Influence of drug use on mental health and criminal activity

(1)

Faculty of Economics and Business

Amsterdam School of Economics

Requirements thesis MSc in Econometrics.

1. The thesis should have the nature of a scientic paper. Consequently the thesis is divided

up into a number of sections and contains references. An outline can be something like (this

is an example for an empirical thesis, for a theoretical thesis have a look at a relevant paper

from the literature):

(a) Front page (requirements see below)

(b) Statement of originality (compulsary, separate page)

(c) Introduction

(d) Theoretical background

(e) Model

(f) Data

(g) Empirical Analysis

(h) Conclusions

(i) References (compulsary)

If preferred you can change the number and order of the sections (but the order you

use should be logical) and the heading of the sections. You have a free choice how to

list your references but be consistent. References in the text should contain the names

of the authors and the year of publication. E.g. Heckman and McFadden (2013). In

the case of three or more authors: list all names and year of publication in case of the

rst reference and use the rst name and et al and year of publication for the other

references. Provide page numbers.

2. As a guideline, the thesis usually contains 25-40 pages using a normal page format. All that

actually matters is that your supervisor agrees with your thesis.

3. The front page should contain:

(a) The logo of the UvA, a reference to the Amsterdam School of Economics and the Faculty

as in the heading of this document. This combination is provided on Blackboard (in

MSc Econometrics Theses & Presentations).

(b) The title of the thesis

(c) Your name and student number

(d) Date of submission nal version

(e) MSc in Econometrics

(f) Your track of the MSc in Econometrics

Master’s Thesis

Influence of drug use

on mental health and criminal activity

Matylda Leoniak

Student number: 11792574

Date of final version: July 9, 2018

Master’s programme: Econometrics

Specialisation: Free Track

Supervisor: dr. J. C. M. van Ophem

Second reader: dr. K. A. Lasak

(2)

Statement of Originality

This document is written by Matylda Leoniak who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

(3)

List of Tables

3.1 Descriptive statistics - general characteristics . . . 12

3.2 Descriptive statistics - drug use and mental health . . . 13

5.1 First step - Bivariate Probit Model for Drug Use . . . 21

5.2 Second step - Crime Model . . . 23

5.3 Second step - Mental Health Model . . . 24

5.4 Second step - Crime SNP Model . . . 25

5.5 Second step - Mental Health SNP Model . . . 26

5.6 Marginal Effects . . . 27

5.7 Marginal Effects - Gender Comparison . . . 30

B.1 Second step - Crime Logit Model . . . 36

B.2 Second step - Mental Health Logit Model . . . 37

B.3 Marginal Effects . . . 38

C.1 Crime Second Step - Gender Comparison . . . 39

(5)

Chapter 1

Introduction

The subject matter of this thesis revolves around the problem of drug use. According to the estimates of the United Nations Office on Drugs and Crime the number of drug users globally increased from 208 million in 2006 to 255 million in 2015 (UNODC (2017)). The adverse aftermath of substance use can be assessed by the number of deaths resulting from drug overdose. In 2016 the rate of substance overdose deaths in the USA was more than three times higher compared to 1999. The number of drug overdose deaths amounted to 63 600 and has been continuously growing since 2012 in the USA (Hedegaard et al. (2017)). Moreover, the number of new identified psychoactive substances in 2015 has almost doubled compared to 2012 as it added up to 483, which is a worrying proof that the market for especially dangerous synthetic drugs is constantly developing (UNODC (2017)).

The direct impact of drug use indicated by detrimental influence on physical health is com-monly known. It facilitates the spread of infectious diseases, it is linked with higher risk of tuberculosis and hepatitis C, it can cause seizures, strokes, heart attacks and other cardiac diseases, just to name a few examples. What helps to visualise the magnitude of damage that drug use can inflict are the so called DALYs, an abbreviation for disability-adjusted life years. They denote the number of healthy life years lost due to a premature death or disability. In 2010 this number amounted globally to 20 million of lost years attributable to the aftermath of drug use, out of which the heaviest burden (around 9 million years) resulted from opioid dependence (Degenhardt et al. (2013)).

All of the aforementioned figures show that the drug market nowadays is prospering which makes the potential consequences of drug use increasingly relevant and worth investigating in detail since they go beyond the dangers linked solely with physical health. Indirect effects of excessive substance use include negative repercussions for the development, feeling of safety, crime rates and, as recent studies suggest, also mental health. Numerous sources, described in detail in subsequent chapters, show that the risk of developing mental health issues such as e.g. depression, psychosis or schizophrenia are higher among the people who used to consume drugs in the past.

Out of all the theoretically possible dangers, this thesis will focus on investigating the influence of drug use on mental health condition and criminal activity. The main challenge

(6)

CHAPTER 1. INTRODUCTION in the estimation procedure lies in dealing with endogeneity of drug use related variables. This is done by constructing a two step model with correction terms controlling for endogeneity. Later on the estimation procedure is carried out by means of a parametric probit and a semi-nonparametric technique first proposed by Gallant and Nychka (1987). The details of the estimation method are given in chapter 4.

The remainder of this thesis is organized as follows. Chapter 2 contains a literature review summarizing the underlying background as well as empirical results up to date. Chapter 3 describes the data set under consideration as well as general sample characteristics. Chapter 4 describes the applied estimation technique in detail and touches upon some methodological issues. Results of the model and robustness checks are presented in chapter 5 and finally chapter 6 concludes and suggests some improvements for future research.

(7)

Chapter 2

Literature Review

2.1 Drug use and crime

2.1.1 Theoretical background

Drug use is often intuitively linked with crime, both in its individual aspect and in a broader context, e.g. drug trafficking often constitutes an important source of revenue for organized crime groups, because of the fact that it is illegal and hence linked with much higher profits. In this paper the focus will lie on investigating the potential influence of drug use on individual criminal activity. This is a very elaborate issue, since it is not easy to establish whether drug use in fact has an effect on the propensity to break the law or the tendency is reversed and criminals are already inclined to get involved in substance abuse because of their environment encouraging such behaviour. Furthermore, other factors including poverty, social rejection or unemployment can be significant crime motives as well. Naturally, it is important to emphasize that the majority of people who try drugs do not become deeply addicted and do not commit any crimes other than the use of illegal substances itself, which for them is just a one-time experiment or a form of infrequent social activity.

However, according to the data published by National Council on Alcoholism and Drug Dependence (NCADD) alcohol and drugs were involved in around 80% of law violations ending in incarceration in the United States. Moreover, almost half of the inmates are clinically addicted and estimated 60% of convicts tested positive for illegal drugs at the moment of arrest. This percentage is also high among juvenile arrests, since 1.9 million out of 2.4 million juvenile arrests involved drug abuse and addiction (NCADD (2018)). These figures suggest that the correlation between drugs and crime does in fact exist.

NCADD differentiates three types of drug induced crimes:

• use-related crimes - stem purely from the effect of drugs on the individual’s thoughts and behaviour,

• economic-related crimes - committed in order to obtain funds for drugs, for example theft or prostitution,

(8)

2.1. DRUG USE AND CRIME CHAPTER 2. LITERATURE REVIEW • system-related crimes - involved in the process of production, transport and sale of drugs. In 2004 17% of state prisoners and 18% of federal inmates claimed that they perpetrated the crime in order to ”feed the habit” (NCADD (2018)). This includes offenses such as robbery, theft or selling stolen goods. According to the study of Johnson (2004) based on a sample of Australian female inmates 42% of them were under the influence of drugs at the time of law violation. In a self reported survey half of the property offenders declared that their main motive was obtaining funds for drugs. The same fraction amounted to 87% among inmates whose favoured narcotic was heroin. When it comes to chronological order of narcotics use and crime, evidence showed that for two thirds of the inmates drug use preceded criminal behaviour, which suggests that it could have played a role in generating the onset of the prisoner’s criminal career. When asked for a commentary, inmates said that drugs made them feel psychotic, that they could not tell a difference between right or wrong and that they felt like they could do anything, so they chose to commit crime. Other inmates with a serious drug problem often reported a ”couldn’t care less” attitude when it comes to the consequences of obtaining money through crime (Simpson (2003)). Another major crime caused by drugs is driving while intoxicated, which is the third most commonly reported crime in the USA (NCADD (2018)).

Taking into consideration all the aforementioned facts there seems to be a possibility that curbing the drug market and treating substance abuse could be a part of crime prevention programs. According to NCADD estimates about 50% of state and federal inmates comply with drug abuse and dependence criteria and yet less than one out of five prisoners receives the necessary treatment. In this situation it is quite likely that without any kind of addiction therapy inmates will return to drug use after being released from prison. This often results in rearrest, frequently due to a drug-driven offense.

In order to break this vicious circle effective drug abuse treatment programs, both in prisons and outside of them, are needed. Benefits of such programs go beyond crime prevention and include increased perceived quality of life due to lower fear of crime and financial benefits due to lower functioning costs of criminal justice system and lower costs to victims. Naturally, the detrimental implications of narcotics use are self-evident for the policy makers, which can be observed on the example of the American ”War on Drugs” started by the Congress in 1988 by passing the Anti-Drug Abuse Act, which was supposed to make America drug-free by 1995. As it turned out, drug consumption among the minors still increased in the years 1988-1995, even though the annual Federal drug control budget rose from $2.8 billion in 1985 to $11-$13 billion in the 1990s (White and Gorman (2011)). After this misperformance American drug policy switched from a ”zero tolerance” one to a ”harm reduction” approach, since it became obvious that total eradication of drug use is a utopian vision.

(9)

2.1. DRUG USE AND CRIME CHAPTER 2. LITERATURE REVIEW

2.1.2 Empirical results

The aforementioned arguments suggest that a link between narcotics use and crime exists, the question remains whether it is a causal one. Previous empirical research on this subject often showed contradictory findings, both when it comes to causal and chronological analysis of the drug-crime relation. Some sources claim that there is no cause and effect relation between drug use and crime, rather it is more likely that both of them are caused by demographic or behavioural determinants such as irregular work, low self control or weak bond with family (Chaiken and Chaiken (1990), Hayhurst et al. (2013), Gottfredson and Hirschi (1990)). When it comes to chronological order it is often the case that committing a crime precedes the onset of drug use and hence rules out the hypothesis that narcotics initiate criminal offenses (Pierce et al. (2015), Kokkevi et al. (1993), Menard et al. (2001)). As shown by Pierce et al. (2015) offenders who tested positive for opiates and/or cocaine were characterised by higher prior offending rates compared to those who tested negative, however the influence of other prior substance use remains unknown.

On the contrary, in many cases researchers acknowledged the positive impact of narcotics use on the propensity to commit a crime, e.g. in French et al. (2000) who found a significant relation between drug use and crime. As shown in Douglas Anglin and Speckart (2006) at the time of high drug use the levels of both property crime (theft, robbery) and selling drugs were the highest among a sample of drug addicts. Moreover, data showed evidence that most extreme and violent crimes were perpetrated at times of highest levels of narcotics use. The impersonal, less violent and serious crimes, such as petty stealings, were prevailing at times of intermediate levels of drug addiction. Harrison and Gfroerer (1992) also acknowledged a positive influence of drug use on criminal behaviour. They reported that narcotics use is a strong correlate for being arrested for breaking the law and the influence was particularly strong when it came to cocaine use in large metropolitan areas. The aforementioned examples are in line with a more general finding given by Bennett et al. (2008) in their meta-analysis of the drug-crime relationship based on a collection of 30 studies and aimed at summarizing the previous results in form of a single indicator. They came to the conclusion that the odds of breaking the law were 2.8-3.8 times higher for drug users compared to non-users. The influence depended on the type of drug consumed and was the strongest among crack users (odds ratio around 6), followed by heroin users (OR=3) and cocaine users (OR=2.5).

Nonetheless, due to the complexity of the drug-crime relationship it has often been concluded that a simple cause and effect model is an oversimplification and it is more likely a case of mutual causation (Menard et al. (2001), Hammersley et al. (1989), Derzon and Lipsey (1999), Seddon (2000)). As shown in a different example of a meta-analysis by Derzon and Lipsey (1999) illicit

(10)

2.2. DRUG USE AND MENTAL HEALTH CHAPTER 2. LITERATURE REVIEW substance use and delinquent behaviour often are closely intertwined and happen at a similar time, but substance use is correlated with current criminal behaviour and cannot serve as a predictor for future delinquency.

However, it is White and Gorman (2011) who highlight an important aspect of the drug-crime relationship. When analyzing the correlation between drug use and crime across 17 American cities they found no systematic relation between any kind of narcotics and any kind of crime. They came to the conclusion that there are various sorts of drug users and crimi-nals differing due to their diverse paths to substance use and crime. Since this population is highly heterogeneous, so are the causal patterns in the drug-crime relationship and they can be summarized in three categories:

1. Drug use influences crime 2. Crime leads to drug use

3. Both drug use and crime are induced by some other common factors

According to White and Gorman (2011) all of these statements can be empirically proven right but they highly depend on the subgroup of drug addicts and criminals under consideration. This could account for the heterogeneity in the previous empirical findings in this field of research.

2.2 Drug use and mental health

2.2.1 Theoretical background

Regarding the relationship between drug use and mental health condition, similar problems as the ones described in section 2.1 can be encountered. There certainly exists a link between these two factors, however it is not obvious whether the relation is a causal or maybe even mutual one or perhaps both factors are induced by other common determinants.

Undoubtedly, drug use is likely to impair the mental health condition due to the fact that psychoactive substances can substantially affect human memory, awareness and central nervous system functions. Moreover, there are many cases of reported psychotic episodes evoked by drug use among generally healthy people (Andr´easson et al. (1987)). According to the National Institute on Drug Abuse (NIDA) continuous use of certain narcotics can result in short and long-term alterations in the brain and this can eventually lead to mental disorders such as angst, paranoia, schizophrenia, depression and delusions among others (NIDA (2018)).

However, the reversed causation is also possible. For many individuals already diagnosed with mental health issues drugs are a form of coping with every day life and escaping their problems. In other cases, narcotics use can take the form of self-treatment and help mitigate the symptoms of an illness. Sometimes drug use is a form of doctor supervised therapy, e.g. use

(11)

2.2. DRUG USE AND MENTAL HEALTH CHAPTER 2. LITERATURE REVIEW of medical marijuana. Nevertheless, when an individual engages in an excessive consumption of highly addictive substances this can turn into a short-term solution that can do more harm than good.

Finally, both narcotics use and mental condition can be triggered by other common factors including the environmental pressure, stress, childhood experiences or even genetics, which according to NIDA estimates is responsible for 40-60 percent of individual’s susceptibility to substance abuse (NIDA (2018)). To sum up, again three main causal paths in the drugs-mental health relation can be discerned:

1. Substance use triggers mental health disorders 2. Mental health issues influence drug use

3. Both mental health condition and substance abuse depend on other common factors Due to the prospering drug market and growing depression rates both among adults and juve-niles the issue of drug-mental health relation became particularly interesting for the researchers. Some of the empirical results are summarized in the following subsection.

2.2.2 Empirical results

The empirical results available up-to-date are highly heterogeneous but generally indicate that there is a link between drug use and mental health. Naturally, sources which conclude that there is no statistically significant influence between drug use and mental health condition exist (Danielsson et al. (2015)), but examples proving that substance use can in fact have an adverse effect on psychological condition are abundant. Examples given below will focus on three possible areas of drug use aftermath: suicidal tendency, depression or anxiety and schizophrenia.

When it comes to suicidal developments certain studies find only gender specific conse-quences of drug use, as in the case of van Ours et al. (2013) and Shalit et al. (2016). In both longitudinal studies heavy cannabis use is linked with the development of suicidal tendencies only among males. However, other sources come to the conclusion that consumption of cannabis has a statistically significant influence on later suicidal ideation, understood as thinking about taking ones life, or even on serious suicidal attempts regardless of one’s gender (Delforterie et al. (2015), Rasic et al. (2012), Chabrol et al. (2008), Pedersen (2008), Beautrais et al. (1999)). Sim-ilar results can be found when examining samples restricted to older people as in Choi et al. (2015) who investigated the influence of cannabis and other illicit drug use on suicidal tenden-cies and major depressive episodes (MDE) among people aged 50 and older. Results showed that chances of having an MDE or suicidal thoughts were higher among any substance users and people consuming many kinds of drugs were in stronger need for treatment due to higher

(12)

2.2. DRUG USE AND MENTAL HEALTH CHAPTER 2. LITERATURE REVIEW rates of substance use disorder and MDE.

The possible influence of cannabis on anxiety and depression symptoms has been acknowl-edged in numerous studies. As shown in Tramer et al. (2001) in their study of cannabinoids and alleviating the symptoms of sickness and vomiting after chemotherapy 13% of the patients given cannabinoids drugs reported anxiety or depression among the side-effects, compared to only 0.3% from the placebo group. Nevertheless, it is important to note that the subsample of cancer patients is probably not representative of the general population. Another study con-ducted by van Ours and Williams (2010) on a less particular subsample of Australian residents shows that marijuana use increased the probability of having mental health problems such as anxiety or depression. The researchers constructed a trivariate system of equations including hazard functions for starting and ending drug use in order to control for unobserved heterogene-ity. Results proved that marijuana use had an adverse impact on mental condition as gauged by the K10 measure of psychological distress. Similar findings are given in Poulin et al. (2005), who identified cannabis as an independent predictor of strengthened depressive symptoms.

The impact of drug use can extend to serious mental disorders such as schizophrenia and psychosis. In order to investigate the influence of long-term drug use and such complex after-effects thoroughly it is most suitable to conduct a longitudinal study. An example is given in Andr´easson et al. (1987) who found out that Swedish conscripts consuming large quantities of cannabis were more likely to suffer from schizophrenia according to a follow-up study conducted after 15 years. Another study by van Os et al. (2002) constructed as a 3 year long follow-up on a sample of over 4000 residents of the Netherlands focused on the cannabis use and its potential impact on the onset of psychosis. The quality of data was most likely much higher compared to the study of Andr´easson et al. (1987) simply because cannabis use is legal in the Netherlands, so subjects were less likely to under-report the frequency and quantity of use. Still, the study confirmed previous findings suggesting that cannabis use can be a risk factor of triggering psy-chosis in healthy adults. Similar result was obtained by Moore et al. (2007), who concluded that cannabis use can increase the risk of psychotic effects going beyond the transient reactions to intoxication. Similarly, Fergusson et al. (2005) explored the relation between cannabis use and psychosis in a 25 years long study during which a birth cohort of over a thousand of New Zealand children has been surveyed at the ages of 18, 21 and 25. According to the results, daily users demonstrated 1.6-1.8 times higher rates of psychotic symptoms compared to non-users. Moreover, the researchers made an attempt to establish a causal link between cannabis use and psychotic symptoms. They dealt with unobserved heterogeneity by constructing a fixed effects model and determined the direction of causality by building a series of structural equa-tions models allowing for reciprocal causality patterns. Results showed that cannabis use had

(13)

2.2. DRUG USE AND MENTAL HEALTH CHAPTER 2. LITERATURE REVIEW statistically significant positive influence on the risk of psychotic syndromes, which indicates potential causality between drug use and psychosis. On the other hand, when analyzing the reversed relation psychotic symptoms had a negative influence on cannabis use, although the impact was not statistically significant.

Another subject related to drug use which has been of particular interest among the re-searchers is the influence of early onset into drug use on mental health condition, because adolescent brain is especially susceptible to the influence of illicit substances (Squeglia et al. (2009)). Results are in line with the intuition since they generally show that those who start using drugs as teenagers are at higher risk of future mental problems (Brook et al. (2002), Patton et al. (2002), Hayatbakhsh et al. (2007), Fergusson et al. (1996), Marmorstein et al. (2009)). As shown in Fergusson et al. (1996) those who began using cannabis before the age of 15 had significantly higher rates of suicidal ideation (odds ratio 3.6), anxiety (odds ratio 2.7) and depression (odds ratio 2.9). Similar result was obtained in a longitudinal study by Marmorstein et al. (2009) who concluded that drug dependence at the ages 17-20 predicted higher risk of major depression in the early adulthood (ages 20-24).

So far the empirical results were concerned primarily with the use of cannabis, however the negative influence of other drugs can be considerable as well. One example is given in Haasen et al. (2005), who found out that the intensity of cocaine and crack use can also have an adverse effect on mental health condition. The investigation of Kim et al. (2011) discusses ecstasy consumption among adolescents and concludes that the rate of suicide attempts among people who used in the past year are almost nine times that of people who have never used any illicit substances.

Nevertheless, use of other illegal substances than cannabis has not been investigated as thoroughly yet, mainly due to the challenge of obtaining high quality data sets representative of the whole population. Drug use is neither legal, nor socially acceptable and due to this fact respondents tend to severely under-report their usage.

(14)

Chapter 3

Data

3.1 Data set

The data set used in order to conduct the analysis comes from the National Household Survey on Drug Use and Health (NSDUH), specifically from the 2016 wave carried out in the United States. NSDUH is managed by the Substance Abuse and Mental Health Services Administration (SAMHSA), which is an agency in the Department of Health and Human Services (DHHS). It was first carried out in 1971 and since then has been conducted annually in the USA. Its primary goal is providing information about trends in tobacco, alcohol and drug consumption as well as about the mental health condition and other health issues of the respondents in the United States in order to monitor potentially dangerous developments.

The NSDUH data files are available publically and they are not only used by individual researchers but also by large private or government institutions such as the U.S. Department of Justice and White House Office of National Drug Control Policy in order to supervise the efficiency of drug prevention procedures (NSDUH (2018)) .

The sample was obtained through a multi-staged and highly stratified selection design in-cluding respondents from 50 American states and the District of Colombia. In the end the sample size of the 2016 wave of the NSDUH survey amounted to around 57 000 respondents aged 12 and older. Respondents were financially motivated to fill in the survey since they re-ceived $30 upon completion of the questionnaire, an incentive that has significantly increased the response rates of NSDUH since its introduction in 2002. For the 2016 survey edition the interview response rate amounted to 68.44%. Data was collected through computer-assisted per-sonal interviews (CAPI) in the general part of the survey and through audio computer-assisted self-interviews (ACASI) for the more sensitive questions to ensure more privacy.

Altogether the data file consists of around 2 600 variables. Apart from general demographic and socioeconomic characteristics of the respondents they include detailed information about the consumption and frequency of tobacco, alcohol and drug use, including substances such as marijuana, heroin, cocaine, crack, hallucinogens and methamphetamines among others. More-over, the depression module included in the survey allows for the analysis of the respondents’

(15)

3.2. DESCRIPTIVE STATISTICS CHAPTER 3. DATA mental health condition since it includes numerous questions about self-reported psychological well-being and outlook on life.

3.2 Descriptive statistics

A summary of the descriptive statistics is presented separately for general characteristics of the respondents (Table 3.1) and for variables denoting drug use, criminal activity and mental health specifically (Table 3.2). However, not all of the variables included in the tables will be taken into account in the estimation procedure. They are presented here to describe the sample profile and patterns in drug use and mental health condition.

3.2.1 General characteristics

The sample under consideration has been restricted to people aged 18 and older due to numerous missing or incompatible answers in the depression module for adolescents compared to adults. After this alteration and deleting nonsensical or blank answers the final sample size amounts to 41.115. When it comes to gender the sample is quite balanced with a slight dominance of women as 46.5% of respondents is male. The vast majority of the interviewees identifies themselves as heterosexual (93.7%) and 89% are covered by any health insurance (private or public). Moving on to the financial condition of the sample under consideration almost in 48% of cases the family income exceeds $50 000 and it is lower than $20 000 for one fifth. The majority of respondents is employed, either full time or part time (68%). Around 36.5% of subjects have obtained either a Bachelor, Associate or Master degree, one fourth of the sample has attended some college but has not graduated, for 26% the highest level of education is finishing high school and circa 12% attended but have not graduated high school. More than 40% of the respondents are married, only 3% are widowed and 11% are divorced or separated.

3.2.2 Mental health, criminal activity and drug use

When it comes to the mental health condition of the interviewees around 15% have undergone a Major Depression Episode (MDE) in their lifetime and in 8.5% of cases this occurred in the year preceding the survey. The mean value of the Kessler Psychological Distress Scale (K6) amounts to 5.7 on a scale from 0 to 24, which generally indicates that the majority of respondents is in a good psychological condition. The K6 indicator is calculated from the answers to questions about the frequency of self-reported symptoms of mental distress, e.g. feeling hopeless, depressed or worthless, and is often used in order to monitor the psychological condition of subjects.

(16)

3.2. DESCRIPTIVE STATISTICS CHAPTER 3. DATA

Table 3.1: Descriptive statistics - general characteristics

Variable Mean St. Dev. Min Max

Marital status

Married 0.413 0.492 0 1

Widowed 0.030 0.171 0 1

Divorced 0.112 0.315 0 1

Never married 0.445 0.497 0 1

Highest level of education

Up to 12th grade but no diploma 0.123 0.328 0 1

Graduated high school 0.263 0.440 0 1

College but no degree 0.249 0.433 0 1

Bachelor/Associate/Master degree 0.365 0.481 0 1 Age categories 18-25 0.318 0.466 0 1 26-34 0.206 0.404 0 1 35-49 0.268 0.443 0 1 50+ 0.209 0.406 0 1 Employment status Employed 0.680 0.466 0 1 Unemployed 0.060 0.238 0 1 Other 0.260 0.438 0 1 Family income less than $20 000 0.205 0.404 0 1 $20 000-$50 000 0.315 0.465 0 1 more than $50 000 0.479 0.500 0 1 Household size 1-2 people 0.385 0.487 0 1 3-4 people 0.431 0.495 0 1 5+ people 0.184 0.388 0 1 Other characteristics

Sexual identity - heterosexual 0.937 0.243 0 1

Covered by any health insurance 0.890 0.313 0 1

Gender - male 0.465 0.499 0 1

(17)

3.2. DESCRIPTIVE STATISTICS CHAPTER 3. DATA As far as the criminal activity of the respondents in the year prior to the survey 3% have been arrested and booked for breaking the law. This percentage increased considerably and amounted to 17.7% when asked about any arrest in the subjects’ lifetime. Criminal activity of the respondents includes offenses such as serious violent assault, motor vehicle theft, robbery, arson, driving under influence or sex offense, and does not include petty misdemeanors like minor traffic violations. Since driving under the influence is a common law violation in the United States and the sample is restricted to people aged 18 and more this percentage might seem particularly high.

Table 3.2: Descriptive statistics - drug use and mental health

Variable Mean St. Dev. Min Max

Mental health

Lifetime MDE 0.156 0.363 0 1

Past year MDE 0.085 0.279 0 1

K6 mental health indicator 5.700 6.029 0 24

Criminal activity

Lifetime arrest 0.177 0.382 0 1

Past year arrest 0.030 0.171 0 1

Drug use Marijuana 0.512 0.499 0 1 Hallucinogens 0.181 0.385 0 1 Cocaine 0.152 0.359 0 1 Inhalants 0.105 0.307 0 1 Methamphetamines 0.058 0.233 0 1 Crack 0.034 0.182 0 1 Heroin 0.021 0.144 0 1

Past year drug abuse/dependence 0.039 0.194 0 1

Past year soft drug use 0.204 0.403 0 1

Past year hard drug use 0.053 0.223 0 1

The magnitude of drug consumption highly depends on a kind of substance. Figures pre-sented in table 3.2 refer to dummy variables denoting whether a person has ever, even once, tried a given narcotic. Not included in the table, but available in the survey, are data consid-ering the monthly and yearly frequency of each substance use, as well as information about the age of first use and a binary indicator whether an individual has tried given drug before the age

(18)

3.3. VARIABLE SELECTION FOR THE MODELS CHAPTER 3. DATA of 21. It turns out that marijuana is the most commonly used drug, tried at least once by more than half of the sample. This result is hardly surprising as it often is the easiest drug to obtain and people are convinced about its benign health implications. Second most popular are hallu-cinogens consumed at least once by 18% of the respondents. The general group of halluhallu-cinogens includes substances such as LSD (”acid”), PCP (”angel dust”), ecstasy , mescaline, ketamine, foxy, DMT, AMT, psilocybin (”mushrooms”) and salvia divinorum. Other popular substances among the interviewees were cocaine tried by 15% of the subjects and inhalants consumed by every tenth person. The category of inhalants includes all kinds of aerosol sprays, glues, paints, markers and other substances inhaled by people in order to feel intoxicated.

Over one fifth of the sample has consumed soft drugs in the 12 months preceding the survey and the percentage decreased to around 5% for the use of hard drugs. Finally, the table includes an indicator of any drug abuse or dependence based on the respondents’ answers to questions about being able to set limits to drug use or needing to consume more in order to feel the same effect as before. According to the results 4% of the subjects struggled with drug abuse or dependence in the year prior to the survey.

3.3 Variable selection for the models

In the first model considering the relation between drug use and mental health the dependent variable is binary and takes value 1 if the respondent has serious mental health issues based on the Kessler Psychological Distress Scale (K6) calculated from the mental condition in the last month prior to the survey.

68.75 25.38 4.619 1.255 0 20 40 60 80 % 0 1 2 3 4 K6 scale categories Recoded

(19)

3.3. VARIABLE SELECTION FOR THE MODELS CHAPTER 3. DATA The original variable represents the intensity of psychological distress on a scale from 0 to 24 and has been recorded following the interpretation of Prochaska et al. (2012) - the K6 values below 6 characterize subjects with no mental health issues (1), values between 6 and 13 suggest moderate psychological distress (2), values above 13 indicate a severe mental health problem (3) and values higher than 20 are the extreme cases (4). In case of the mental health model the focus lies on the respondents from categories 3 and 4. As can be seen from the graph around 5.8% of the sample are dealing with serious psychological issues, for those subjects a value of 1 will be assigned to the dependent variable.

In the second model considering crime the explanatory variable is a binary variable taking the value 1 if a respondent has been arrested for committing a crime in the last 12 months prior to the survey.

The set of explanatory variables in the crime and mental health equations consists of two parts, firstly general characteristics of the respondents described in subsection 3.2.1 and sec-ondly variables denoting the drug use in the year prior to the survey. These variables include two dummies indicating whether the interviewee has consumed soft or hard drugs within 12 months prior to the survey. Hard drugs include physically addictive and more difficult to ob-tain substances such as heroin, cocaine, methamphetamine, crack and hallucinogens. Soft drugs are far easier to obtain and are commonly believed to be less harmful, in the survey they include cannabis and inhalants. Among respondents constituting the sample 20.4% have consumed soft drugs and 5.3% consumed hard drugs in the year before the survey.

(20)

Chapter 4

Model

4.1 Estimation method

4.1.1 Correcting for endogeneity

The interest lies on estimating the influence of two binary variables denoting drug use on the outcome variable that is binary as well. The main issue is the endogeneity of both drug use variables. Simply including them in the probit model and ignoring potential endogeneity could result in biased estimates due to the correlation between the endogenous variables and the error term. Moreover, the most common solution to the endogeneity issue i.e. the instrumental variables method is of no use in this particular case since the model is non-linear and additionally it is almost impossible to find valid instruments for drug use to control for unobserved factors. Since common estimation techniques are in this particular case too complicated, in order to overcome the endogeneity issue a two step model will be constructed. First step includes a bivariate probit model for the joint estimation of the use of soft and hard drugs. In the next step correction terms will be calculated and included to the main outcome equation as additional covariates. The whole procedure is based on the method first proposed by Heckman (1976) and later applied in case of binary models with dummy endogenous variables by Arendt and Holm (2006). The model under consideration is of the following form:

y1= 1(γ1z1+ α2y2+ α3y3+ ε1 > 0) y2= 1(γ2z2+ ε2 > 0)

y3= 1(γ3z3+ ε3 > 0)

(4.1)

in which y1 denotes crime in the first model and mental health in the second one, y2 use of soft drugs, y3 use of hard drugs, z sociodemographic characteristics, ε error terms, 1(.) is an indicator function and α0s and γ0s are parameters to be estimated.

In the first step both drug use equations are jointly estimated by means of a bivariate probit model allowing the error terms ε2 and ε3 to be correlated. The set of explanatory variables including sociodemographic characteristics such as marital status, education level, employment

(21)

4.1. ESTIMATION METHOD CHAPTER 4. MODEL variables and identification of the parameters is based on the nonlinearity of the model). The underlying joint normal distribution has means equal to 0, variances equal to 1 and a correlation parameter given by ρ23. Initial estimates of parameters γ2, γ3 and ρ23are derived from the first step in order to move on to the calculation of correction terms based on a trivariate heckit-type of approximation as proposed by (Heckman (1976)),according to which the first moment of a trivariate truncated normal distribution needs to be obtained. The procedure for deriving the correction terms combines results given by Maddala with the Rosenbaum’s formula (also found in Maddala (1983)). The general design of the correction term under the assumption of normality is as follows: P (γ1z1+ α2y2+ α3y3+ ε1> 0|ε2 > −γ2z2, ε3 > −γ3z3) E(ε1|ε2< a, ε3 < b) = ρ12M23+ ρ13M32 Mkj = Pk− ρ23Pj 1 − ρ2₂₃ Pk= E(εk|ε2 < a, ε3< b), k = 2, 3 (4.2)

By applying the procedure outlined above for four possible combinations of values assigned to binary variables y2 and y3 we obtain the final correction terms M23 and M32. The explicit formulas can be found in the Appendix. As a result, the final form of main outcome equation considering y1 together with the correction terms can be expressed by:

y1 = 1(γ1z1+ α2y2+ α3y3+ ρ12M23+ ρ13M32+ ε∗1> 0) ε∗₁ = ε1− ρ12M23− ρ13M32

(4.3)

where ρ12and ρ13are additional parameters to be estimated and a set of additional explanatory variables z1 includes information about respondent’s gender, income and age (hence differs from z2 and z3). Correction terms have the same structure both for the crime and mental health model and the only difference in the final equation 4.3 lies in the dependent variable denoted by y1.

4.1.2 Semi-nonparametric maximum likelihood estimation

In the second step the main outcome equation 4.3 will be estimated by means of two meth-ods, firstly a parametric probit model including the correction terms and secondly by a semi-nonparametric maximum likelihood procedure first proposed by Gallant and Nychka (1987) and later applied in case of binary models with binary endogenous variables by Stewart et al. (2004). Estimation results for both techniques will be compared in the following chapter.

(22)

con-4.2. METHODOLOGICAL ISSUES CHAPTER 4. MODEL cerning the unknown distribution of the error term. The estimates of fully parametric probit can be inconsistent if the actual distribution considerably deviates from the assumptions. The estimation of the SNP model is carried out by substituting the unknown specification of the density function by an approximation given by Hermite polynomial expansion i.e. a product of the normal density and a squared polynomial. The coefficients of the polynomial are restricted so that it integrates to one and estimation can be conducted for various orders of the polynomial starting from 3. All things considered, the approximation of the density can be expressed by:

fK(ε) = 1 θ( K X k=0 γkεk)2φ(ε) θ = Z ∞ −∞ ( K X k=0 γkεk)2φ(ε)dε (4.4)

,in which φ(ε) stands for the standard normal density function. Following upon the estimate of the density the distribution function is of the following form:

FK(u) = Ru −∞( PK k=0γkεk)2φ(ε)dε R∞ −∞( PK k=0γkεk)2φ(ε)dε (4.5) As a result consistent estimates of the parameters of interest are derived by maximizing the usual probit loglikelihood function based on the distribution function given in 4.5:

logL = N X

i=1

[yiln(FK(u)) + (1 − yi)ln(1 − FK(u))] (4.6)

Theoretically, estimation based on higher order polynomials would be possible in case of this model given that the sample size is large. The results of the models corresponding to various polynomial orders can later be assessed by means of likelihood ratio tests or standard model comparison criteria such as Akaike, Bayesian-Schwarz or Hannan-Quinn information criteria in order to identify the best alternative.

4.2 Methodological issues

Major drawback of this study is the nature of self-reported cross-sectional data itself. Given that the topics of interest are extremely sensitive, since they include drug use, mental well being and crime, it is very likely that the respondents are either not disclosing the truth in the survey or are under-reporting their extent of drug use. Even though the answers to the most sensitive questions were anonymous and collected in privacy to make the interviewees more comfortable this does not guarantee full honesty and might to some extent influence the results.

(23)

4.2. METHODOLOGICAL ISSUES CHAPTER 4. MODEL Moreover, self-reported data may also suffer from a recall error in case of questions referring to the past, e.g. about the age of first substance use, however such variables are not included in the final version of the model, so this should not be a relevant issue.

Lastly, cross-sectional data make it difficult or almost impossible to find out whether sub-stance use preceded or followed issues with mental health or criminal activity and hence analyze the causality in drug-crime and drug-mental health relations. In case of this thesis this issue is valid especially in the case of crime model, since both the dependent and explanatory variables refer to an activity in the same period of time, namely past 12 months. In case of the mental health model the dependent variable refers to the past single month, however this still does not facilitate inferring causality.

Another challenge stemmed from the endogeneity of drug use variables combined with the fact that common estimation techniques were in this case very complicated. As a result, the number of endogenous variables had to be limited to two in order to facilitate the procedure. Unfortunately, the endogenous variables in case of this model are the variables of main interest since they convey information about respondents’ drug use patterns. In the end, the variables denoting frequency of drug use have not been included in the model and substance consump-tion had to be generalized and grouped into use of soft and hard drugs. Moreover, the available information considering mental health condition of the respondent has also not been fully ex-ploited, since the Kessler Psychological Distress Scale has been recoded into a dummy. This issue of limited information available in the final model is definitely a weak point of this thesis and leaves room for improvement in terms of future research.

When it comes to the estimation procedure itself it would have been more adequate to estimate the first step semi-nonparametrically as well, whereas in this thesis the first step parametric bivariate probit is shared both for the second step parametric estimation as well as the SNP model.

Final issue is linked with the risk of introducing heteroscedasticity to the model. If the original error term ε1 is homoscedastic, then the transformed one ε∗1 = ε1− ρ12M23− ρ13M32 can suffer from heteroscedasticity. This problem has not been addressed in this thesis and is another point that can be improved in terms of future research.

(24)

Chapter 5

Results

5.1 First step - Bivariate Probit for Drug Use

Estimation results of a bivariate probit corresponding to drug use equations can be found in Table 5.1. Categorical variables have been recoded into dummies and for each variable one category has been dropped in order to avoid strict multicollinearity. The reference categories are: single respondents for the marital status, people who have not graduated high school for the education status, unemployed for the employment status and those living in a small household (with one or two people) for the household size. The main goal of the first step model is obtaining initial estimates of the variables listed in the table as well as deriving the correlation coefficient between ε2and ε3. It is presented in the Table as a ”Rhobit” estimate corresponding to a Fisher’s Transformation given below:

Rhobit = ln(1 + ρ23 1 − ρ23

) (5.1)

As follows from the transformation the correlation amounts to ˆρ23 ≈ 0.72 (SE ≈ 0, 009 based on the delta method), this value will be needed in order to construct the correction terms.

The results of the first step estimation will not be discussed in detail, however some general trends can be discerned based on the signs of the coefficients and the significance levels. All marital status variables are significant at the 0.01 level and signs of the coefficients suggest that single people are more likely to consume both hard and soft drugs. Highest level of the respondent’s education does not seem to play an important role in terms of influencing drug use, the only statistically significant variable in both equations denotes people who have attended some college but have not graduated. Positive coefficient suggests a positive influence on the outcome variable. On the other hand, the employment status of a respondent seems to be of higher importance when it comes to drug consumption - both in the case of hard and soft drugs the influence on the probability of using is negative among people who are employed compared to the reference category of the unemployed ones. Variables denoting household size and military service will not be addressed, since they do not appear to be of high significance. Finally, the probability of using both hard and soft drugs seems to be lower among people who are insured and for those respondents who identify themselves as heterosexual.

(25)

5.1. FIRST STEP - BIVARIATE PROBIT FOR DRUG USE CHAPTER 5. RESULTS Table 5.1: First step - Bivariate Probit Model for Drug Use

Variable Coefficient SE z-value p-value

Equation 1: Use of soft drugs

Married −0.743 0.017 −43.396 p < 0.001∗∗∗

Widowed −1.035 0.062 −16.696 p < 0.001∗∗∗

Divorced −0.427 0.024 −17.566 p < 0.001∗∗∗

Graduated high school 0.055 0.025 2.170 p = 0.030∗∗

College but no degree 0.183 0.026 7.086 p < 0.001∗∗∗

BA/MA/Associate degree −0.029 0.026 −1.141 p = 0.254

Employed −0.149 0.029 −5.159 p < 0.001∗∗∗

Other form of employment −0.333 0.031 −10.596 p < 0.001∗∗∗

Insured −0.086 0.023 −3.780 p < 0.001∗∗∗

Household Medium −0.006 0.016 −0.370 p = 0.712

Household Large −0.083 0.022 −3.847 p < 0.001∗∗∗

Heterosexual −0.446 0.027 −16.694 p < 0.001∗∗∗

Military service −0.112 0.034 −3.260 p = 0.001∗∗∗

Equation 2: Use of hard drugs

Married −0.777 0.028 −27.244 p < 0.001∗∗∗

Widowed −0.934 0.113 −8.235 p < 0.001∗∗∗

Divorced −0.347 0.035 −9.838 p < 0.001∗∗∗

Graduated high school −0.053 0.036 −1.468 p = 0.142

College but no degree 0.115 0.036 3.205 p = 0.001∗∗∗

BA/MA/Associate degree −0.061 0.037 −1.618 p = 0.106

Employed −0.182 0.038 −4.805 p < 0.001∗∗∗

Other form of employment −0.336 0.042 −7.923 p < 0.001∗∗∗

Insured −0.134 0.031 −4.358 p < 0.001∗∗∗ Household Medium −0.006 0.024 −0.243 p = 0.808 Household Large −0.062 0.031 −1.958 p = 0.050 Heterosexual −0.364 0.034 −10.740 p < 0.001∗∗∗ Military service −0.083 0.055 −1.512 p = 0.131 Intercept 1 0.134 0.045 3.014 p = 0.002∗∗∗ Intercept 2 −0.686 0.058 −11.737 p < 0.001∗∗∗ Rhobit 1.814 0.036 50.513 p < 0.001∗∗∗ Observations 41,115 Log Likelihood -25006.52

(26)

5.2. SECOND STEP - PARAMETRIC ESTIMATION CHAPTER 5. RESULTS Generally, the results for both equations are quite comparable when it comes to coefficient signs and significance levels, which suggests that the use of both soft and hard drugs could be influenced by similar factors. When comparing the results of probit estimation for use of both soft and hard drugs with the estimation of the model in which dependent variable denotes the use of any kind of drug generally, so combines the soft and hard drugs variables, the LR test statistic indicates that the general model in fact fits the data as well as the separate estimation for various kind of drugs (corresponding p-value<0.0001).

5.2 Second step - Parametric Estimation

Results of the probit models considering influence of drug use on crime and mental health can be found in Tables 5.2 and 5.3. The coefficients ρ12and ρ13correspond to the two correction terms M23 and M32. The reference categories are people aged 50 and older for the age variables and people whose total family income is lower than $20 000 per year for the income variables. Due to the fact that the estimation procedure is a two-step model all standard errors and z-values presented in the following sections have been bootstrapped based on 300 replications.

5.2.1 Crime Probit Model

As can be seen from the table all estimates except for the correction terms coefficients are statistically significant at the 0.01 level. Probability of committing a crime appears to be higher among males and among younger people. For the respondents aged 18-34 the influence on the outcome variable is the strongest and slightly diminishes but remains positive for those aged 35-49 compared to the reference category of people 50+. The propensity to commit a crime also depends on income, the probability that dependent variable equals 1 decreases the higher the yearly family income compared to the respondents with income lower than $20 000. Moving on to the variables of main interest, both the use of soft and hard drugs in the 12 months prior to the survey have a positive and statistically significant influence on the probability of committing a crime in the same period, however the influence of hard drugs is much stronger, which can be assessed based on the values of marginal effects described in detail in section 5.4. Surprisingly, neither of the correction terms seems to have a significant influence on the outcome variable. The probit model under consideration has been compared to a simple probit model without the correction terms by means of a likelihood ratio test. Based on the chi-squared test statistic with two degrees of freedom the test shows that there is no evidence to reject the null hypothesis and claim that the model with higher number of parameters fits the data better (corresponding p-value=0.412).

(27)

5.2. SECOND STEP - PARAMETRIC ESTIMATION CHAPTER 5. RESULTS Table 5.2: Second step - Crime Model

Constant −2.389 0.051 −47.143 p < 0.001∗∗∗ Gender - male 0.380 0.029 13.057 p < 0.001∗∗∗ Age 18-25 0.487 0.048 10.159 p < 0.001∗∗∗ Age 26-34 0.488 0.050 9.755 p < 0.001∗∗∗ Age 35-49 0.314 0.051 6.122 p < 0.001∗∗∗ Income $20 000-$50 000 −0.178 0.034 −5.175 p < 0.001∗∗∗ Income $50 000+ −0.489 0.034 −14.280 p < 0.001∗∗∗ Soft drugs 0.351 0.032 11.039 p < 0.001∗∗∗ Hard drugs 0.546 0.047 11.678 p < 0.001∗∗∗ ρ12 0.001 0.002 0.317 p = 0.752 ρ13 0.005 0.006 0.926 p = 0.355 Observations 41,115 Log Likelihood -4,903.176

Akaike Inf. Crit. 9,828.353

Note 1: ∗∗p<0.05;∗∗∗p<0.01

Note 2: SE and z-values are a result of a bootstrap based on 300 replications

5.2.2 Mental Health Probit Model

Results of the parametric probit estimation of mental health second step equation can be found in Table 5.3. According to the results women appear to be more likely than men to suffer from a mental health condition, since the estimate of the coefficient corresponding to the gender variable is negative. Additionally, it seems like younger people are dealing with more psycho-logical distress, the influence on the probability of struggling with mental issues is the strongest among the respondents aged 18 to 25 compared to those 50 and older, this can be said with full confidence basing on the value of the marginal effect (see Table 5.6). Moreover, financial situation of the respondent seems to influence his psychological well-being, since the higher the yearly family income the less likely a subject is to have a mental health problem in comparison to the reference category of people with the annual income not exceeding $20 000.

When it comes to drug use variables, in case of this model all of them are statistically significant. Consumption of both soft and hard drugs in the year prior to the survey positively influenced the probability of having a serious mental health issue in the month before the survey. Moving on to the correction terms, both are statistically significant (ρ12 at 0.05 level and ρ13 at 0.01 level) but their influence on the outcome variable is quite small. However, this time the

(28)

5.3. SECOND STEP - SEMI-NONPARAMETRIC ESTIMATION CHAPTER 5. RESULTS Likelihood Ratio test statistic with corresponding p-value equal to p = 0.002 suggests that in case of the mental health model the correction procedure is in fact improving the fit to the data and the simple probit model without the correction terms should not be chosen over the model with larger number of parameters. Finally, it is worth noting that the signs of the correction terms’ coefficients are negative even though the signs of the drug use coefficients are positive, which is a slightly unexpected finding.

Table 5.3: Second step - Mental Health Model

Constant −1.645 0.033 −49.546 p < 0.001∗∗∗ Gender - male −0.200 0.021 −9.421 p < 0.001∗∗∗ Age 18-25 0.427 0.035 12.205 p < 0.001∗∗∗ Age 26-34 0.260 0.036 7.157 p < 0.001∗∗∗ Age 35-49 0.291 0.035 8.427 p < 0.001∗∗∗ Income $20 000-$50 000 −0.198 0.026 −7.728 p < 0.001∗∗∗ Income $50 000+ −0.436 0.025 −17.500 p < 0.001∗∗∗ Soft drugs 0.283 0.029 9.938 p < 0.001∗∗∗ Hard drugs 0.391 0.043 9.155 p < 0.001∗∗∗ ρ12 −0.003 0.001 −2.289 p = 0.023∗∗ ρ13 −0.014 0.004 −3.305 p = 0.001∗∗∗ Observations 41,115 Log Likelihood -8,577.434

Akaike Inf. Crit. 17,176.870

Note 1: ∗∗p<0.05;∗∗∗p<0.01

5.3 Second step - Semi-Nonparametric Estimation

In case of the SNP models all explanatory variables and so the reference categories remain the same. The only difference is that there is a restriction placed on the constant and it is fixed at its probit estimate. As mentioned before, estimation of this model for higher order polynomials is theoretically possible due to a sufficiently large sample size. However, in that case the loglikelihood convergence was reached after a considerably higher number of iterations which strongly influenced the computation time especially in the bootstrapping part. Due to technical limitations the estimation results presented here are based on the third order polynomial.

(29)

5.3. SECOND STEP - SEMI-NONPARAMETRIC ESTIMATION CHAPTER 5. RESULTS

5.3.1 Crime SNP Model

Results presented in Table 5.4 do not strongly deviate from those generated by the aforemen-tioned parametric probit when it comes to the general patterns. All signs of the coefficients as well as the statistical significance levels remained the same. This means that both correction terms coefficients remained statistically insignificant also in the semi-nonparametric estimation. In case of the SNP estimation both values of the coefficients and of the standard errors deviate from those generated by the parametric probit, due to the fact that the variance is no longer equal to 1. Hence instead of comparing the coefficients, influence of the variables will be assessed based on marginal effects in subsection 5.4.

Table 5.4: Second step - Crime SNP Model

Constant −2.389 F ixed Gender - male 0.378 0.056 6.70 p < 0.001∗∗∗ Age 18-25 0.455 0.075 6.06 p < 0.001∗∗∗ Age 26-34 0.456 0.069 6.60 p < 0.001∗∗∗ Age 35-49 0.267 0.057 4.72 p < 0.001∗∗∗ Income $20 000-$50 000 −0.219 0.046 −4.73 p < 0.001∗∗∗ Income $50 000+ −0.499 0.069 −7.29 p < 0.001∗∗∗ Soft drugs 0.372 0.059 6.29 p < 0.001∗∗∗ Hard drugs 0.817 0.252 3.24 p = 0.001∗∗∗ ρ12 0.001 0.001 0.37 p = 0.710 ρ13 0.006 0.006 0.98 p = 0.325 Observations 41,115 Log Likelihood -4,887.407 Note 1: ∗∗p<0.05; ∗∗∗p<0.01

According to the likelihood ratio test of a probit model against the SNP model there is enough evidence to reject the null hypothesis that the parametric probit model is a better fit to the data than the SNP model (p-value<0.0001).

(30)

5.3. SECOND STEP - SEMI-NONPARAMETRIC ESTIMATION CHAPTER 5. RESULTS

5.3.2 Mental Health SNP Model

When comparing the parametric and semi-nonparametric estimation results, similar conclusions can be drawn also in case of the mental health model. Again, the general patterns such as signs of the coefficients and significance levels remained almost the same as in the case of parametric estimation. The fact that the results of the SNP model are characterized by higher values of the coefficients as well as by higher bootstrapped standard errors is again attributable to the difference in variance.

Moreover, in case of the Gallant & Nychka procedure the unintuitive negative signs of the ρ12 and ρ13 coefficients can be found in the estimation results just like in the parametric case.

Table 5.5: Second step - Mental Health SNP Model

Constant −1.645 F ixed Gender - male −0.309 0.052 −5.92 p < 0.001∗∗∗ Age 18-25 0.755 0.118 6.39 p < 0.001∗∗∗ Age 26-34 0.351 0.070 4.99 p < 0.001∗∗∗ Age 35-49 0.382 0.066 5.79 p < 0.001∗∗∗ Income $20 000-$50 000 −0.459 0.087 −5.29 p < 0.001∗∗∗ Income $50 000+ −0.827 0.120 −6.90 p < 0.001∗∗∗ Soft drugs 0.528 0.080 6.58 p < 0.001∗∗∗ Hard drugs 1.046 0.233 4.49 p < 0.001∗∗∗ ρ12 −0.003 0.002 −1.85 p = 0.065 ρ13 −0.022 0.008 −2.75 p = 0.006∗∗∗ Observations 41,115 Log Likelihood -8,558.978 Note 1: ∗∗p<0.05; ∗∗∗p<0.01

When it comes to the comparison of both models, the likelihood ratio test of parametric probit model against the SNP model concludes that there is evidence to reject the null hypothesis and the probit is not a better alternative over the SNP model (p-value<0.0001).

(31)

5.4. MARGINAL EFFECTS CHAPTER 5. RESULTS

5.4 Marginal Effects

A comparison of marginal effects for both crime and mental health models estimated by para-metric and semi-nonparapara-metric techniques can be found in Table 5.6. Standard errors presented in brackets have been calculated by a bootstrap based on 300 replications. Marginal effects have been calculated as average marginal effects instead of as marginal effects at means of the vari-ables because of the fact that all explanatory varivari-ables are binary and so treating the mean as a reference point is inadequate.

Table 5.6: Marginal Effects

Variable Crime Probit Crime SNP Mental Health Probit Mental Health SNP

Gender - male 0.023∗∗∗ 0.021∗∗∗ −0.022∗∗∗ _−0.018∗∗∗ (0.0017) (0.0019) (0.0023) (0.0024) Age 18-25 0.034∗∗∗ 0.025∗∗∗ 0.052∗∗∗ 0.044∗∗∗ (0.0043) (0.0027) (0.0049) (0.0035) Age 26-34 0.039∗∗∗ 0.025∗∗∗ 0.032∗∗∗ 0.020∗∗∗ (0.0056) (0.0025) (0.0053) (0.0035) Age 35-49 0.023∗∗∗ 0.015∗∗∗ 0.036∗∗∗ 0.022∗∗∗ (0.0044) (0.0026) (0.0049) (0.0035) Income $20-$50 000 −0.011∗∗∗ −0.012∗∗∗ −0.021∗∗∗ −0.027∗∗∗ (0.0020) (0.0019) (0.0027) (0.0033) Income $50 000+ −0.028∗∗∗ _−0.028∗∗∗ _−0.046∗∗∗ _−0.048∗∗∗ (0.0021) (0.0023) (0.0030) (0.0028) Soft drugs 0.024∗∗∗ 0.021∗∗∗ 0.035∗∗∗ 0.031∗∗∗ (0.0027) (0.0018) (0.0038) (0.0032) Hard drugs 0.049∗∗∗ 0.045∗∗∗ 0.055∗∗∗ 0.061∗∗∗ (0.0061) (0.0088) (0.0077) (0.0130) Note 1: ∗∗p<0.05; ∗∗∗p<0.01

Note 2: MEs calculated as average marginal effects instead of at means

Note 3: Bootstrapped standard errors based on 300 replications are presented in brackets

Variables with positive values of marginal effects influence the probability of committing a crime as well as the probability of having mental health issues positively. As can be seen from the table marginal effects are negative only for the income variables in both models and for the gender variable in mental health models. This means that men are less likely to have

(32)

5.4. MARGINAL EFFECTS CHAPTER 5. RESULTS mental health issues, probability that the outcome variable is equal to 1 for men is lower by 2.2% according to the parametric estimate and by 1.8% according to the SNP model compared to women. On the other hand, men appear to be more likely to commit a crime, the probability is higher by around 2% in comparison to women. When it comes to the respondents’ financial situation, the higher the respondents income the lower his propensity to commit a crime or develop a psychological condition. Probability to commit a crime is lower by around 1.1% for income category $20 000-$50 000 and by 2.8% for the category $50 000+ compared to the respondents whose yearly family income is lower than $20 000.

The risk of having mental health problems is also lower for those subjects who are in better financial condition, among the respondents from the highest income category the probability of having a serious mental issue is lower by 4.6%-4.8% compared to the lowest income category.

Moving on to age, we can see that people aged 50 and older are less likely to both commit crimes and have mental health issues, since marginal effects for all lower age categories are positive. What stands out is that respondents aged 18-25 are 5.2% (parametric)/4.4% (SNP) more likely to have psychological problems compared to the highest age category. The difference amounts to around 3% (parametric)/2% (SNP) for respondents aged 26-49. In case of the crime model the influence of age is a bit more moderate and marginal effects are the highest for subjects aged 26-34, they amount to 3.9% according to the parametric estimate and 2.5% according to the SNP ones.

Finally, both variables of main interest denoting the use of soft and hard drugs have a positive influence on the probability of committing a crime and having serious mental health problems. Moreover, both models suggest that the influence of hard drugs is stronger compared to that of soft drugs. According to the estimates of the first model respondents who have used soft drugs were around 2.1%-2.4% more likely to commit a crime and the same percentage amounted to around 4.5%-4.9% for those who consumed hard drugs. Looking at the results of the second model we can see that the influence of drug use is a bit stronger on the mental health condition, since the probability of having serious psychological problems was 3.1%-3.5% higher among the respondents who used soft drugs and as much as 5.5%-6.1% higher for those who consumed hard drugs.

When it comes to the comparison of parametric and semi-nonparametric estimates, the values were quite often really close to each other and the difference between the marginal effects estimates was never larger than 0.014. One final remark that stands out from the table is that in case of all the estimated models the variable denoting use of hard drugs had the highest influence on the propensity to commit a crime or develop a mental health condition, which is in line with initial intuitive predictions.

(33)

5.5. ROBUSTNESS OF THE RESULTS CHAPTER 5. RESULTS

5.5 Robustness of the results

The results of the second step parametric estimation can be assessed by two robustness checks. First one, already described in detail in previous sections, is the semi-nonparametric estimation of the same model. As we could see from the results in Table 5.6, the estimated influence of explanatory variables on the outcome variables is quite comparable for both the parametric and semi-nonparametric models. This suggests that the assumptions considering the distribution of the error term in the parametric model did not deviate from the actual distribution to a great extent and the results of the probit estimation are not too far off compared to the SNP model. Second robustness check has been carried out by performing a logistic regression of the same model in order to see whether the results would differ if we applied a logistic link function corresponding to a logistic cumulative distribution function instead of the inverse of the normal link function and a standard normal cumulative distribution function as is in the case of the probit model. Results of the logit estimation can be found in the Appendix, they include estimation of the second step crime model as well as the second step mental health model and calculation of the marginal effects. Again, all standard errors have been bootstrapped based on 300 replications.

The results once again suggest that the estimates of the parametric probit can be treated with a dose of certainty. First thing that can be noticed is that all coefficient signs and sig-nificance levels are in line with those of the parametric probit estimation. Since values of the coefficients cannot be compared in non-linear models the focus in this case lies on marginal ef-fects. Comparing tables 5.6 and B.3 we can see that the estimated influence of the explanatory variables on the probability of committing a crime or having mental health issues in case of logistic regression is very close to the probit estimates.

Additionally, estimation has been carried out separately on a subsample of women and men in order to compare the results between genders. Tables with the second step parametric estimation results including gender comparison can be found in Appendix C and calculated marginal effects for the corresponding probit models in Table 5.7.

In case of the crime model absolute values of marginal effects are higher among males, which indicates that the influence of each variable included in the model on the propensity to commit a crime is higher among males. When it comes to the drug related variables, males who consume hard drugs are 4.4% more likely to commit a crime and for those who used soft drugs the marginal effect amounts to 3%. The corresponding statistics for women amount to 2.4% and 1.4%, which indicates that the influence of drug use on the probability of committing a crime is less intense among females.