone 1.50 [20]

Oxycodone-Morphine 1.50 [18] 0.70 [19]

Oxycodone-Morphine 1.50 [20]

(mean) 1.46 0.71 0.70

11
We use the information presented in Table V to develop a composite measure for pain relievers,

weighting the number of grams for each drug (fentanyl, hydromorphone, meperidine, methadone,

and oxycodone) by the corresponding mean equianalgesic oral dose ratio presented there. Morphine

serves as our calibration measure and receives a weight of 1. Summing over the weighted values and

dividing by the corresponding population produces a composite per capita measure for pain relievers

("PR composite"). The composite measure is calculated for each state, for each year.1

Fentanyl poses a problem because it is not ordinarily administered orally (although there is a

lozenge available that is intended for sublingual use). We assume the relative potency of fentanyl

administered orally to be equal to its relative potency when administered subcutaneously. While there

is no direct evidence in support of this calculation, there is indirect evidence demonstrating similarity

of equianalgesic dose ratios between hydromorphone administered orally and subcutaneously, and

fentanyl and hydromorphone administered subcutaneously. By deduction, the assignment of this

value seems reasonable. In any case, since our objective is simply to maintain some approximation to

relative potency our assumption is not likely to introduce a significant source of measurement error.

A measure comparable to PR composite is developed for stimulants ("ST composite") where,

following convention established by standard dose-equivalence tables, the ratio of amphetamine to

methylphenidate is assumed to be 2:1. As before, the composite measure is calculated for each

state, for each year.

1This approach is conceptually similar to various methods that have been used to estimate the availability of illicit

drugs (heroin and cocaine). In such cases it is necessary to control for the presence of dilutants and adulterants.

Standard measures of "grams pure" are therefore developed that can be examined over time and relative to other factors

such as price (see for example Arkes et al. [21] who make use of a somewhat more refined model that incorporates

information on consumer expectations).

12
The composites are intended to provide potency-adjusted measures of the total supply of pain

relievers and stimulants in each state. Since the drugs in a particular group differ in potency and

may not all move together in the same direction over time they may exert mutually offsetting effects

on supply. The composites allow us to compensate for this. They also offer substantial consistency

with the treatment admission-based measures of pain reliever and stimulant abuse that will be used

in our analysis (we discuss this issue at length below).

There are some general limitations associated with defining supply in terms of grams per capita.

Anecdotal evidence suggests that drugs are not necessarily sold to patients in the same area in which

they are purchased by dispensers. A large mail-order pharmaceutical house located in a particular

state may thus distort estimates of supply that are based on purchases made by dispensers alone. At

the same time, research on psychostimulants has produced empirical evidence demonstrating a strong

relationship between per capita measures of grams ordered and the number of prescriptions filled at

the zip code level (Bokhari et al. [22]).

Abuse data. The Treatment Episode Data Set (TEDS) maintained by the Substance Abuse

and Mental Health Services Administration (SAMHSA) constitutes our source of data on abuse. The

system includes all individuals admitted to state-licensed drug treatment programs in the United

States. Data are captured on state, Metropolitan Statistical Area (MSA), and Core-Based Statistical

Area (CBSA); on demographics and prior treatment history; and perhaps most importantly for our

purposes, on primary, secondary and tertiary substances of abuse. Since our measures of supply are

limited to include Schedule II pain relievers and stimulants we constrain abuse accordingly.

13
Our measure for pain relievers is defined by TEDS codes for "non-prescription methadone" and

"other opiates and synthetics" (which implicitly includes hydromorphone, meperidine, morphine and

oxycodone); and our measure for stimulants is defined by TEDS codes for "other amphetamines"

(which explicitly excludes methamphetamine) and "other stimulants" (which is assumed to include

methylphenidate). Any individual admitted to treatment with an indication that the primary, secondary or tertiary substance of abuse is a prescription pain reliever receives a value of 1 for the pain

reliever measure (0 otherwise); and any individual admitted to treatment with an indication that the

primary, secondary or tertiary substance of abuse is a prescription stimulant receives a value of 1 for

the stimulant measure (0 otherwise). Per capita measures of pain reliever and stimulant abuse are

constructed by summing over these individual values and dividing by the corresponding population

for each state, for each year.

Defining abuse based upon treatment admissions carries with it some limitations as well. Although

TEDS includes records on "first admissions" only (thereby excluding all transfer activity) there is still

some tendency for one individual to experience multiple admissions during a calendar year. This is

not common; nonetheless, the phenomenon does occur. Throughout the text we refer to "individuals

admitted to treatment" with this caveat in mind.

It is also important to remember that admission to treatment represents the culmination of a

pattern of behavior in which experimentation leads to abuse and eventually to dependence. But many

people who abuse drugs never seek treatment. And our own research shows that the probability of

seeking treatment varies as a function of individual characteristics (Simeone et al. [23,24]). Thus,

without modeling in some way the conditional probability of admission to treatment, we may be able

to generalize only to those who actually seek treatment during a particular period of time.

14
3 A Multilevel Aggregate Model

One factor that figures prominently in the decision to use a particular drug is the local availability of

that drug. A relatively low supply may indicate a reduced probability of prescription for the drug;

it may indicate a reduced probability that the drug will be diverted to the illicit market; and it may

indicate a reduced level of convenience associated with obtaining the drug via illicit means.

Figures 1-8 provide information on supply over time for each pain reliever and stimulant included

in our analysis. Per capita measures are transformed to rates per 100,000 as an aid to the reader.

We distinguish between states that do not have a PDMP program ("non-PDMP") and states that do

("PDMP"). There are upward secular trends for all pain relievers with the exception of meperidine;

and rates for pain relievers are higher in non-PDMP states than in PDMP states for all pain relievers

with the exception of hydromorphone.2 The difference in rates between non-PDMP and PDMP states

appears to be especially pronounced for oxycodone (Figure 6). Findings are similar for stimulants.

There are secular trends for amphetamine and methylphenidate; and in both cases the rates are higher

for non-PDMP states than for PDMP states.

Figures 9-16 provide the same information presented in Figures 1-8 with the exception being that

here we distinguish between states that do not have a PDMP which monitors proactively ("nonXPDMP") and states that do ("XPDMP"). The findings are similar although the differences in

rates that exist between non-XPDMP states and XPDMP states may be more pronounced than the

differences in rates that exist between non-PDMP and PDMP states.

2Methadone is something of a special case since it is prescribed both as a pain reliever and as a treatment for heroin

addiction. Figure 4 depicts sales to pharmacies only. If we examine sales to Narcotics Treatment Providers (NTPs)

we see an upward secular trend in non-PDMP states; but a higher per capita rate generally in PDMP states. This

likely reflects the relative sizes of heroin-using populations in non-PDMP and PDMP states.

15
Figure 1. Fe ntanyl (Grams per 100,000)

0

20

40

60

80

100

120

140

1997 1998 1999 2000 2001 2002 2003

non-PDM P PDMP

Figure 2. Hydromorphone (Grams per 100,000)

0

50

100

150

200

250

1997 1998 1999 2000 2001 2002 2003

non-PDM P PDMP

Figure 3. M epe ridine (Grams per 100,000)

0

500

1,000

1,500

2,000

2,500

3,000

1997 1998 1999 2000 2001 2002 2003

non-PDM P PDMP

Figure 4. M e thadone (Grams pe r 100,000)

0

200

400

600

800

1,000

1,200

1,400

1,600

1997 1998 1999 2000 2001 2002 2003

non-PDM P PDMP

Figure 5. M orphine (Grams pe r 100,000)

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

1997 1998 1999 2000 2001 2002 2003

non-PDM P PDMP

Figure 6. Oxycodone (Grams pe r 100,000)

0

2,000

4,000

6,000

8,000

10,000

12,000

1997 1998 1999 2000 2001 2002 2003

non-PDM P PDMP

Figure 7. Amphe tamine (Grams per 100,000)

0

500

1,000

1,500

2,000

2,500

1997 1998 1999 2000 2001 2002 2003

non-PDM P PDMP

Figure 8. M e thylphe nidate (Grams pe r 100,000)

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

1997 1998 1999 2000 2001 2002 2003

non-PDM P PDMP

16
Figure 9. Fe ntanyl (Grams pe r 100,000)

0

20

40

60

80

100

120

140

1997 1998 1999 2000 2001 2002 2003

non-XPDM P XPDMP

Figure 10. Hydromorphone (Grams per 100,000)

0

50

100

150

200

250

1997 1998 1999 2000 2001 2002 2003

non-XPDM P XPDMP

Figure 11. M e pe ridine (Grams pe r 100,000)

0

500

1,000

1,500

2,000

2,500

1997 1998 1999 2000 2001 2002 2003

non-XPDM P XPDMP

Figure 12. M e thadone (Grams pe r 100,000)

0

200

400

600

800

1,000

1,200

1,400

1,600

1997 1998 1999 2000 2001 2002 2003

non-XPDM P XPDMP

Figure 13. M orphine (Grams pe r 100,000)

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

1997 1998 1999 2000 2001 2002 2003

non-XPDM P XPDMP

Figure 14. Oxycodone (Grams pe r 100,000)

0

2,000

4,000

6,000

8,000

10,000

12,000

1997 1998 1999 2000 2001 2002 2003

non-XPDM P XPDMP

Figure 15. Amphe tamine (Grams pe r 100,000)

0

500

1,000

1,500

2,000

2,500

1997 1998 1999 2000 2001 2002 2003

non-XPDM P XPDMP

Figure 16. M e thylphe nidate (Grams pe r 100,000)

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

1997 1998 1999 2000 2001 2002 2003

non-XPDM P XPDMP

17
Figures 17-18 provide information on our summary measures for pain relievers (PR composite)

and stimulants (ST composite). As before, we differentiate between non-PDMP and PDMP states.

We see that the combination and weighting of individual measures produces greater linearization for

both pain relievers and stimulants. In each case there is a strong secular trend with rates higher in

non-PDMP states than in PDMP states.

Figures 19-20 provide the same information on our summary measures as that presented in Figures

17-18 but here we distinguish between non-XPDMP and XPDMP states. We see that the patterns

initially identified in Figures 17-18 persist and are perhaps more pronounced for both pain relievers

and stimulants.

Figure 17. PR Composite (Grams per 100,000)

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

50,000

1997 1998 1999 2000 2001 2002 2003

non-PDM P PDMP

Figure 18. ST Composite (Grams per 100,000)

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

1997 1998 1999 2000 2001 2002 2003

non-PDM P PDMP

Figure 19. PR Composite (Grams pe r 100,000)

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

50,000

1997 1998 1999 2000 2001 2002 2003

non-XPDM P XPDM P

Figure 20. ST Composite (Grams per 100,000)

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

1997 1998 1999 2000 2001 2002 2003

non-XPDM P XPDMP

18
Figures 21-22 provide information on abuse involving pain relievers ("PR admissions") or stimulants ("ST admissions"). Per capita measures are again transformed to rates per 100,000 and we

begin by distinguishing between non-PDMP states and PDMP states. There is a secular trend for

pain relievers but not for stimulants. The rate of pain reliever admissions is lower in non-PDMP

states than in PDMP states; and the rate of stimulant admissions is higher in non-PDMP states than

in PDMP states. Figures 23-24 provide the same information as that presented in Figures 21-22

except that here we distinguish between non-XPDMP and XPDMP states. The findings essentially

mirror those described above.

Figure 21. PR Admissions (Number per 100,000)

0

5

10

15

20

25

30

35

40

1997 1998 1999 2000 2001 2002 2003

non-PDM P PDMP

Figure 22. ST Admissions (Numbe r pe r 100,000)

0

5

10

15

20

25

1997 1998 1999 2000 2001 2002 2003

non-PDM P PDMP

Figure 23. PR Admissions (Number per 100,000)

0

5

10

15

20

25

30

35

40

1997 1998 1999 2000 2001 2002 2003

non-XPDM P XPDMP

Figure 24. ST Admissions (Numbe r pe r 100,000)

0

5

10

15

20

25

1997 1998 1999 2000 2001 2002 2003

non-XPDM P XPDMP

For completeness we provide numerical information in Table VI related to the trends that have

been discussed in this section. Material is presented there on rates per 100,000 for the separate

drugs that we have characterized as pain relievers and stimulants, for our composite measures of pain

relievers and stimulants, and for treatment admissions that involve pain relievers and stimulants.

19
Table VI: Summary of Rates per 100,000

1997 2003 Change 1997 2003 Change

Fentanyl 28 115 88 27 103 76

Hydromorphone 83 196 113 96 202 107

Meperidine 2,488 2,259 -229 1,708 1,375 -333

Methadone 188 1,422 1,234 193 1,132 939

Morphine 2,235 4,648 2,413 2,075 3,863 1,788

Oxycodone 1,973 11,263 9,291 1,249 7,314 6,064

Amphetamine 576 2,254 1,679 444 1,690 1,246

Methylphenidate 3,387 4,671 1,283 2,783 4,013 1,231

PR composite 9,714 45,333 35,619 8,503 34,857 26,354

ST composite 4,539 9,179 4,641 3,671 7,394 3,724

PR admissions 13 33 20 15 35 19

ST admissions 18 20 1 9 10 1

1997 2003 Change 1997 2003 Change

Fentanyl 28 117 89 25 93 67

Hydromorphone 83 196 113 100 205 104

Meperidine 2,336 2,085 -251 1,650 1,208 -442

Methadone 186 1,375 1,189 200 1,057 858

Morphine 2,219 4,469 2,250 2,034 3,762 1,727

Oxycodone 1,936 10,664 8,727 1,004 6,223 5,218

Amphetamine 562 2,190 1,628 413 1,494 1,081

Methylphenidate 3,373 4,673 1,299 2,548 3,636 1,088

PR composite 9,671 43,924 34,253 8,059 31,613 23,553

ST composite 4,497 9,052 4,555 3,374 6,624 3,250

PR admissions 13 34 21 17 34 18

ST admissions 17 17 0 8 11 2

non-PDMP PDMP

Pain Relievers

Stimulants

Composites

Admissions

Pain Relievers

Stimulants

Composites

Admissions

non-XPDMP XPDMP

Figures 1-24 would seem to indicate that PDMPs reduce supply while having a mixed impact on

abuse. But visual inspection alone does not allow us to identify mediating factors or to determine

whether PDMPs account for the differences that we observe. For this we will need a mathematical

model of the phenomena under study.

20
The model. We seek to examine changes over time in our measures of supply and abuse and to

make comparisons between non-PDMP and PDMP states. Consistent with the preceding discussion

we will differentiate between states that are reactive in their approach to prescription monitoring and

states that are proactive in their approach to prescription monitoring. In an attempt to identify

demographic characteristics likely to be related to the supply and abuse of prescription drugs we will

introduce measures derived from United States Census Bureau and United States Bureau of Labor

Statistics (BLS) data.

As mentioned earlier, the aggregate model allows us to examine two possible channels by which a

PDMP might affect the probability of prescription drug abuse. The first is indirect, operating through

the per capita supply of controlled substances. A model for supply might be specified as follows,

SUP PLYkt = α0 + α1MALEkt + α2WHITEkt + α3AGEkt + α4UNEMPkt + α5HLT HINSkt

+ α6INCOMEkt + α7TIMEt + α8PDMPkt + α9XPDMPkt + u1k + e1kt (1)

where the subscript for drug is suppressed in the interest of parsimony, SUP P LYkt is the per capita

supply of prescription drugs in state k at time t, MALEkt is the proportion male, WHITEkt is the

proportion white, AGEkt is the mean age, UNEMPkt is the proportion unemployed, HLTHINSkt

is the proportion with health insurance, INCOMEkt is the per capita personal income, and TIMEt

is measured as year/1000. PDMPkt and XPDMPkt are defined, respectively, as follows,

PDMPkt =

⎧

⎪⎪⎨

⎪⎪⎩

1 if state k is covered by a PDMP at time t

0 otherwise

(2)

21
XPDMPkt =

⎧

⎪⎪⎨

⎪⎪⎩

1 if state k is proactively monitoring at time t

0 otherwise

(3)

Finally, u1k represents an unobserved, randomly distributed state effect and e1kt is a randomly distributed error term. We assume

E(u1k) = E(e1kt)=0

V ar(u1k) = σ2

u1

V ar(e1kt) = σ2

e1

Cov(e1kt, u1k)=0

The second channel is more direct. The probability of abuse may be related to supply, with the

presence of a PDMP having an independent effect. A model for abuse might be specified as follows,

ABUSEkt = β0 + β1MALEkt + β2WHITEkt + β3AGEkt + β4UNEMPkt

+ β5HLT HINSkt + β6INCOMEkt + β7TIMEt + β8PDMPkt + β9XPDMPkt

+ β10HEROINkt + β11COCAINEkt + β12SUP PLYkt + u2k + e2kt (4)

where ABUSEkt, HEROINkt, and COCAINEkt are the per capita rates for admissions involving

prescription drugs, for admissions with heroin as the primary substance of abuse, and for admissions

with cocaine as the primary substance of abuse, respectively, in state k at time t and where we assume

E(u2k) = E(e2kt)=0

V ar(u2k) = σ2

u2

V ar(e2kt) = σ2

e2

Cov(e2kt, u2k)=0

22
Our interest in examining the possible relationship between prescription drug abuse and illicit

drug use motivates the inclusion of HEROINkt and COCAINEkt in Equation (4). It would not be

surprising to find per capita admissions for heroin as the primary substance of abuse associated with

per capita admissions for pain relievers (which given our operational definition might be the secondary

or tertiary substance of abuse). Heroin and prescription pain relievers are both opioid agonists and

therefore to some degree substitutable entities. The same reasoning holds true regarding per capita

admissions for cocaine as the primary substance of abuse and per capita admissions for stimulants

(again as the secondary or tertiary substance of abuse) since both cocaine and prescription stimulants

are dopaminergic. Interaction terms will be examined as well but are not represented above.

Equations (1) and (4) together constitute a multi-level simultaneous system which could be solved

by ordinary least squares were it not for the random effects terms. But it is not practical to propose

a fixed-effects model here due to limited sample size (states are monitored over seven time periods

producing only 357 observations). Consistent with arguments by Teachman et al. [25] we therefore

treat idiosyncratic and unmeasured differences that exist among states as nuisance parameters. The

system is estimated for each of our composite measures using the SAS GLIMMIX procedure.

Results. Table VII presents information on the final SUP P LY models for pain relievers (PR

composite) and stimulants (ST composite). All coefficients are significant at the .0001 level. The

equations for pain relievers and stimulants are quite similar. Both indicate positive effects for TIME;

and both indicate a positive change in intercept and a negative change in slope associated with

XPDMP and TIME ∗ XPDMP. The latter terms are consistent with the lower grams per capita

trajectories for pain reliever and stimulant composites observed in XPDMP states (and depicted in

Figures 19-20).

23
Table VII: Supply Estimates

Intercept TIME XPDMP TIME*XPDMP

PR composite -114.8300 57.5336 36.4649 -18.2416

s.e. 2.8216 1.4107 4.7973 2.3985

t Value -40.70 40.78 7.60 -7.61

pr>t <.0001 <.0001 <.0001 <.0001

ST composite -15.7870 7.9265 4.4720 -2.2403

s.e. 0.3592 0.1796 0.6107 0.3053

t Value -43.95 44.13 7.32 -7.34

pr>t <.0001 <.0001 <.0001 <.0001

Table VIII presents information on the final ABUSE models for pain relievers and stimulants.

Measures involving treatment admissions are rescaled by a factor of 100,000. All coefficients are

significant at the .0006 level. The results indicate that ABUSE of pain relievers (PR admissions)

is positively related to AGE, HEROIN and SUP P LY (PR composite). The HEROIN finding is

consistent with substitution among opioid agonists. Similarly, ABUSE of stimulants (ST admissions)

is positively related to COCAINE and SUP P LY (ST composite). The COCAINE finding is

consistent with substitution among dopaminergic agents.

Table VIII: Abuse Estimates

Intercept AGE HEROIN COCAINE PR composite ST composite

PR admissions -201.2607 5.6591 0.1400 54.2018

s.e. 55.0075 1.5554 0.0150 5.1124

t Value -3.66 3.64 9.36 10.60

pr>t 0.0006 0.0003 <.0001 <.0001

ST admissions 0.0663 77.0654

s.e. 0.0149 18.5215

t Value 4.44 4.16

pr>t <.0001 0.0001

Taken together these findings suggest that PDMPs (particularly those which monitor proactively)

play a role in reducing supply and in so doing have an indirect effect on abuse. But in order to

assess whether variability in supply actually affects the decision to abuse prescription drugs it will be

necessary to develop an individual response model. We pursue this task in the following section.

24
4 A Multilevel Individual Response Model

The aggregate model is informative in that it allows us to examine states as observable units over

time, and to assess formally whether there are differences that exist in supply or abuse which may

be attributable to the action of a PDMP. But models at this level do not allow us to understand

much about individual choice. And one of the things that we are interested in learning more about is

whether the presence of a PDMP, either through its effect on supply or directly, affects individual drugusing behavior. For this, we develop a multilevel model that focuses on drug choice as a function

of both aggregate and individual factors. The specification of an empirical model to test for the

impact of a PDMP draws upon the rational addiction literature. The theory of rational addiction

rests on the notion that forward-looking individuals weigh the present value of the benefits of abusing

an addictive substance against the present value of its associated costs, where costs and benefits are

measured in terms of utility (Becker and Murphy [26]; Becker et al. [27]). Empirical results stemming

from this research indicate that the demand for addictive substances is sensitive to changes in cost

(Saffer and Chaloupka [28]; Grossman et al. [29]; Grossman [30]). Phenomena that increase the cost

in utility associated with the abuse of a particular substance include an increase in its own price,

a reduction in its availability, a decrease in the price of substitute goods, and an increase in the

price of complementary goods. All things being equal, the existence of a PDMP can be assumed to

reduce the availability of prescription drugs and thereby reduce their demand relative to illicit drugs.

The existing literature gives no definitive conclusion as to how addictive substances enter the utility

function jointly. Grossman et al. [31] cite several studies which tentatively suggest that cigarettes,

alcohol, and illegal drugs may be complements. However, to the best of our knowledge, there is no

empirical work documenting similarly the relationship between illicit and prescription drugs.

25
The Model. As before, we assume that a PDMP operates by regulating prescribing and dispensing behavior. Within the context of this model both the presence of a PDMP and supply are

regarded as exogenous to abuse. We make use of aggregate measures for PDMP and supply and

individual response measures for abuse. The relationships between the aggregate measures and abuse

may be mediated by other individual response measures: gender, race, age, employment status, and

heroin or cocaine as the primary substance of abuse. Unfortunately, individual response measures

for insurance coverage and income are not available for most TEDS cases. But a measure is available

for highest grade completed

Let the propensity of the i

th individual admitted in state k at time t to exhibit prescription drug

abuse be represented by the random variate Y ∗

ikt, defined over the entire real line. We assume that this

propensity depends on Xikt, a matrix of explanatory variables comprising his personal characteristics,

the characteristics of his environment, and time. For notational convenience, we partition Xikt into

three sets of explanatory variables as follows: let X1ikt represent those variables that vary across

individuals as well as across state and time; let X2ikt represent those variables that vary across state

and time but not across individuals; and let X3ikt represent those variables designed to capture timerelated effects. To simplify notation, we take advantage of the following identities,

X2ikt = X2lkt = X2kt

X3ikt = X3lmt = X3t

Thus, we drop the subscript i when referring to state-level variables that do not vary over i for a given

state k and a given time t, and we drop the subscripts i and k when referring to time-related variables

that do not vary over i and k for a given time t.

26
The vectors of X1 are circumscribed by the set of personal characteristics in the TEDS dataset

that are relevant to our analysis. As noted above, these include gender, race, age, employment status,

and educational attainment; as well as heroin or cocaine as the primary substance of abuse.

The vectors of X2 include SUP PLYkt, PDMPkt, and XPDMPkt as defined above in Equation

(1). In addition, as an alternative to the hypothesis of state random effects, the large number of

observations in the TEDS dataset permits testing for state fixed effects, an option that was unavailable

to us in the aggregate analysis.

Allowing X3 to include a deterministic term is one way of modeling how the probability of admission

involving prescription drug abuse has changed over time, all else being equal. Indeed, a preliminary

review of estimates of prescription drug abuse derived from a variety of sources, such as the Drug

Abuse Warning Network (DAWN), the NSDUH, and TEDS, suggests a strong secular trend during

our observation period. Alternatively, changes over time could be modeled using time fixed effects.

The large number of observations in the TEDS dataset also permits inclusion of interactions

between the columns of X1, X2, and X3. For example, interactions between appropriate columns of X1

and X2 allow us to test for variation in the impact of PDMPs on the probability of admission involving

prescription drug abuse by various personal characteristics; while interactions between appropriate

columns of X2 and X3 allow us to test for variation in the impact of PDMPs on the probability of

admission involving prescription drug abuse over time. We can also test for the presence of random

variation in slopes across states; or slopes can be allowed to vary deterministically across states.

Thus Y ∗

ikt is an unobservable response variable that, assuming randomly distributed state effects,

has the following three-level linear specification,

27
Y ∗

ikt = γ0ikt + γ1kX1ikt + γ2kX2kt + γ3X3t

+ γ4X1iktX2kt + γ5X1iktX3t + γ6X2ktX3t

γ0i = γ0 + uk + eikt

γn2k = γn + δnk

⎫

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

k = 1, ..., 51;

t = 1, ..., 7;

n = 1, ..., 6

(5)

where uk represents an unobserved, randomly distributed state effect, eikt is a randomly distributed

error term, and δnk captures the random variation in the slopes by state.3 In addition, we assume

E(uk) = E(eikt) = E(δnk)=0, ∀n

V ar(uk) = σ2

u

V ar(eikt) = σ2

e

V ar(δnk) = σ2

δn, ∀n

Cov(uk, δnk) = σun, ∀n

Cov(eikt, uk) = Cov(eikt, δnk)=0, ∀n

(6)

In practice, however, we actually observe a binary response variable, Yikt, defined by

Yikt =

⎧

⎪⎪⎨

⎪⎪⎩

1 if Y ∗

ikt > 0

0 otherwise

(7)

Thus, if Y ∗

ikt > 0, then the iktth individual admitted for treatment reports that she does indeed abuse

a prescription drug and we observe Yikt = 1. If she reports otherwise, then we observe Yikt = 0, an

indication that Y ∗

ikt ≤ 0.

3A fixed effects model with analogous interaction terms will be estimated as well.

28
Continuing with the example presented in Equation (5), the conditional expectation of Y ∗

ikt, given

particular values for the explanatory variables, can be expressed as follows,

E(Y ∗

ikt|Xikt) = γ0 + γ1X1ikt + γ2X2kt + γ3X3kt + γ4X1iktX2kt + γ5X1iktX3t + γ6X2ktX3t

Then the probability of observing abuse of a prescription drug by individual ikt is

P(Yikt = 1|Xikt) =

= P(Y ∗

ikt > 0 | Xikt)

= P(eikt > −γ0 − (γ1 + δ1k)X1ikt − (γ2 + δ2k)X2kt − (γ3 + δ3k)X3kt

− (γ4 + δ4k)X1iktX2kt − (γ5 + δ5k)X1iktX3t − (γ6 + δ6k)X2ktX3t − uk)

= F(γ0 + (γ1 + δ1k)X1ikt + (γ2 + δ2k)X2kt + (γ3 + δ3k)X3kt

+ (γ4 + δ4k)X1iktX2kt + (γ5 + δ5k)X1iktX3t + (γ6 + δ6k)X2ktX3t + uk)

= F(γ0 + γ1kX1ikt + γ2kX2kt + γ3X3t + γ4X1iktX2kt + γ5X1iktX3t

+ γ6X2ktX3t + uk)

= πikt

(8)

where F(·) is the cumulative distribution function for the random error term, eikt. The observed values

of Yikt are thus realizations of a binomial process with probability πikt, such that Yikt ∼ Bin(1, πikt)

with conditional variance πikt(1−πikt), implying the following general form for the likelihood function,

L(γ | X, u, δ) = Y

7

t=1

Y

51

k=1

Y

N

i=1

πYikt

ikt (1 − πikt)

(1−Yikt) (9)

29
A more detailed specification of the likelihood requires additional assumptions about the distributions of uk, δ1k, δ2k, and eikt. Following convention, we assume that uk, δ1k, and δ2k are distributed

as N(0, σ2

u), N(0, σ2

δ1), and N(0, σ2δ2), respectively. Also following convention, we assume two possible

distributions for eikt: the logistic distribution with σ2

e constrained to equal unity, giving rise to the

multilevel logit model; and the cumulative standard normal distribution, giving rise to a multilevel

probit model. The logit model implies the following functional form for πikt,

πikt =

exp (γ0 + γ1kX1ikt + γ2kX2kt + γ3X3t + γ4X1iktX2kt + γ5X1iktX3t + γ6X2ktX3t + uk)

1 + exp (γ0 + γ1kX1ikt + γ2kX2kt + γ3X3t + γ4X1iktX2kt + γ5X1iktX3t + γ6X2ktX3t + uk) (10)

implying in turn the following linear form for the multilevel logit regression model,

Yikt = πikt + eiktzikt

where zikt = pπikt(1 − πikt) represents the binomial standard deviation. Solving Equation (10) for

the exponentiated expression yields,

ln μ πikt

1 − πikt ¶

= γ0 + γ1kX1ikt + γ2kX2kt + γ3X3t + γ4X1iktX2kt + γ5X1iktX3t + γ6X2ktX3t + uk

which has the familiar interpretation of the log odds of observing Yikt = 1. Alternatively, the probit

model implies the following functional form for πikt,

πikt =

Φ (γ0 + γ1kX1ikt + γ2kX2kt + γ3X3t + γ4X1iktX2kt + γ5X1iktX3t + γ6X2ktX3t + uk) (11)

where Φ(·) denotes the cumulative standard normal distribution.

30
The logistic and cumulative standard normal distributions are similar in that both transform a

variable defined over the interval between and including 0 and 1 into an interval defined over the entire

real line. However, the logistic distribution is thicker in the tails.

Results. We estimate the model described in the previous section with particular interest in the

sign and size of the elements of γ2k and γ6. Indeed, our interest in these parameters supersedes our

interest in estimates of Yikt itself. This prioritization of objectives is not trivial since, as criteria for

model selection, the two are not necessarily compatible (Greene [32]).

For samples that are well-balanced between values of Yikt, the choice is less important since logit

and probit models are known to give similar results. But in this case the proportion of individuals

admitted to treatment who report prescription drug abuse (Yikt = 1) is relatively small (less than 10

percent). And under these circumstances, the two models can give very different results (see Greene

[33]). It will therefore be informative to assess the stability of our estimates relative to alternative

distributional assumptions.

Equations (10) and (11) indicate that our coefficients are distribution-dependent; and therefore

the results produced by a logit model may not be consistent with the results produced by a comparable

probit model. As an aid to assessing stability across models we calculate the marginal effect associated

with each explanatory variable following Greene [32]. Thus,

∂E [Y ∗]

∂X =

∙

dF (γ0

X)

d(γ0X)

 ̧

γ

where F(·) is the cumulative distribution function referenced in Equation (8).

31
Model selection is made further problematic by the large size of the dataset. Teachman et al. [25]

point out that as sample size increases hypothesis tests based on the chi-square statistic may result

in rejection of a null hypothesis that is "only trivially false." With this observation in mind, we seek

the most parsimonious model in which coefficient estimates are found to be insensitive to marginal

changes in specification. Only coefficients statistically different from 0 at the .0001 level are accepted

for inclusion.

We begin by presenting the random effects logit model. Estimates for the most parsimonious

versions of Equation (5) are provided in Table IX for pain relievers and in Table X for stimulants,

along with their standard errors, t-statistics, and marginal effects. The findings indicate that for both

classes of drugs, women have higher probabilities of admission involving abuse than men. Again for

both classes of drugs, whites have higher probabilities of admission involving abuse than non-whites.

While the probability of admission involving pain reliever abuse increases with age, the opposite holds

true for the probability of admission involving stimulant abuse. For both classes of drugs, full-time

employment reduces the probability of admission involving abuse. Educational attainment increases

the probability of admission involving pain reliever abuse and decreases the probability of admission

involving stimulant abuse. Heroin abuse increases the probability of admission involving pain reliever

abuse, while cocaine abuse appears to have the opposite effect. As suggested earlier by the results of

our aggregate analysis, this may indicate substitution among opioid agonists. Both heroin and cocaine

abuse reduce the probability of admission involving stimulant abuse. Increasing the SUP P LY of

pain relievers (PR composite) increases the probability of admission involving pain reliever abuse; and

increasing the SUP PLY of stimulants (ST composite) increases the probability of admission involving

stimulant abuse.

32
Table IX: Pain Reliever Abuse Estimates (Random Effects Logit Model)

Estimate s.e. t Value pr > t Marginal Effect

Intercept -5.3003 0.0952 -55.66 <.0001 -0.1289

Male -0.5900 0.0033 -179.68 <.0001 -0.0144

White 1.0970 0.0045 244.75 <.0001 0.0267

Age 0.0107 0.0001 75.63 <.0001 0.0003

Employment -0.1893 0.0040 -47.35 <.0001 -0.0046

Education 0.2156 0.0017 125.87 <.0001 0.0052

Heroin 0.3000 0.0044 68.45 <.0001 0.0073

Cocaine -1.0215 0.0073 -140.07 <.0001 -0.0248

PR composite 2.4733 0.0136 181.45 <.0001 0.0602

Covariance parameter 0.4580 0.0920

Table X: Stimulant Abuse Estimates (Random Effects Logit Model)

Estimate s.e. t Value pr > t Marginal Effect

Intercept -3.8337 0.1438 -26.65 <.0001 -0.0410

Male -0.4707 0.0045 -105.31 <.0001 -0.0050

White 0.9835 0.0061 162.45 <.0001 0.0105

Age -0.0734 0.0010 -77.21 <.0001 -0.0008

Employment -0.3991 0.0055 -72.37 <.0001 -0.0043

Education -0.0678 0.0024 -27.87 <.0001 -0.0007

Heroin -1.1517 0.0106 -109.00 <.0001 -0.0123

Cocaine -0.8100 0.0093 -87.55 <.0001 -0.0087

ST composite 2.4943 0.1436 17.37 <.0001 0.0267

Covariance parameter 1.0430 0.2088

We are particularly interested in the relationship between abuse and SUP P LY . Figure 25 depicts

the probability of admission involving pain reliever abuse as a function of SUP PLY (PR composite)

holding constant the values of all other explanatory variables. The relationship is nonlinear and

accelerating thus suggesting the potential for a substantial return on efforts to curtail availability.

Figure 26 depicts analogously the probability of admission involving stimulant abuse as a function of

SUP PLY (ST composite). This relationship is more linear.

33
Figure 25: PR Abuse by PR Composite Figure 26: ST Abuse by ST Composite

As noted above it will be useful to examine the effects of alternative model specifications (state

fixed effects versus state random effects) and distributional assumptions (logistic versus cumulative

standard normal) on the stability of our estimates.

We begin by presenting the results from a logit model with state fixed effects in Table XI for pain

relievers and Table XII for stimulants. The coefficients are remarkably similar to those presented in

Tables IX and X.

We then re-estimate using a probit model with state fixed effects. With highly unbalanced

samples such as this the logit and probit models can give different results. However, comparing the

marginal effects in Tables XIII and XIV to those in Tables XI and XII, we see that the models are

consistent. They support the hypothesis that the probability of admission involving prescription drug

abuse responds positively to increases in drug supply and (by inference) negatively to the presence of

a proactively monitoring PDMP.

34
Table XI: Pain Reliever Abuse Estimates (Fixed Effects Logit Model)

Estimate s.e. t Value pr > t Marginal Effect

Intercept -5.9552 0.0403 -147.61 <.0001 -0.1448

Male -0.5900 0.0033 -179.68 <.0001 -0.0144

White 1.0970 0.0045 244.74 <.0001 0.0267

Age 0.0107 0.0001 75.63 <.0001 0.0003

Employment -0.1893 0.0040 -47.35 <.0001 -0.0046

Education 0.2156 0.0017 125.86 <.0001 0.0052

Heroin 0.3000 0.0044 68.44 <.0001 0.0073

Cocaine -1.0215 0.0073 -140.08 <.0001 -0.0248

PR composite 2.4733 0.0136 181.43 <.0001 0.0602

Alabama 1.6178 0.0411 39.41 <.0001 0.0393

Alaska -0.2891 0.0541 -5.34 <.0001 -0.0070

Arizona -0.9918 0.1042 -9.52 <.0001 -0.0241

Arkansas 0.9314 0.0428 21.75 <.0001 0.0227

California 0.4877 0.0400 12.18 <.0001 0.0119

Colorado -0.2496 0.0421 -5.93 <.0001 -0.0061

Connecticut 0.6641 0.0407 16.33 <.0001 0.0162

Delaware 0.4623 0.0480 9.63 <.0001 0.0112

District of Columbia -0.1187 0.0750 -1.58 0.1133 -0.0029

Florida 0.9200 0.0402 22.87 <.0001 0.0224

Georgia 1.4196 0.1604 8.85 <.0001 0.0345

Hawaii 0.7331 0.0497 14.76 <.0001 0.0178

Idaho 0.0963 0.0518 1.86 0.0631 0.0023

Illinois 0.1039 0.0425 2.45 0.0144 0.0025

Indiana 1.2222 0.0409 29.88 <.0001 0.0297

Iowa -0.0321 0.0437 -0.73 0.4631 -0.0008

Kansas 0.1896 0.0462 4.10 <.0001 0.0046

Kentucky 1.2726 0.0414 30.75 <.0001 0.0310

Louisiana 1.7543 0.0409 42.94 <.0001 0.0427

Maine 1.4966 0.0411 36.38 <.0001 0.0364

Maryland 0.7957 0.0404 19.71 <.0001 0.0194

Massachusetts 1.0685 0.0401 26.67 <.0001 0.0260

Michigan 1.1824 0.0402 29.42 <.0001 0.0288

Minnesota 0.6069 0.0412 14.72 <.0001 0.0148

Mississippi 1.9330 0.0463 41.73 <.0001 0.0470

Missouri -0.1290 0.0422 -3.06 0.0022 -0.0031

Montana 0.8535 0.0446 19.14 <.0001 0.0208

Nebraska -0.1132 0.0527 -2.15 0.0316 -0.0028

Nevada -0.4040 0.0476 -8.49 <.0001 -0.0098

New Hampshire 0.3962 0.0474 8.36 <.0001 0.0096

New Jersey 0.6901 0.0407 16.97 <.0001 0.0168

New Mexico 0.3889 0.0561 6.94 <.0001 0.0095

New York 0.7822 0.0399 19.63 <.0001 0.0190

North Carolina 0.8643 0.0413 20.95 <.0001 0.0210

North Dakota 0.8464 0.0574 14.74 <.0001 0.0206

Ohio 0.6425 0.0405 15.85 <.0001 0.0156

Oklahoma 0.8038 0.0425 18.90 <.0001 0.0195

Oregon -0.5042 0.0417 -12.10 <.0001 -0.0123

Pennsylvania 0.9622 0.0403 23.89 <.0001 0.0234

Rhode Island 1.3893 0.0418 33.22 <.0001 0.0338

South Carolina 0.7090 0.0419 16.92 <.0001 0.0172

South Dakota -0.5368 0.0610 -8.80 <.0001 -0.0131

Tennessee 1.9650 0.0425 46.20 <.0001 0.0478

Texas 1.6153 0.0409 39.54 <.0001 0.0393

Utah 0.8150 0.0427 19.09 <.0001 0.0198

Vermont 1.1462 0.0453 25.30 <.0001 0.0279

Virginia 1.3499 0.0415 32.51 <.0001 0.0328

Washington 0.5796 0.0406 14.28 <.0001 0.0141

West Virginia 0.9371 0.0497 18.85 <.0001 0.0228

Wisconsin 0.0604 0.0443 1.36 0.1724 0.0015

Wyoming 0.0000 . . . 0.0000

35
Table XII: Stimulant Abuse Estimates (Fixed Effects Logit Model)

Estimate s.e. t Value pr > t Marginal Effect

Intercept -2.4930 0.0254 -97.98 <.0001 -0.0209

Male -0.4665 0.0045 -104.31 <.0001 -0.0039

White 0.9839 0.0061 162.51 <.0001 0.0082

Age -0.0180 0.0002 -89.37 <.0001 -0.0002

Employment -0.4036 0.0055 -73.15 <.0001 -0.0034

Education -0.0630 0.0024 -26.18 <.0001 -0.0005

Heroin -1.1518 0.0106 -109.03 <.0001 -0.0097

Cocaine -0.8138 0.0092 -88.01 <.0001 -0.0068

ST composite 2.5162 0.1437 17.52 <.0001 0.0211

Alabama -1.0852 0.0308 -35.27 <.0001 -0.0091

Alaska -0.8956 0.0431 -20.76 <.0001 -0.0075

Arizona -1.3472 0.0732 -18.41 <.0001 -0.0113

Arkansas 1.8387 0.0236 77.78 <.0001 0.0154

California -1.2817 0.0241 -53.30 <.0001 -0.0107

Colorado -2.1101 0.0308 -68.53 <.0001 -0.0177

Connecticut -2.3080 0.0359 -64.39 <.0001 -0.0194

Delaware -2.2540 0.0728 -30.95 <.0001 -0.0189

District of Columbia -0.7688 0.0656 -11.71 <.0001 -0.0064

Florida -1.9830 0.0280 -70.88 <.0001 -0.0166

Georgia -1.5129 0.3820 -3.96 <.0001 -0.0127

Hawaii -1.1833 0.0482 -24.55 <.0001 -0.0099

Idaho -1.8181 0.0465 -39.13 <.0001 -0.0152

Illinois -0.4466 0.0244 -18.34 <.0001 -0.0037

Indiana -1.6279 0.0311 -52.28 <.0001 -0.0136

Iowa -2.0557 0.0325 -63.31 <.0001 -0.0172

Kansas -1.2641 0.0328 -38.52 <.0001 -0.0106

Kentucky -1.4767 0.0341 -43.34 <.0001 -0.0124

Louisiana -0.7764 0.0285 -27.27 <.0001 -0.0065

Maine -1.8836 0.0411 -45.85 <.0001 -0.0158

Maryland -2.4678 0.0334 -73.85 <.0001 -0.0207

Massachusetts -2.5212 0.0329 -76.73 <.0001 -0.0211

Michigan -2.2813 0.0297 -76.94 <.0001 -0.0191

Minnesota -1.3321 0.0271 -49.15 <.0001 -0.0112

Mississippi -1.1709 0.0618 -18.94 <.0001 -0.0098

Missouri -1.8028 0.0293 -61.50 <.0001 -0.0151

Montana -1.3441 0.0410 -32.81 <.0001 -0.0113

Nebraska -2.0983 0.0525 -39.98 <.0001 -0.0176

Nevada -0.5407 0.0305 -17.71 <.0001 -0.0045

New Hampshire -1.5649 0.0475 -32.93 <.0001 -0.0131

New Jersey -1.9364 0.0323 -60.03 <.0001 -0.0162

New Mexico -1.0256 0.0481 -21.31 <.0001 -0.0086

New York -1.8552 0.0243 -76.49 <.0001 -0.0156

North Carolina -1.8646 0.0328 -56.92 <.0001 -0.0156

North Dakota -0.1791 0.0421 -4.25 <.0001 -0.0015

Ohio -1.8905 0.0272 -69.58 <.0001 -0.0159

Oklahoma 0.0523 0.0256 2.04 0.0411 0.0004

Oregon 1.7898 0.0226 79.06 <.0001 0.0150

Pennsylvania -1.8422 0.0281 -65.47 <.0001 -0.0154

Rhode Island -2.4572 0.0570 -43.12 <.0001 -0.0206

South Carolina -2.2875 0.0370 -61.76 <.0001 -0.0192

South Dakota 0.7050 0.0261 26.98 <.0001 0.0059

Tennessee -0.3887 0.0325 -11.97 <.0001 -0.0033

Texas 0.9459 0.0235 40.21 <.0001 0.0079

Utah -1.2430 0.0328 -37.85 <.0001 -0.0104

Vermont -2.1863 0.0678 -32.26 <.0001 -0.0183

Virginia -1.1377 0.0321 -35.48 <.0001 -0.0095

Washington -0.8360 0.0247 -33.85 <.0001 -0.0070

West Virginia -2.0920 0.0797 -26.26 <.0001 -0.0175

Wisconsin -2.2710 0.0410 -55.42 <.0001 -0.0190

Wyoming 0.0000 . . . 0.0000

36
Table XIII: Pain Reliever Abuse Estimates (Fixed Effects Probit Model)

Estimate s.e. t Value pr > t Marginal Effect

Intercept -2.9986 0.0168 -178.40 <.0001 -0.1805

Male -0.2756 0.0015 -179.89 <.0001 -0.0166

White 0.4731 0.0019 251.90 <.0001 0.0285

Age 0.0056 0.0001 84.66 <.0001 0.0003

Employment -0.0841 0.0018 -46.35 <.0001 -0.0051

Education 0.0993 0.0008 125.64 <.0001 0.0060

Heroin 0.1443 0.0020 71.06 <.0001 0.0087

Cocaine -0.4427 0.0030 -147.48 <.0001 -0.0267

PR composite 1.1573 0.0064 181.06 <.0001 0.0697

Alabama 0.7394 0.0173 42.69 <.0001 0.0445

Alaska -0.1427 0.0227 -6.28 <.0001 -0.0086

Arizona -0.4005 0.0398 -10.07 <.0001 -0.0241

Arkansas 0.3997 0.0181 22.06 <.0001 0.0241

California 0.2146 0.0166 12.90 <.0001 0.0129

Colorado -0.0982 0.0174 -5.65 <.0001 -0.0059

Connecticut 0.2877 0.0170 16.96 <.0001 0.0173

Delaware 0.1955 0.0204 9.56 <.0001 0.0118

District of Columbia -0.0070 0.0285 -0.25 0.8051 -0.0004

Florida 0.4060 0.0168 24.20 <.0001 0.0244

Georgia 0.6419 0.0792 8.11 <.0001 0.0386

Hawaii 0.3165 0.0211 15.00 <.0001 0.0191

Idaho 0.0438 0.0215 2.04 0.0416 0.0026

Illinois 0.0748 0.0175 4.28 <.0001 0.0045

Indiana 0.5497 0.0172 32.02 <.0001 0.0331

Iowa -0.0047 0.0181 -0.26 0.7945 -0.0003

Kansas 0.0905 0.0192 4.72 <.0001 0.0054

Kentucky 0.5828 0.0175 33.27 <.0001 0.0351

Louisiana 0.8025 0.0172 46.62 <.0001 0.0483

Maine 0.7228 0.0175 41.36 <.0001 0.0435

Maryland 0.3379 0.0168 20.07 <.0001 0.0203

Massachusetts 0.4785 0.0167 28.65 <.0001 0.0288

Michigan 0.5259 0.0168 31.40 <.0001 0.0317

Minnesota 0.2664 0.0172 15.49 <.0001 0.0160

Mississippi 0.8911 0.0207 43.00 <.0001 0.0536

Missouri -0.0637 0.0175 -3.64 0.0003 -0.0038

Montana 0.3806 0.0191 19.93 <.0001 0.0229

Nebraska -0.0257 0.0214 -1.20 0.2311 -0.0015

Nevada -0.1796 0.0199 -9.04 <.0001 -0.0108

New Hampshire 0.1667 0.0203 8.20 <.0001 0.0100

New Jersey 0.3005 0.0170 17.73 <.0001 0.0181

New Mexico 0.1791 0.0234 7.66 <.0001 0.0108

New York 0.3451 0.0166 20.84 <.0001 0.0208

North Carolina 0.3682 0.0173 21.33 <.0001 0.0222

North Dakota 0.3820 0.0249 15.33 <.0001 0.0230

Ohio 0.2805 0.0169 16.62 <.0001 0.0169

Oklahoma 0.3522 0.0179 19.67 <.0001 0.0212

Oregon -0.2265 0.0173 -13.09 <.0001 -0.0136

Pennsylvania 0.4255 0.0168 25.32 <.0001 0.0256

Rhode Island 0.6338 0.0177 35.75 <.0001 0.0382

South Carolina 0.2997 0.0175 17.11 <.0001 0.0180

South Dakota -0.1901 0.0240 -7.94 <.0001 -0.0114

Tennessee 0.9124 0.0183 49.81 <.0001 0.0549

Texas 0.7255 0.0171 42.38 <.0001 0.0437

Utah 0.3597 0.0181 19.93 <.0001 0.0217

Vermont 0.5192 0.0197 26.31 <.0001 0.0313

Virginia 0.5990 0.0175 34.15 <.0001 0.0361

Washington 0.2539 0.0169 14.99 <.0001 0.0153

West Virginia 0.4307 0.0219 19.67 <.0001 0.0259

Wisconsin 0.0228 0.0184 1.24 0.2146 0.0014

Wyoming 0.0000 . . . 0.0000

37
Table XIV: Stimulant Abuse Estimates (Fixed Effects Probit Model)

Estimate s.e. t Value pr > t Marginal Effect

Intercept -1.3961 0.0121 -115.67 <.0001 -0.0337

Male -0.2018 0.0020 -98.52 <.0001 -0.0049

White 0.3992 0.0025 158.37 <.0001 0.0096

Age -0.0085 0.0001 -92.33 <.0001 -0.0002

Employment -0.1591 0.0025 -63.99 <.0001 -0.0038

Education -0.0216 0.0011 -19.68 <.0001 -0.0005

Heroin -0.4617 0.0043 -108.44 <.0001 -0.0111

Cocaine -0.3282 0.0038 -86.65 <.0001 -0.0079

ST composite 1.0332 0.0657 15.73 <.0001 0.0249

Alabama -0.4982 0.0139 -35.74 <.0001 -0.0120

Alaska -0.4096 0.0187 -21.94 <.0001 -0.0099

Arizona -0.5934 0.0297 -19.98 <.0001 -0.0143

Arkansas 0.9580 0.0117 81.61 <.0001 0.0231

California -0.5507 0.0114 -48.32 <.0001 -0.0133

Colorado -0.8746 0.0132 -66.15 <.0001 -0.0211

Connecticut -0.9347 0.0145 -64.30 <.0001 -0.0226

Delaware -0.9262 0.0268 -34.59 <.0001 -0.0223

District of Columbia -0.2940 0.0245 -12.02 <.0001 -0.0071

Florida -0.8431 0.0125 -67.46 <.0001 -0.0203

Georgia -0.6561 0.1486 -4.41 <.0001 -0.0158

Hawaii -0.5207 0.0199 -26.17 <.0001 -0.0126

Idaho -0.7868 0.0192 -41.10 <.0001 -0.0190

Illinois -0.2033 0.0116 -17.50 <.0001 -0.0049

Indiana -0.7067 0.0137 -51.42 <.0001 -0.0171

Iowa -0.8762 0.0140 -62.62 <.0001 -0.0211

Kansas -0.5633 0.0146 -38.59 <.0001 -0.0136

Kentucky -0.6461 0.0149 -43.30 <.0001 -0.0156

Louisiana -0.3637 0.0132 -27.52 <.0001 -0.0088

Maine -0.8140 0.0171 -47.66 <.0001 -0.0196

Maryland -1.0105 0.0139 -72.82 <.0001 -0.0244

Massachusetts -1.0215 0.0137 -74.83 <.0001 -0.0247

Michigan -0.9529 0.0129 -73.81 <.0001 -0.0230

Minnesota -0.5934 0.0125 -47.58 <.0001 -0.0143

Mississippi -0.5276 0.0256 -20.59 <.0001 -0.0127

Missouri -0.7772 0.0130 -59.60 <.0001 -0.0188

Montana -0.5901 0.0176 -33.56 <.0001 -0.0142

Nebraska -0.8790 0.0204 -43.03 <.0001 -0.0212

Nevada -0.2553 0.0142 -17.94 <.0001 -0.0062

New Hampshire -0.6934 0.0200 -34.64 <.0001 -0.0167

New Jersey -0.8064 0.0137 -58.92 <.0001 -0.0195

New Mexico -0.4634 0.0205 -22.57 <.0001 -0.0112

New York -0.7708 0.0114 -67.80 <.0001 -0.0186

North Carolina -0.7887 0.0140 -56.30 <.0001 -0.0190

North Dakota -0.0823 0.0199 -4.14 <.0001 -0.0020

Ohio -0.8046 0.0123 -65.48 <.0001 -0.0194

Oklahoma 0.0244 0.0124 1.97 0.0485 0.0006

Oregon 0.9538 0.0111 86.31 <.0001 0.0230

Pennsylvania -0.7878 0.0126 -62.52 <.0001 -0.0190

Rhode Island -1.0125 0.0214 -47.23 <.0001 -0.0244

South Carolina -0.9534 0.0152 -62.75 <.0001 -0.0230

South Dakota 0.3589 0.0129 27.73 <.0001 0.0087

Tennessee -0.1952 0.0152 -12.81 <.0001 -0.0047

Texas 0.4184 0.0115 36.43 <.0001 0.0101

Utah -0.5477 0.0146 -37.41 <.0001 -0.0132

Vermont -0.9284 0.0260 -35.73 <.0001 -0.0224

Virginia -0.4942 0.0143 -34.61 <.0001 -0.0119

Washington -0.3772 0.0117 -32.16 <.0001 -0.0091

West Virginia -0.8897 0.0306 -29.12 <.0001 -0.0215

Wisconsin -0.9548 0.0165 -57.72 <.0001 -0.0230

Wyoming 0.0000 . . . 0.0000

38
5 Discussion

This work examines the direct and indirect effects of PDMPs on the abuse of prescription drugs.

Within this context we focus on the impact that PDMPs have on the supply of prescription drugs;

and on the impact that PDMPs and supply together have on abuse. Methodological considerations

lead us to focus on Schedule II pain relievers and stimulants, and composite measures for these two

classes of drugs are developed for use in our analysis. Our approach involves estimation of both

aggregate and individual response models.

The aggregate model suggests that the presence of a PDMP reduces per capita supply of prescription pain relievers and stimulants, and that this in turn reduces the probability of abuse for such

drugs (the probability of prescription pain reliever abuse is a function of the per capita supply of

prescription pain relievers, and the probability of prescription stimulant abuse is a function of the per

capita supply of prescription stimulants). The evidence also suggests that states which are proactive

in their approach to regulation may be more effective in reducing the per capita supply of prescription

pain relievers and stimulants than states which are reactive in their approach to regulation.

The individual response model assesses the effects of aggregate characteristics (such as the presence

of a PDMP and the supply of prescription pain relievers and stimulants) and personal characteristics

(such as gender, race, age, employment status, educational attainment, and heroin or cocaine abuse)

on the probability of prescription drug abuse. The findings are consistent with those provided by the

aggregate model, suggesting that the probability of prescription pain reliever abuse is a function of

the per capita supply of pain relievers, and that the probability of prescription stimulant abuse is a

function of the per capita supply of stimulants.

39
We noted earlier that the probability of prescription pain reliever abuse is actually higher in states

that have monitoring programs than in states that do not. On the surface this appears difficult to

explain since these states have been effective in reducing the per capita supply of pain relievers. And

we know from our individual response model that the decision to abuse pain relievers is sensitive to

supply. We are thus drawn to return to our aggregate model in an effort to explain this paradox and

to quantify the impact of PDMPs.

Taking the coefficients from Table VII we project values for per capita supply in states that monitor

proactively as though no programs existed there. The coefficients from Table VIII are then used with

these projected values for supply, as well as with population means for age and the per capita rates at

which individuals report heroin and cocaine abuse on admission to treatment, to produce "synthetic

estimates" of the probability of abuse in the absence of program intervention.

The results of this simulation are expressed as admissions per 100,000 and presented in Figures

27-28. They indicate that by 2003 the rate of pain reliever abuse would have been 10.1 percent

higher and the rate of stimulant abuse would have been 4.1 percent higher in the absence of proactive

regulatory control.

Figure 27. Pain Reliever Admissions in XPDMP States

15

20

25

30

35

40

1997 1998 1999 2000 2001 2002 2003

Without XPDMP With XPDMP

Figure 28: Stimulant Admissions in XPDMP States

15

20

25

30

35

40

1997 1998 1999 2000 2001 2002 2003

Without XPDMP With XPDMP

40
In summary, the results from our aggregate and individual response models indicate that PDMPs

which monitor proactively have inhibited growth in prescription sales (for pain relievers and stimulants) and in so doing exerted an indirect effect on the probability of abuse for these drugs.

Directions for future research. The rational addiction model suggests the importance of

illicit drug prices in the decision to abuse prescription drugs. It is well known that illicit drug users

often compensate for reduced supply by substituting licit drugs that have similar effects. We might

therefore reasonably expect prescription pain relievers to become popular in areas, and during times

when, the price of heroin is relatively high. It may thus be instructive to introduce measures of

price per gram pure for heroin, cocaine, crack, and methamphetamine into our model and to examine

possible substitution effects in greater detail.

In 2004 the RAND corporation received a contract from the Office of National Drug Control Policy

(ONDCP) to develop a consistent series of estimates for price and purity (Arkes et al. [21]). The

System to Retrieve Information from Drug Evidence (STRIDE) provided the basis for these efforts.4

Data availability allowed price and purity estimates to be made for 29 cities, quarterly, for each drug

identified above, and these exist over the duration of our study period. ONDCP has made the RAND

estimates available to SAI for use in its analysis. We propose to develop a model that draws upon

this information in subsequent work.

4 STRIDE is a DEA database that retains information on seizures, purchases, and other drug acquisition events that

occur during the course of law enforcement activity. It is designed primarily to control forensic inventory and to provide

scientific evidence in support of prosecution. Because STRIDE data are not intended to support research of the kind

being conducted here, they do not constitute a random sample of all drug transactions that occur within any geographic

area. This limits the consistency with which places are represented over time, the statistical techniques that can be

used to analyze the data, and the inferences that can be drawn based upon the results of such analyses (see Manski et

al. [34]; and Horowitz [35]). The system nonetheless remains the best available source of information on illicit drug

prices and purity (Saffer and Chaloupka [28]; Manski et al. [34]; DeSimone [36]).

41
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