Causal association between alcohol consumption and mental health problems

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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

Causal association between alcohol

consumption and mental health problems

Miriam Veenstra

(10588086)

MSc in Econometrics Track: Econometrics

Date of final version: June 29, 2017 Supervisor: Dr. J.C.M. van Ophem

Second reader: Dr. N.P.A. van Giersbergen

Abstract

In this thesis it is investigated whether alcohol consumption causes mental health problems. In doing so, the issue of potentially unobserved common confounding factors affecting both alcohol consumption and mental health is accounted for by employing a discrete factor approach. That is, the dynamics in alcohol consumption and mental health are estimated jointly, allowing the unobserved heterogeneity terms in the equations to be correlated. The main finding is that alcohol consumption increases the likelihood of having mental health problems only when consumed daily. Additionally, unobserved common confounding factors do not seem to be an issue.

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Statement of Originality

This document is written by Miriam Veenstra who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is 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.

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1 Introduction

Alcohol is one of the most popular and most commonly used drugs worldwide. Its popular-ity is essentially derived from the stimulant effects alcohol can have. For example, drinking alcohol can result in increased energy and feelings of happiness. However, alcohol is actually classified as a depressant: it has the quality of depressing the vital activities of the brain. The type of effect alcohol has, stimulant or depressant, is determined by the amount of alcohol consumed. Moderate alcohol consumption leads to a stimulant effect, whereas excessive alcohol consumption leads to a depressant effect. In addition to the depressant effects, excessive alcohol consumption can have damaging effects on the brain. In particular for young people excessive alcohol consumption can be harmful, as in adolescence the brain is still developing. As a result, alcohol consumption is associated with mental health problems. What remains unclear is to what extent alcohol consumption causes mental health problems.

Knowledge about the relationship between alcohol consumption and mental health is of particular interest from a policy perspective. First of all, alcohol consumption is legal from a certain age onwards, referred to as the minimum legal drinking age (MLDA). The MLDA differs across countries, for example in the United States the MLDA is 21 years, whereas in Luxembourg it is 16 years. The most commonly used MLDA worldwide is 18 years, which is also the MLDA currently in the Netherlands. In the Netherlands the minimum legal drinking age was raised from 16 to 18 years in 2014, to discourage young people from drinking. Despite the MLDA, initiation of alcohol consumption typically starts in the early to mid teen years: in 2015, 45% of Dutch school pupils aged 12 to 16 years had consumed alcohol in their lifetime (Van Dorsselaer et al., 2016), suggesting that the enforcement of the MLDA is not strict enough. Hence, knowledge of the effect of alcohol consumption on mental health is helpful for determining the suitable MLDA as well as enforcement strategies. Secondly, if alcohol consumption causes mental health problems, other alcohol policy measures may be necessary. For example, both initiation of alcohol consumption and the level of alcohol consumption may be reduced by educating teenagers about the risks of alcohol consumption. Clearly, this topic is of ongoing interest.

A difficulty in establishing the causal effect of alcohol consumption on mental health prob-lems, is the potential for unobserved common confounding factors affecting both alcohol con-sumption and mental health. As stated by Pudney (2010), even the most extensive longitudinal survey cannot comprehend every relevant aspect of the individual and his or her environment. Consequently, there may exist relevant variables affecting both alcohol consumption and mental health that are unobserved. The neglect of unobserved heterogeneity may lead to a considerable bias in the estimates and erroneous inferences. Hence, in order to obtain a reliable estimate of the causal effect of alcohol consumption on mental health problems, the role of unobserved heterogeneity must be taken into account. The purpose of this thesis is therefore to investigate to which extent alcohol consumption causes mental health problems, while addressing the issue of potentially unobserved common confounding factors.

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1 Introduction

To investigate the causal relationship between alcohol consumption and mental health prob-lems, a trivariate system of equations is estimated. The three-equation system consists of a proportional piecewise constant hazard model for the rate of initiation into alcohol consump-tion, a probit model for the decision to quit drinking alcohol and a Poisson regression model for the mental health measure. Furthermore, to address the issue of potentially unobserved common confounding factors, a discrete factor approach as introduced by Heckman and Singer (1984) is employed. That is, a discrete distribution of unobserved heterogeneity is assumed within each equation and the unobserved heterogeneity terms are allowed to be correlated across the multiple equations.

The model is estimated using data from the Longitudinal Internet Studies for the Social sciences (LISS) panel. In particular, the Alcohol and Drugs study and the Health core study, both collected in 2008, together with background variables, are used. These studies contain in-formation about the age of first drinking, the current state of drinking (past drinkers / current drinkers) and the mental health of the respondents, which are used to construct the depen-dent variables. In addition, the explanatory variables include demographic, socio-economic and health related factors.

The remainder of this thesis is organized as follows. Chapter 2 contains a literature review on addressing unobserved heterogeneity and unobserved common confounding factors, in particular in the context of duration models. Next, Chapter 3 presents the econometric methodology. Chapter 4 describes and analyses the LISS panel data and introduces the relevant variables. The results from estimation are then presented in Chapter 5. Subsequently, a sensitivity analysis is presented in Chapter 6 and finally, Chapter 7 concludes and provides suggestions for further research.

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2 Literature review of unobserved heterogeneity

To gain insides into methods for addressing the issue of potentially unobserved common con-founding factors, this chapter presents results from previous studies on unobserved heterogene-ity, in particular in the context of duration models. First, Section 2.1 provides the basic concepts of duration data. Next, Section 2.2 discusses the analysis of unobserved heterogeneity in dura-tion models. Finally, Secdura-tion 2.3 elaborates on accounting for unobserved common confounding factors by discussing the paper of Van Ours and Williams (2011).

2.1 Basic concepts duration analysis

This section provides the key concepts of duration analysis. Duration models are concerned with modeling the length of time spent in a given state, the duration or spell length, before transition to another state, denoted T . The transition to another state is referred to as the event of a failure. The first key concept in duration analysis is the cumulative distribution function of T , that is, the probability that the duration is less than or equal to t, which is defined as

F (t) = Pr[T ≤ t]

= Z t

0

f (s)ds,

where f (t) = dF (t)/dt is the density function of T . The probability that T exceeds t, is then defined as

S(t) = Pr[T > t] = 1 − F (t),

and is called the survivor function. Next, the instantaneous probability of leaving a state conditional on survival to time t, is defined as

λ(t) = lim ∆t→0 Pr[t ≤ T < t + ∆t|T ≥ t ∆t = f (t) S(t),

and is called the hazard function. The final key concept is the integrated hazard function, denoted Λ(t): Λ(t) = Z t 0 λ(s)ds = − ln S(t).

(Cameron and Trivedi, 2005, p. 576-577). Note that all of the aforementioned concepts are somehow related to each other. Now that the basic concepts of duration analysis are introduced, the next section discusses the role of unobserved heterogeneity in duration models.

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2.2 Unobserved heterogeneity

This section provides an overview of duration models using continuous and discrete representa-tions of unobserved heterogeneity, referred to as continuous and discrete heterogeneity models, respectively. First, concerning continuous heterogeneity models, a form of multiplicative un-observed heterogeneity is considered and thereafter, regarding discrete heterogeneity models, a finite mixture model is explored.

First, focussing on continuous heterogeneity models, consider the proportional hazard spec-ification of the conditional hazard rate

λ(t|x, β) = λ0(t)φ(x, β),

where λ0(t) is the baseline hazard and is a function of t alone, and φ(x, β) is a function of x alone. To address the issue of unobserved heterogeneity, Lancaster (1979) introduced an extension of the proportional hazard model, by including a multiplicative error term ν. That is, the conditional hazard rate becomes

λ(t|x, β) = λ0(t)φ(x, β)ν, ν > 0,

where the additional error term ν can be interpreted as the unobserved heterogeneity and is assumed to be independent of the regressors. Estimation of the model typically involves pos-tulating a distribution for the unobserved heterogeneity term and then obtaining the marginal distribution of the spell t, by integrating the error term ν out. Lancaster (1979) assumes a Gamma distribution for the heterogeneity term, though there is no real justification for the choice of heterogeneity distribution other than that of computational convenience. Conse-quently, specification of the heterogeneity distribution is often rather arbitrary.

However, misspecification of the functional form of the heterogeneity distribution may lead to biased estimates. Heckman and Singer (1984) show that the parameter estimates of the hazard model are sensitive to the assumptions about the parametric specifications of unob-served heterogeneity. That is, the choice of heterogeneity distribution may lead to considerable distorted inferences. To overcome this issue, Heckman and Singer (1984) introduced a nonpara-metric technique for the estimation of the heterogeneity distribution, where the distribution of unobserved heterogeneity is assumed to be discrete. This model is considered next.

The discrete heterogeneity model introduced by Heckman and Singer (1984) is a restricted formulation of the finite mixture model. In the finite mixture model all parameters of the explanatory variables are allowed to differ across a number of latent classes. In the discrete heterogeneity model however, only the constant is allowed to differ. To be more precise, in the aforementioned continuous heterogeneity model, the distribution of the unobserved heterogene-ity term has infinite points of support. The discrete heterogeneheterogene-ity model, on the other hand, assumes a finite number of support points, say m, referred to as components. This can be interpreted as follows: the continuous unobserved heterogeneity distribution of the parametric approach is approximated by a discrete distribution, denoted by pj(j = 1, . . . , m) with m points

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of support. By letting the number of support points grow, any distribution can be approximated to the required degree. This leads to the following marginal mixture distribution:

g(ti|xi, pj, β) = m X j=1 f1(ti|xi, νj, β)pj, 0 ≤ pj ≤ 1, m X j=1 pj = 1,

where f1(·) is the individual likelihood contribution depending on the actually chosen model, νj denotes a support point and pj is the associated probability, the so-called mixing probability (Cameron and Trivedi, 2005, p. 621-622). The mixing probabilities pj, j = 1, . . . , m, are usually unknown and hence estimation of the model involves both the mixing probabilities and the component parameters. Estimation of the model is by maximum likelihood and the maximum likelihood estimator introduced by Heckman and Singer (1984) is called the nonparametric maximum likelihood estimator (NPMLE). It must be remarked that the nonparametric element is the number of components, though the estimation method is in fact semiparametric, as it is combined with parametric models for the components.

Note that although the discrete heterogeneity model presented above is considered in the context of duration models, it can also be applied to other econometric models. For example, suppose that the dependent variable y is a random count. Analogous to the duration model, the distribution of the unobserved heterogeneity term is assumed to have m points of support (νj, j = 1, . . . , m) each with an associated probability (pj, j = 1, . . . , m). The marginal finite mixture distribution is g(yi|xi, pj, θ) = m X j=1 f (yi|xi, νj, θ)pj, 0 ≤ pj ≤ 1, m X j=1 pj = 1,

conformable to the discrete heterogeneity model considered in the context of duration models (Cameron and Trivedi, 2005, p. 678-679).

So far unobserved heterogeneity is considered only in a single equation. However, the purpose of this thesis is to account for unobserved common confounding factors across multiple equations. This is obtained by allowing the unobserved heterogeneity terms of the multiple equations to be correlated. This is further elaborated on in the next section by discussing the paper of Van Ours and Williams (2011).

2.3 Unobserved common confounding factors

In order to gain insides into the method to account for unobserved common confounding factors, this section discusses the paper of Van Ours and Williams (2011). Van Ours and Williams investigate the extent to which cannabis use causes mental health problems and in doing so address the issue of potentially unobserved common confounding factors. They argue that the existence of unobserved common confounding factors is a possible explanation for the growing evidence of an association between cannabis use and mental health problems. As such, their paper provides the background for the methodology of this thesis.

To account for the potential of unobserved common confounding factors affecting both cannabis use and mental health, Van Ours and Williams exploit a discrete-factor approach

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and estimate a trivariate system of equations. The trivariate system consists of hazard func-tions for the rate of uptake of cannabis and the quit rate from cannabis, and a Tobit model for the production of mental health. For the hazard functions, Van Ours and Williams follow Heckman and Singer (1984) and assume mixed proportional hazard functions to account for unobserved heterogeneity, that is, they use the semiparametric heterogeneity model presented in the previous section. The Tobit model for the production of mental health also accounts for unobserved heterogeneity using the discrete-factor approach: the error term for each individual is assumed to be composed of two components, a discrete factor and a term drawn from a nor-mal distribution. By allowing for common factors, one allows the unobserved discrete factors across the multiple equations to be correlated.

Van Ours and Williams find that the joint distribution of unobserved heterogeneity for the rate uptake of cannabis use, the quit rate from cannabis use and the production of mental health has eight points of support. Furthermore, their results suggest that, after accounting for potentially unobserved common confounding factors, current and past cannabis use does have an adverse effect on mental health.

In this chapter methods to account for unobserved heterogeneity in a single equation as well as unobserved common confounding factors across multiple equations have been explored. These methods provide the basis for addressing the issue of potential unobserved common confounding factors affecting both alcohol consumption and mental health. The next chapter presents the empirical methodology.

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3 Methodology

This chapter presents the empirical methodology. First, Section 3.1 focusses on modeling the rate of initiation into alcohol consumption and the decision to quit consuming alcohol. Subse-quently, Section 3.2 focusses on modeling the measure for mental health. Finally, Section 3.3 considers the joint model for alcohol consumption and mental health, accounting for unobserved common confounding factors.

3.1 Dynamics in alcohol consumption

The first part of the model comprises the decisions to start drinking alcohol and quit drinking alcohol. First, the starting rate for drinking alcohol and the decision to quit drinking alcohol are considered separately. Thereafter, the starting and quitting models are considered jointly in a bivariate framework, to account for potentially correlated unobserved heterogeneity driving both processes.

First, regarding the initiation into alcohol consumption, a proportional piecewise constant hazard model is assumed. That is, the starting rate for drinking alcohol, at time t, is specified as

λs(t|x, u) = λ0(t) exp(x0βs+ u), (1)

where x contains observed characteristics and u contains unobserved characteristics. The base-line hazard is a step function with k segments: λ0(t) = exp(P_kλ0kIk(t)), where Ik(t) is an indicator function that equals one if t falls in category k. The potential exposure to alcohol is assumed to start from the age of 12, hence t is from the age of 12. Furthermore, the spell length is one year. A distinction is made between 15 age categories: 14 of which are for individual ages (age 12, 13, . . . , 25) and the last category is for individuals aged 26 or older. As the model also includes a constant term, the following identification assumption is employed: λ01= 0.

The data used in this thesis contains both individuals who have started drinking alcohol and hence have a completed duration until first use, and individuals who have not drunk any alcohol at the time of the survey and hence have a right-censored duration until first use. The conditional density function for the completed spells until first use is defined as

fs(t|x, u) = λs(t|x, u) exp

−Λs(t|x, u)

, (2)

and the survival function for right-censored spells until first use is defined as

Ss(t, |x, u) = exp

−Λ_s(t|x, u)

, (3)

where Λs(t|x, u) denotes the integrated hazard function. As mentioned above, the baseline hazard is a step function with k segments. As a result, the integrated hazard function has a straightforward specification (see, for example, Murphy (1996)). To be precise the integrated baseline hazard, denoted I(t), can be written as

I(t) = Z t 0 exp P kλ0kIk(s) ds = ( _P_m k=1eλ0k if t in age category m, PK−1 k=1 eλ0k + (t − 14)eλ0K if t ≥ 15, (4)

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3 Methodology

and consequently the integrated hazard function is

Λs(t|x, u) = Z t

0

λs(s|x, u)ds = exp(x0βs+ u)I(t). (5)

It then follows that the likelihood function for the duration until first use is given by

`s= fs(t|x, u)δSs(t|x, u)1−δ, (6)

where

δ = (

1 for completed spells until first drinking, 0 for right-censored spells until first drinking.

Furthermore, the distribution of the unobserved heterogeneity term, u, is assumed to have a fixed number of support points: uj, j = 1, . . . , J . The probabilities associated with each support point are assumed to have a multinomial logit specification: p(uj) = Pexp(αj)

jexp(αj), where αJ = 0.

The likelihood function for the duration until fist drinking can be written as

`start= X

j

`s(uj)p(uj), (7)

and the log-likelihood function is obtained by taking the natural logarithm and summing over all individuals: L_start= N X i=1 log `start,i. (8)

Estimation of the model is by maximum likelihood. Furthermore, the number of support points, J , is determined with an upward-testing approach. Starting with one point of support, the number of support points is increased until the points converge to each other and the log-likelihood does not improve anymore.

Next, the quit rate from alcohol consumption is considered. Note that the quitting rate from alcohol consumption is only relevant for the individuals who have initiated into alcohol consumption. However, the observation of quitting alcohol consumption is incompletely ob-served: no information is available about the age of quitting, it is only observed whether an individual has stopped or is still drinking. As a consequence of this limited information, a duration model for the decision to quit drinking is less sensible and instead a probit model for the decision to quit drinking is employed.

That is, the dependent variable, denoted q, is a dummy variable equal to one if the individual has quit drinking alcohol and zero otherwise. The conditional probability of the probit model considered is specified as

p = Pr[q = 1|x] = Φ(x0βq+ ψaf + v), (9)

where Φ(·) is the standard normal cdf, x contains observed characteristics, af is the age of first drinking and v contains unobserved characteristics. The conditional density for the decision to quit drinking is then defined as

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3 Methodology

As mentioned before, the decision to quit drinking alcohol only applies to individuals who have initiated into alcohol consumption. As a result, the likelihood function for the decision to quit drinking alcohol is given by

`q= fq(q|x, v)γ, (11)

where

γ = (

1 for individuals who have initiated into alcohol consumption, 0 for individuals who have not initiated into alcohol consumption.

The distribution of the unobserved heterogeneity term, v, is also assumed to have a fixed number of support points: vk, k = 1, . . . , K. The probabilities associated with each support point are assumed to have a multinomial logit specification: p(vk) = Pexp(αk)

kexp(αk), where αK = 0. The

likelihood function for the decision to quit drinking can be written as

`quit= X

k

`q(vk)p(vk), (12)

and the log-likelihood function is obtained by taking the natural logarithm and summing over all individuals: L_quit = N X i=1 log `quit,i. (13)

Estimation of the model is by maximum likelihood. Furthermore, the number of support points, K, is also determined with an upward-testing approach. Starting with one point of support, the number of support points is increased until the support points converge to each other and the log-likelihood does not improve anymore.

Finally, to account for potentially correlated unobserved components in the models for start-ing and quittstart-ing drinkstart-ing, a bivariate mixed framework is employed. To be precise, the duration until first drinking alcohol and the decision to quit drinking alcohol are estimated jointly, and the unobserved heterogeneity terms within each model are allowed to be correlated. Each com-bination of the support points, (uj, vk), has an associated probability, denoted p(uj, vk). The joint likelihood for the duration until first drinking, t, and the decision to quit drinking, q, is then given by `alcohol= X j X k `s(uj)`q(vk)p(uj, vk). (14)

The probabilities associated with each combination of support points are assumed to have a multinomial logit specification: p(uj, vk) =

exp(αjk)

P

jkexp(αjk), where αJ K = 0. The log-likehood

function is obtained by taking the natural logarithm and summing over all individuals:

L_alcohol= N X

i=1

log `alcohol,i. (15)

Estimation of the model is by maximum likelihood. Next, the model for mental health is considered.

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3 Methodology

3.2 Mental health

This section focusses on modeling the measure for mental health. The measure for mental health is the sum of scored responses to five questions and ranges from 0 to 25, which is explained in more detail in the next chapter. Due to discrete nature of the measure, it is treated as a count and accordingly a finite mixture Poisson regression model is assumed. That is, the probability mass function for the mental health score is specified as

Pr[Y = y] = e −µ_µy

y! , µ = exp(x

0

mβm+ θ1cd + θ2pd + η), (16) where µ is the intensity parameter, xm contains observed characteristics and η contains unob-served characteristics. Furthermore, cd and pd are dummy variables indicating whether or not an individual is a current drinker or past drinker, respectively.

As before, the distribution of the unobserved heterogeneity term is assumed to have a fixed number of support points: ηl, l = 1, . . . , L, with associated probability p(ηl). The likelihood function is given by

`mental= X

l

Pr[Y = y|ηl]p(ηl). (17)

The probabilities associated with each support point are assumed to have a multinomial logit specification: p(ηl) = Pexp(αl)

lexp(αl), where αL = 0. The log-likelihood function is obtained by

taking the natural logarithm and summing over all individuals:

L_mental= N X

i=1

log `mental,i. (18)

Estimation of the model is by maximum likelihood and again the number of support points, L, is determined with an upward-testing approach. Next, the joint model for alcohol consumption and mental health is considered.

3.3 The joint model of alcohol consumption and mental health

Lastly, the joint model for alcohol consumption and mental health, accounting for unobserved common confounding factors, is considered. The dynamics in alcohol consumption and the mental health model are estimated jointly and the unobserved heterogeneity terms are allowed to be correlated. Each combination of support points, (uj, vk, ηl), has an associated probability, denoted p(uj, vk, ηl). This results in the following joint likelihood function:

`joint = X j X k X l

`s(uj)`q(vk) Pr[Y = y|ηl]p(uj, vk, ηl). (19)

As before, the probabilities associated with each combination of support points are assumed to have a multinomial logit specification: p(uj, vk, ηl) =

exp(αjkl)

P

jklexp(αjkl). Estimation of the

three-equation model is by maximum likelihood and the log-likelihood function to be maximized is Ljoint = N X i=1 log `joint,i. (20)

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4 Data

This chapter introduces the dataset and presents the dependent and explanatory variables. First, Section 4.1 explains how the data is obtained. Subsequently, Section 4.2 discusses the relevant variables and finally, Section 4.3 presents some descriptive statistics.

4.1 LISS panel data

The data used in this study is obtained from the Longitudinal Internet Studies for the Social sciences (LISS) panel administered by CentERdata (Tilburg University, The Netherlands). The LISS panel is based on a true probability sample of Dutch households drawn from the population register and consists of 4,500 households, comprising 7,000 individuals aged 16 years or older. Individuals participate in monthly Internet surveys and households that could not otherwise participate are provided with a computer and Internet connection. The LISS panel includes the LISS Core Study, a longitudinal study covering a large variety of domains including health, education, income and work, which is repeated yearly. In addition to these core studies, the LISS panel also contains single wave studies collected for different research purposes.

The studies used in this thesis are the Alcohol and Drugs study and the second wave of the Health core study. Both studies are collected in the period 2008-11-03 to 2008-11-26. The Health core study consists of 5,961 responses and the Alcohol and Drugs study consists of 5,616 responses. Aforementioned studies are combined with background information of the respondent collected in November 2008. After combining the data files and dropping the observations that are not merged the number of observations is 5,539. Furthermore, after dropping incomplete and unusable (explained in more detail in the next sections) observations, the final sample consists of 4,098 observations.

4.2 Variables

This section introduces the relevant variables. First, Section 4.2.1 discusses the measures related to alcohol consumption used in the analysis. Thereafter, Section 4.2.2 elaborates on the measure of mental health. Finally, Section 4.2.3 and Section 4.2.4 introduce the explanatory variables incorporated in the analysis of alcohol consumption and mental health, respectively.

4.2.1 Alcohol consumption

To model the dynamics in alcohol consumption, information is needed on the age at which alcohol was first consumed and the duration of alcohol consumption. The following question was asked to all respondents who reported that they had ever drunk alcohol: ‘At what age, ap-proximately, did you first drink alcohol?’. The age of first use is constructed from the responses to this question. Furthermore, the following assumption is made: the potential exposure to alcohol starts from the age of 12. Responses including an age of first use below the age of 12 are considered not reliable and are dropped from the analysis, resulting in 83 dropped observations.

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4 Data

Next, information about the duration of alcohol consumption is desired. Unfortunately, no such question was asked to the respondents. However, the respondents were asked the following question: ‘How often did you have a drink containing alcohol over the last 12 months?’. The responses included the following categories: almost every day, five or six days per week, three or four days per week, once or twice a week, once or twice a month, once every two months, once or twice a year or not at all over the last 12 months. The responses to this question are used to define current and past drinkers. Individuals who have ever drunk alcohol but who have not consumed alcohol in the year prior to the survey are assumed to be past drinkers and hence have quit drinking. Analogously, individuals who have ever drunk alcohol and who have drunk at least once in the year prior to the survey are assumed to be current drinkers and hence have not quit drinking. In addition, the aforementioned question is also used to categorize current drinkers by frequency of alcohol consumption, to be able to investigate whether the effect of alcohol consumption on mental health differs by frequency of alcohol consumption.

4.2.2 Mental health

The measure of mental health used in the analysis is closely related to the Kessler 6 (K6) scale of psychological distress. The K6 scale was developed for use in the U.S National Health Interview Survey (NHIS) as a measure of non-specific psychological distress (Kessler et al., 2002). It is based on the following 6 questions: ‘During the past 30 days, about how often did you feel . . . ’: 1. nervous? 2. hopeless? 3. restless or fidgety? 4. so depressed that nothing could cheer you up? 5. that everything was an effort? 6. worthless?. A five-level response scale is used: (0) none of the time, (1) a little of the time, (2) some of the time, (3) most of the time and (4) all of the time. The score of psychological distress is constructed as the sum of scored responses and ranges from 0 to 24. In a clinical validation study, Kessler et al. (2003) show that the optimal cut point on the K6 is 0-12 versus 13+, where a score of 13 or higher indicates the presence of psychological distress.

The K6 scale is not present in the LISS dataset, however the respondents were presented with the following five statements: ‘This past month . . . ’: 1. I felt very anxious. 2. I felt so down that nothing could cheer me up. 3. I felt calm and peaceful. 4. I felt depressed and gloomy. 5. I felt happy. For every statement, the respondent was asked to choose the answer that best describes how he or she felt during the past month, using the following six-level response scale: (1) never, (2) seldom, (3) sometimes, (4) often, (5) mostly and (6) continuously. These five statements are used to construct a measure of mental health similar to the K6 measure. Note that statement 3 and 5 are statements describing positive feelings, whereas statements 1, 2 and 4 are statements describing negative feelings. In order to be able to construct a score of psychological distress, the response scales of statement 3 and 5 must be reversed. The score of psychological distress is then constructed as the sum of scored responses to the five questions minus 5, and hence ranges from 0 to 25. Analogous to the K6 scale, a score of 13 or higher is assumed to indicate the presence of psychological distress.

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4 Data

4.2.3 Explanatory variables alcohol consumption

This section discusses the explanatory variables included in the analysis of the dynamics of al-cohol consumption. The explanatory variables include demographic, socio-economic and health related factors.

Firstly, the demographic variables incorporated in the analysis are discussed. Earlier re-search on alcohol has revealed the existence of gender differences in alcohol consumption. For example, Wilsnack et al. (2000) showed that men typically consume alcohol more frequently than women do. Furthermore, they showed that women are more likely to be life-time abstain-ers of alcohol than men. To account for these gender differences in alcohol consumption, a dummy variable for gender is included in the analysis. The dummy variable equals one if the respondent is a female and zero otherwise. Next, the urban character of the place of residence of the respondent is considered. Living in urban or suburban areas is often associated with an increased likelihood of frequently drinking (Martin and Pritchard, 1991). Therefore, four dummy variables for the following urban categories are included in the analysis: slightly urban, moderately urban, very urban and extremely urban, where the reference category is not urban. Finally, the birth year of the respondent is included as an explanatory variable in the analysis to account for birth cohort size effects.

Secondly, the socio-economic variables are considered. Previous studies have shown that individuals with a lower social economic status (SES) are more likely to consume alcohol com-pared to individuals with a higher SES (Fillmore et al., 1998). To describe a person’s SES, the educational level of the respondent as well as the respondent’s income is included in the analysis. Five eduction dummy variables are included in the analysis. Each of the five dummy variables equals 1 if the respondents highest level of education is intermediate secondary school, higher secondary school, intermediate vocational school, higher vocational school and univer-sity, respectively, and zero otherwise. The reference category is primary school. Respondents indicating that they had not yet completed any education were dropped from the analysis. The income variable describes the respondent’s personal gross monthly income in Euros (divided by 100). If the respondent did not answer the question, the income was again asked in terms of categories and the average of the indicated category was imputed as his or her personal gross monthly income.

Lastly, the health related factors included in the analysis are reviewed. It is well established in the literature that an individual who uses one type of substance has an increased likelihood of using other substances (see, for example, Kandel et al. (1992)). To account for this, a dummy variable expressing whether the respondent is a current smoker or not is incorporated in the analysis. In addition, a dummy variable encompassing whether a respondent has ever used any other substance, including cannabis, ecstasy (XTC), cocaine and heroine, is included as an explanatory variable.

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4 Data

4.2.4 Explanatory variables mental health

This section discusses the explanatory variables incorporated in the analysis of mental health. Again, the explanatory variables include demographic, socio-economic and health related fac-tors.

First, the demographic factors included in the analysis of mental health are discussed. In their study, Kessler et al. (1994) found that both depression and anxiety declined with age. To control for such age effects, the age of the respondent is included as an explanatory variable. Kessler et al. (1994) also found that women have a higher prevalence of anxiety and depression, whereas men have higher rates of substance abuse and antisocial disorders. To account for these gender differences in mental health, a dummy variable for gender is incorporated in the analysis. The gender dummy equals one for females and zero otherwise. Next the marital status of the respondent is considered. Simon (2002) showed that being married is emotionally advantageous for both men and women, whereas the lack of marriage is emotionally disadvantageous. A dummy variable for the marital status of the respondent is therefore included as an explanatory variable. The dummy variable equals one if the respondent is married and zero otherwise.

Secondly, the socio-economic factors are reviewed. Earlier research has revealed that there is an increased likelihood of having a major psychiatric disorder among individuals with a low socio-economic status (SES) (see, for example, Dohrenwend (1990)). To describe an individual’s SES, both the educational level of the respondent and the respondent’s income are incorporated in the analysis. Both variables are defined as before: the education dummy variables describe the highest level of education of the respondent and the income variable represents the respondent’s personal gross monthly income in Euros (divided by 100).

The last class of variables considered are the health related characteristics. Mental health problems are often associated with worse physical health. For example, Goldberg (2010) re-ports that the prevalence of depression is significantly higher among individuals that have chronic physical illnesses. Two explanatory variables are included in the analysis to describe the individuals physical health: number of comorbidities and perceived health status. Each respondent was asked whether they were diagnosed with one of the following twelve diseases or problems in the year prior to the survey: angina, heart disease, high blood pressure, high cholesterol, stroke, diabetes, chronic lung disease, asthma, arthritis, cancer, Parkinson’s disease or Alzheimer’s disease. The comorbidity variable counts the number of conditions an individual suffers from and hence ranges from 0 to 12. The perceived mental health dummy variables are constructed from the following question asked to all respondents: ‘How would you describe your health, generally speaking?’. A five-level response scale was used: 1. Excellent, 2. Very good, 3. Good, 4. Moderate and 5. Poor. The four dummy variables included in the analysis equal one if the response of the respondent is very good, good, moderate and poor, respectively, and zero otherwise. The reference category is excellent.

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4 Data

4.3 Descriptive statistics

After discussing the dependent and explanatory variables, it is of interest to gain insights into the characteristics of the data. Table 1 provides some descriptive statistics of the data. It should be emphasized that although the continuous variables are categorized into groups to show the distribution of these variables, they remain continuous when estimating the model.

Of the 4,098 individuals in the sample, 3,870 (94.4%) have drunk alcohol in their lifetime, whereas 228 (5.6%) have never consumed alcohol. Conditional on ever drinking, about 57% of the individuals started drinking between the ages of 12 and 16 and about 37% started drinking between the ages of 17 and 21. It is furthermore noteworthy that the majority of the respondents are current drinkers (89.1%). Of the current drinkers in the sample, 1,071 (29.3%) drink on one or two days a week, while 597 (16.4%) drink almost every day.

Next, considering the mental health of the individuals in the sample, most of the respondents (91.4%) have a mental health score of 0-12, whereas only 8.6% of the sample has a score of 13 or higher and hence are considered to have psychological distress.

Furthermore, regarding the demographic variables, about half of the respondents (46.5%) is of age 50 and over and 54.8% of the sample (2,247 individuals) are female. In addition, 2,484 (60.6%) respondents are married. The urbanicity of the residential area of the respondents is more or less equally distributed: 38.5 % of the respondents live in a slightly urban or not urban area, 22.1% of the individuals live in a moderately urban area and 39.4% of the respondents live in in a very urban or extremely urban area.

Moreover, concerning the socioeconomic status of the respondents, for most of the respon-dents (61.5%) the level of education is intermediate vocational school or higher. Additionally, 30.4% of the sample has a monthly income of less than e1000, 24.5% has a monthly income of e1000-e2000, 23.6% has a monthly income of e2000-e3000, 16.6% has a monthly income of e3000-e5000 and finally 4.9% of the sample has a monthly income of e5000 or more.

Finally, considering the health related factors, the majority of the respondents (71.7%) does not suffer from any of the diseases or problems included in the comorbidity variable. In addition, 2,429 individuals (59.3%) described their health as good. Lastly, the percentage of smokers in the sample is 25.4% and 908 respondents (22.2%) indicated that they had ever used cannabis, ecstasy, cocaine or heroine in their lifetime.

To gain additional insights into the dependent variables, Table 2 shows the distribution of the mental health status conditional on alcohol consumption, where a distinction is made between non-drinkers, past drinkers and current drinkers. As mentioned before, an individual is assumed to have psychological distress if the mental health score equals 13 or higher. From Table 2 it follows that that the prevalence rate of psychological distress is of equal magnitude among past drinkers and current drinkers (9%). Furthermore, there is a higher prevalence rate of psychological distress among current and past drinkers compared to non-drinkers, though the difference is marginal: 9% of the current and past users are classified as having psychological distress, whereas only 8% of the non-drinkers are classified as having psychological distress.

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4 Data

Table 1: Descriptive statistics of the data

N %

All 4,098 100%

Ever consumed alcohol

Yes 3,870 94.4%

No 228 5.6%

Age of first use *

12-16 2,204 56.9% 17-21 1,417 36.6% 22-30 220 5.7% 31 and over 29 0.8% Drinkers Current drinker 3,654 89.1% Past drinker 216 5.3% Never drank 228 5.6% Frequency of drinking **

Almost every day 597 16.4%

5-6 days per week 245 6.7%

3-4 days per week 549 15.0%

1-2 days per week 1,071 29.3%

1-2 days per month 582 15.9%

Once every two months 302 8.3%

Once or twice a year 308 8.4%

Mental health score

0-12 3747 91.4% 13+ 351 8.6% Age Below 30 675 16.5% 30-49 1,517 37.0% 50 and over 1,906 46.5% Gender Female 2,247 54.8% Male 1,851 45.2% Marital status Married 2,484 60.6% Other 1,614 39.4% N % Urbanicity Not urban 645 15.7% Slightly urban 934 22.8% Moderately urban 906 22.1% Very urban 1,098 26.8% Extremely urban 515 12.6% Level of education Primary school 156 3.8%

Intermediate secondary school 1,079 26.3%

Higher secondary school 344 8.4%

Intermediate vocational school 992 24.2%

Higher vocational school 1,056 25.8%

University 471 11.5%

Monthly Income

Less thane1000 1,246 30.4%

e1000-e2000 1,005 24.5% e2000-e3000 968 23.6% e3000-e5000 678 16.6% e5000 or more 201 4.9% Number of comorbidities 0 2,938 71.7% 1 736 18.0% 2 or more 424 10.3%

Perceived health status

Poor 42 1.0% Moderate 524 12.8% Good 2,429 59.3% Very good 839 20.5% Excellent 264 6.4% Current smoker Yes 1,042 25.4% No 3,057 74.6%

Ever used any other substances (cannabis, XTC, cocaine, heroine)

Yes 908 22.2%

No 3,190 77.8%

Note: Number of observations (N ) and shares (%) of the relevant variables. * Conditional on ever drinking. ** Conditional on current drinkers.

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4 Data

Table 2: Mental health status conditional on alcohol consumption

Non-drinker Past drinker Current drinker

All (N ) 228 216 3654 No psychological distress N 209 196 3342 % 92% 91% 91% Psychological distress N 19 20 312 % 8% 9% 9%

Note: Number of observations (N ) and shares (%).

Furthermore, Figure 1(a) and Figure 1(b) illustrate the distribution of the age of first drink-ing alcohol (conditional on ever drinkdrink-ing) and the mental health score, respectively. Figure 1(a) shows that alcohol consumption starts at an early age. In particular, almost 25% of the respondents start drinking at the age of 16. In addition, initiation into alcohol consumption rarely occurs after the age of 25. Next, Figure 1(b) illustrates the distribution of the mental health scores. The mental health score has a lower bound of 0 and an upper bound of 25 by construction. The mental health score is a measure of psychological distress with higher scores indicating greater levels of psychological distress. The distribution of the mental health score is somewhat skewed to the right. Furthermore, it follows from the figure that most of the re-spondents have a mental health score of around 5.

Figure 1: Distribution of dependent variables

0 5 10 15 20 25 % 10 20 30 40 50 60 Age

(a) Histogram age of first drinking (percentages)

0 5 10 15 % 0 5 10 15 20 25

Mental health score

(b) Histogram mental health score (percentages)

Finally, it should be remarked that the LISS panel is surveyed on a household level. As a consequence, the sample consists of a number of individuals belonging to the same household and this can have an impact on the standard deviations. This issue is ignored in this thesis.

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5 Results

This chapter presents and analyses the estimation results. First, Section 5.1 presents the results from the models regarding the dynamics in alcohol consumption. Next, Section 5.2 presents the results from the mental health model. Finally, Section 5.3 presents and analyses the results of the joint model for alcohol consumption and mental health.

5.1 Dynamics in alcohol consumption

This section presents and analyses the models concerning the dynamics in alcohol consumption. To determine the number of support points in each equation, the starting rate for drinking alcohol and the decision to quit drinking alcohol are first estimated separately. Regarding the starting rate for drinking alcohol, the log-likelihood does not improve beyond one support point. To be precise, the log-likelihood equals -9872.94 for one support point and -9873.34 for two support points. Additionally, in the model with two support points, the probability for the first and second support points are 99,7% and 0,3%, respectively. Therefore, the results suggest that there is only one support point in the model for the starting rate of drinking alcohol and hence unobserved heterogeneity does not seem to be an issue for this model. The results from estimation of the model with one support point are shown in Table 3.

The parameter estimates indicate first of all that women have a lower uptake of alcohol consumption than males. Furthermore, compared to individuals living in not urban areas, individuals living in moderately, very or extremely urban areas have a lower uptake of alcohol consumption. The coefficient regarding the ’slightly urban’ dummy is not significant. The lower starting rate of alcohol consumption in more urban areas is not in line with the expectation. However, an explanation might be that in more urban areas the regulation of the minimum legal drinking age (MLDA) is stricter. Furthermore, it must be noted that the region dummy variables actually violate the sequentiality as the current place of residence is established at a later time than the decision to start drinking. However, the variable is included in the analysis as a proxy for the place where the respondent grew up, which is expected to be positively correlated with the current place of residence. Regarding the birth year of the respondent, those born in more recent years have a higher uptake of alcohol consumption than those born earlier. Remarkable are the significant positive coefficients of the level of education dummies: compared to individuals who have only completed primary school, individuals who have completed a higher level of education also have a higher uptake of alcohol consumption. Note that the education dummy variables also violate the sequentiality, however they serve as a proxy for the intelligence of the respondent. The estimated coefficient of the income variable is not significant. Besides the region dummy variables and the education dummy variables, the income variable also violates the sequentiality. The income variable serves as a proxy for the socioeconomic status of the household of the respondent when growing up. Lastly, individuals who are current smokers or who have used other substances (cannabis, XTC, cocaine and/or heroine) have a higher starting rate than non-smokers and individuals who have not used other substances.

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5 Results

Table 3: Parameter estimates starting rate model

Estimate (SE)

Explanatory variables

Female -0.335 (0.033) ***

Urban character place of residence:

Slightly urban -0.052 (0.053) Moderately urban -0.088 (0.053) · Very urban -0.140 (0.051) ** Extremely urban -0.290 (0.063) *** Birth year 0.015 (0.001) *** Level of education:

Intermediate secondary school 0.199 (0.094) *

Higher secondary school 0.372 (0.106) ***

Intermediate vocational school 0.357 (0.096) ***

Higher vocational school 0.365 (0.095) ***

University 0.509 (0.103) ***

Income (scaled) 1.53e-04 (2.11e-04)

Smoker 0.174 (0.038) ***

Other substance use 0.608 (0.042) ***

Support point

u1 -33.623 (2.214) ***

Log-likelihood -9872.94

SE = standard error. Significance codes: *** = 0.001, ** = 0.01, * = 0.05, · = 0.1

Next, concerning the decision to quit drinking alcohol, the log-likelihood did not improve beyond two points of support. The support points imply that there exist two distinct types in the sample who are differentiated by their susceptibility to quitting alcohol consumption. As shown in Table 4, the support points are estimated to be -13.439 and -12.970, with probabilities 64.5% and 35.5%, respectively. These support points imply the following average probabilities of quitting: 3.7% and 9.0%. That is, the type in the sample represented by v1 has a very low quit rate, and the type represented by v2 has a moderately higher quit rate.

The results from estimation furthermore indicate that females are more likely to quit drink-ing than males. The dummies for the urban character of the place of residence of the respondent are all insignificant. Concerning the birth year of the respondent, those born in more recent years have a higher probability of quitting than those born earlier. Furthermore noteworthy are the significant negative coefficients of the dummy variables for the level of education of the respondent: individuals who have completed a higher level of education are less likely to quit drinking compared to individuals who have only completed primary school. The estimated coefficients of the income variable, the smoking dummy and the use of other substances dummy are all insignificant. Finally, the probability of quitting drinking increases with the age of first drinking.

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5 Results

Table 4: Parameter estimates quitting decision model

Estimate (SE) Explanatory variables

Female 0.180 (0.083) *

Slightly urban -0.087 (0.115) Moderately urban 0.024 (0.113) Very urban 0.046 (0.108) Extremely urban 0.010 (0.134) Birth year 0.006 (0.003) * Level of education:

Intermediate secondary school -0.484 (0.159) **

Higher secondary school -0.659 (0.201) **

Intermediate vocational school -0.423 (0.165) *

Higher vocational school -0.590 (0.175) ***

University -0.684 (0.207) ***

Income (scaled) -0.005 (0.003)

Smoker 0.008 (0.082)

Other substance use -0.168 (0.099)

Age of first drinking 0.032 (0.009) ·

Support points v1 -13.439 (3.691) *** v2 -12.970 (4.348) *** Distribution p(v1) 0.645 p(v2) 0.355 Log-likelihood -800.390 Log-likelihood 1 support point -800.391

Next, the duration until first drinking alcohol and the decision to quit drinking alcohol are estimated jointly, to account for potentially correlated unobserved components in the models for starting and quitting drinking. However, the results from the model regarding the duration until first drinking imply that unobserved heterogeneity does not play a role in this model. Accordingly, there is no potential for correlated unobserved components in the models for starting and quitting drinking. Nevertheless, for the sake of completeness the joint model for the dynamics in alcohol consumption is estimated and the results from estimation are shown in Table 5.

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5 Results

Table 5: Parameter estimates joint model alcohol consumption

Starting rate Quitting decision

Estimate (SE) Estimate (SE)

Explanatory variables

Female -0.335 (0.033) *** 0.192 (0.087) *

Slightly urban -0.052 (0.053) -0.092 (0.122) Moderately urban -0.088 (0.053) · 0.026 (0.120) Very urban -0.140 (0.051) ** 0.049 (0.115) Extremely urban -0.290 (0.063) *** 0.010 (0.143) Birth year 0.015 (0.001) *** 0.006 (0.003) * Level of education:

Intermediate secondary school 0.200 (0.094) * -0.517 (0.156) ***

Higher secondary school 0.372 (0.106) *** -0.703 (0.198) ***

Intermediate vocational school 0.357 (0.096) *** -0.452 (0.164) **

Higher vocational school 0.365 (0.095) *** -0.629 (0.169) ***

University 0.509 (0.103) *** -0.728 (0.204) ***

Income (scaled) 1.54e-04 (2.11e-04) -0.005 (0.003)

Smoker 0.174 (0.038) *** 0.009 (0.087)

Other substance use 0.607 (0.042) *** -0.179 (0.104) ·

Age of first drinking 0.034 (0.008) ***

Support points (u1, v1) -33.623 (2.214) *** -14.419 (4.014) *** (u1, v2) -33.623 (2.214) *** -13.542 (4.797) ** Distribution p(u1, v1) 0.615 p(u1, v2) 0.385 Log-likelihood -10673.32

Based on the preceding results, the distribution of unobserved heterogeneity is assumed to have two points of support: (u1, v1) and (u1, v2). From Table 5 it follows that these support points are estimated to be (−33.623, −14.419) and (−33.623, −13.542), with associated proba-bilities 61.5% and 38.5%, respectively. Note that the support point of the starting rate model is basically unchanged compared with the results in Table 3, whereas the support points of the model concerning the quitting decision are somewhat increased compared with the results in Table 4. Additionally, the estimated coefficients of the explanatory variables of both models are essentially the same.

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5 Results

5.2 Mental Health

This section presents and analyses the mental health model. Beyond three points of support the location of additional points converged to each other and the log-likelihood did not improve anymore, indicating three recognizable types in the sample. As shown in Table 6, the first support point is estimated to be 1.276, implying an average mental health score of 4.4. The second and third support points are estimated to be 1.896 and 2.451, implying an average mental health score of 8.2 and 14.3 respectively. The distribution of unobserved heterogeneity implies that 53.4% of the sample falls into the group with the low mental health score, 41.8% falls into the group with the mediocre mental health score and 4.8% falls into the group with the high mental health score.

The results shown in Table 6 furthermore indicate that the mental health score decreases with age. Moreover, females have a higher mental health score than males and married in-dividuals have a lower mental health score than inin-dividuals who are not married. All of the aforementioned results are in line with the expectations. Concerning the level of education of the respondent, only for individuals who have completed higher vocational school, the mental health score is lower compared to individuals who have only completed primary school. All the other coefficients of the education dummy variables are insignificant. Additionally, the es-timated coefficient of the income variable is also not significant. The mental health score of individuals increases with the number of comorbidities the individual suffers from. In addition, regarding the individuals perceived health status, the worse the perceived health status, the higher the mental health score, hence the worth the mental health.

However, the main parameters of interest are the ones measuring the effects of current and past drinkers on the mental health score. Unfortunately both parameter estimates do not significantly differ from zero. Hence, the obtained results do not reveal a causal effect of alcohol consumption on mental health problems. The insignificance might be the consequence of the fact that most of the sample (89.1%) are current drinkers, whereas only 5.3% are past drinkers and only 5.6% are non-drinkers. Note that current drinkers are defined as individuals who have drunk alcohol in the 12 months prior to the survey. As a consequence, no distinction is made between individuals who have drunk only once during the 12 months prior to the survey and individuals who have drunk almost every day. In the next chapter, it is therefore investigated whether the mental health score is affected by the frequency of drinking. For the sake of completeness, the joint model for the dynamics and alcohol consumption and mental health is nonetheless estimated to account for the potential of unobserved common confounding factors. The results of this model are presented in the next section.

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5 Results

Table 6: Parameter estimates mental health model

Estimate (SE) Explanatory variables Age -0.006 (0.001) *** Female 0.095 (0.018) *** Married -0.110 (0.019) *** Level of education

Intermediate secondary school -0.074 (0.047)

Higher secondary school 0.012 (0.054)

Intermediate vocational school -0.067 (0.049)

Higher vocational school -0.097 (0.049) *

University -0.004 (0.052)

Income (scaled) -4.16e-06 (1.10e-04)

Number of comorbidities 0.041 (0.011) ***

Perceived health status:

Very good 0.308 (0.044) *** Good 0.531 (0.041) *** Moderate 0.902 (0.047) *** Poor 1.145 (0.089) *** Current drinker 0.035 (0.038) Past drinker -0.008 (0.052) Support points η1 1.276 (0.080) *** η2 2.451 (0.104) *** η3 1.896 (0.089) *** Distribution p(η1) 0.534 p(η2) 0.048 p(η3) 0.418 Log-likelihood -10642.14 Log-likelihood 1 support point -11230.70 2 support points -10667.98

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5 Results

5.3 The joint model of alcohol consumption and mental health

This section presents and analyses the joint model of alcohol consumption and mental health. Based on the earlier obtained results, the distribution of unobserved heterogeneity is assumed to have six points of support: (u1, v1, η1), (u1, v1, η2), (u1, v1, η3), (u1, v2, η1), (u1, v2, η2) and (u1, v2, η3). Table 7 shows the relevant results from estimation of the model. As the estimated coefficients of the other variables included in the analysis are essentially the same as the previous obtained estimates, they are omitted from the table. The complete estimation results can be found in the Appendix. The results indicate that each of the aforementioned support points have an associated probability of 10.3%, 3.0%, 37.9%, 43.0%, 1.9% and 3.9%, respectively. The support points of the starting rate and the mental health model are essentially unchanged compared with the previous estimation results, however the support points of the quitting drinking model are again slightly changed. In fact, they are now estimated to be -12.911 and -12.891, hence the difference between the support points is marginally.

The estimation results suggest that unobserved common confounding factors is not an is-sue for this sample, as the parameter estimates are essentially unaffected when allowing the unobserved components to be correlated. To advocate this inference, a likelihood ratio (LR) test of the null hypothesis of no correlation is performed. To be precise, the restricted model of no correlation is given by the the combination of the models in Tables 5 and 6 and the restricted log-likelihood is simply the summation of the log-likelihoods of these models. The unrestricted log-likelihood is the log-likelihood reported in Table 7. This leads to a LR-statistic of approximately zero. The LR-statistic is asymptotically chi-squared distributed with degrees of freedom equal to the number of restrictions, in this case 2, and hence the null hypothesis of no correlation is not rejected. That is, the LR test substantiates the inference that unobserved common confounding factors affecting both alcohol consumption and mental health is not an issue for this sample.

Furthermore, the parameters measuring the effects of current and past drinkers on the mental health score are again not significantly different from zero. The obtained results therefore again do not reveal a causal effect of alcohol consumption on mental health problems when accounting for possibly unobserved common confounding factors. As stated before, the current drinkers group consists of individuals who have drunk alcohol in the 12 months prior to the survey. As a result, individuals who have drunk only once during the 12 months prior to the survey and individuals who have drunk almost every day fall within the same group, though the amount of alcohol they consume is extremely divergent. The next chapter therefore explores whether the mental health score is affected by the frequency of drinking.

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5 Results

Table 7: Parameter estimates joint model

Estimate (SE) Explanatory variables Current drinker 0.004 (0.038) Past drinker -0.004 (0.054) Support points u1 -33.615 (2.214) *** v1 -12.911 (4.952) *** v2 -12.891 (4.953) *** η1 1.275 (0.080) *** η2 2.450 (0.104) *** η3 1.895 (0.089) *** Distribution p(u1, v1, η1) 0.103 p(u1, v1, η2) 0.030 p(u1, v1, η3) 0.379 p(u1, v2, η1) 0.430 p(u1, v2, η2) 0.019 p(u1, v2, η3) 0.039 Log-likelihood -21315.46

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6 Sensitivity analysis

This chapter presents and analyses the results from a robustness check. It is examined whether the mental health score is affected by the frequency of drinking instead of only making a dis-tinction between current drinkers and past drinkers. The model for mental health and the joint model for alcohol consumption and mental health are re-estimated with frequency of alcohol variables instead of the dummy variables for current drinkers and past drinkers. To be precise, frequency of drinking is measured in the year prior to the survey with the following categories: almost every day, 5-6 days per week, 3-4 days per week, 1-2 days per week, 1-2 days per month, once every two months and once or twice a year. For each category, a dummy variable is in-cluded as explanatory variable in the mental health equation. The main results of estimation of the mental health model and the joint model for alcohol consumption and mental health are illustrated in Table 8. As the estimated coefficients of the other variables included in the anal-ysis are essentially the same as the earlier obtained estimates, they are left out. The complete estimation results can be found in the Appendix.

First of all, note that the estimated support points of both models are essentially the same as before, apart from the support points of the quitting decision model, which are now only marginally significant. In addition the distribution of the unobserved heterogeneity in the joint model of alcohol consumption and mental health is also slightly changed compared to the distribution shown in Table 7. This might be the consequence of the fact that the difference between the support points shown in Table 7 is minimal, whereas in the difference between the support points shown in Table 8 is substantial, inducing a different distribution.

Next, the main parameters of interest are now the ones measuring the effects of frequency of drinking on the mental health score. From Table 8 it follows that only the estimated parameter regarding drinking almost every day is significant. The significant positive coefficient indicates that individuals who drink alcohol almost every day are more likely to have mental health problems compared to individuals who do not drink.

Furthermore, the parameter estimates are essentially unaffected when allowing the unob-served components to be correlated, indicating that unobunob-served common confounding factors is not an issue for this sample. To advocate this inference, a likelihood ratio (LR) test of the null hypothesis of no correlation is performed once more. The LR-statistic equals 2.42 and hence the null hypothesis of no correlation is not rejected. The LR test again substantiates the inference that unobserved common confounding factors is not an issue for this sample.

Comparing the results from estimating the models with and without accounting for the potential of unobserved common confounding factors in Table 8, it follows that the causal effect of drinking alcohol everyday is actually underestimated if one does not account for these unobserved common confounding factors. However, the difference between the coefficients is rather modest. From this one can conclude that after accounting for the potentially unobserved common confounding factors alcohol consumption, if consumed daily, has an adverse effect on mental health.

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6 Sensitivity analysis

Table 8: Parameter estimates mental health model and joint model: frequency of drinking

Mental health model Joint model

Estimate (SE) Estimate (SE)

Frequency of drinking

Almost every day 0.104 (0.036) ** 0.122 (0.046) **

5-6 days per week 0.067 (0.045) 0.085 (0.053)

3-4 days per week 0.016 (0.037) 0.034 (0.046)

1-2 days per week 0.023 (0.032) 0.040 (0.042)

1-2 days per month 0.031 (0.035) 0.048 (0.044)

Once every two months 0.022 (0.041) 0.039 (0.049)

Once or twice a year 0.039 (0.040) 0.056 (0.049)

Support points η1 2.470 (0.104) *** 2.437 (0.100) *** η2 1.298 (0.079) *** 1.276 (0.081) *** η3 1.916 (0.088) *** 1.886 (0.090) *** u1 -33.815 (2.213) *** v1 -10.583 (5.466) · v2 -12.441 (5.543) * Distribution p(η1) 0.049 p(η2) 0.533 p(η3) 0.418 p(u1, v1, η1) 0.005 p(u1, v1, η2) 0.006 p(u1, v1, η3) 0.001 p(u1, v2, η1) 0.051 p(u1, v2, η2) 0.511 p(u1, v2, η3) 0.426 Log-likelihood -10637.22 -21309.33

(31)

7 Conclusions

Insight in the causal association between alcohol consumption and mental health can help determine adequate policy measures regarding alcohol consumption. The aim of this thesis was therefore to investigate to what extent alcohol consumption causes mental health problems. To be able to do so, the potential for unobserved common confounding factors affecting both alcohol consumption and mental health problems was accounted for by employing a discrete factor approach. A trivariate system of equations was assumed, consisting of an equation for the starting rate of initiation into alcohol consumption, an equation for the decision to quit drinking alcohol and an equation for the mental health. Within each equation a discrete distribution of unobserved heterogeneity was assumed, consisting of a finite number of support points. The three-equation system was estimated jointly, allowing the unobserved heterogeneity included in each equation to be correlated.

The results first of all indicated that there was only one support point in the equation for the starting rate of drinking alcohol, suggesting that unobserved heterogeneity is not an issue for this model. The number of support points in the equation for the decision to quit drinking alcohol and the equation for the mental health were found to be two and three, respectively. To be precise, there are two types in the sample who are differentiated by their quit rate: the first type has a quit rate of around 3.7% and the second type has a quit rate of around 9.0%. In addition, there are three types in the sample who are differentiated by their susceptibility to mental health problems: the first and second type have a mental health score of around 4.4 and 8.2 and are considered to have low and mediocre mental health scores, respectively. The third type has a mental health score of around 14.3 and hence are considered to have mental health problems. Furthermore, the obtained distribution of the unobserved heterogeneity of the joint model of alcohol consumption and mental health suggests a correlation between alcohol consumption and mental health. However, two likelihood ratio tests for the null hypothesis of no correlation were not rejected and hence do not confirm that unobserved common confounding factors affecting both alcohol consumption and mental health is an issue in this sample.

The main results of interest, are the results regarding the effect that alcohol consumption has on mental health. The results suggest that alcohol consumption has an adverse effect on mental health, however only when consumed almost every day. In fact, accounting for unobserved common confounding factors enlarges the size of the estimated effect of daily alcohol consumption on mental health. To conclude, the results of this thesis confirm the hypothesis that alcohol consumption increases the likelihood of having mental health problems, though only when consumed almost every day.

Finally, some limitations of this thesis are discussed and in addition some suggestions for further research is provided. A first shortcoming of this study is the potential of reverse causality between alcohol consumption and mental health. That is, there is the potential for mental health problems causing alcohol consumption, as well as alcohol consumption causing mental health problems. As the LISS panel data does not contain any information on the age at which mental

Causal association between alcohol consumption and mental health problems

Faculty of Economics and Business

Amsterdam School of Economics

Requirements thesis MSc in Econometrics.

Causal association between alcohol

consumption and mental health problems

Miriam Veenstra

Contents

1

Introduction

2

Literature review of unobserved heterogeneity

3

Methodology

4

Data

5

Results

6

Sensitivity analysis

7

Conclusions