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It then continues to increase at a slower pace up to age 30 years. Table 3 gives summary statistics for the prevalence rates and the age of onset of daily use of cannabis and homelessness up to age 30 years for our sample. On average, respondents who became homeless by 30 years old did so at an average of about 18 years old. If anything, for women, Figs 1 and 2 seem to suggest the opposite; the proportion experiencing onset of homelessness appears to lead the proportions taking up regular use of cannabis, and transitions into homelessness begin to peak before the peak in drug use.

For men, Figs 1 and 2 are ambiguous in this respect. At the same time the average age of onset for cannabis use precedes that of homelessness Table 3. Table 4 takes a closer look at this question by tabulating the probability that is associated with the possible combinations of timing of events with respect to the onset of homelessness and daily cannabis use uptake in the raw data, separately by gender.

In other words, daily use of cannabis can occur before, coincident with or after the onset of homelessness, with no discernible tendency for one to precede the other among young women, although there is a tendency for daily use of cannabis to precede the onset of homelessness among young men.

Multiple responses were permitted for this question. Other commonly stated factors that differ markedly by age include relationship breakdown and domestic violence or abuse more commonly cited among those first becoming homeless aged under 30 years and financial difficulties and mental and other health issues more commonly cited among those first becoming homeless over 30 years. Our outcome variables are durations until transition from one state to another the onset of homelessness and the onset of daily use of cannabis and the causal effects of interest relate to the realization of one transition on the transition rate of the other.

Given the structure of our model these are established by the timing of events conditional on observable and unobservable characteristics. Abbring and Heckman discussed the additional complications when attempting to model human behaviour in this way. Whereas the failure rates of machines may be constant over time, people may respond to the duration of the process in question. For example, an unemployed worker may lower his standards for accepting a job as the duration of unemployment increases.

If so, the rate of transition from unemployment to a job may increase, and duration models need to account for this duration dependence. Furthermore, whereas machines may be very similar, unemployed individuals may not be, i. For example, more motivated unemployed workers are more likely to find a job quickly.

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Finally, whereas the failure of one machine is a random event, individuals may anticipate events. For example, an unemployed worker who knows exactly when a training programme starts may change his job search behaviour in anticipation of the start of the programme. In this paper we specify a bivariate simultaneous duration model for the onset of homelessness and the onset of daily use of cannabis. In this model, each transition may causally affect the other transition rate, i. A major advantage of using this kind of approach is that, as shown by Abbring and van den Berg , identification of the treatment effect does not rely on a standard conditional independence assumption—we condition on both observables and jointly distributed unobservables—and it is not necessary to have a valid instrument.

Rather, identification comes from the timing of events, i. Because of this advantage bivariate duration modelling has become an increasingly common approach in parts of the social policy literature, e. The bivariate duration approach has also been used in several studies of drug use effects, most commonly to investigate various effects of cannabis use see Van Ours and Williams for a review. For applications to other questions see the references in Abbring and Heckman Although Abbring and van den Berg demonstrated this for a bivariate duration model where one transition is pre defined as the treatment and the other the outcome, Abbring and Heckman showed that this naturally extends to the simultaneous case where each transition can impact the other.

In all respects below we adopt the framework of Abbring and Heckman Let C h be the duration until the onset of daily use of cannabis given the time of initiation into homelessness h , and let H c denote the duration until the onset of homelessness given the time of initiation into daily use of cannabis c.

1 Introduction

Assume that ex ante heterogeneity across agents is fully captured by observed characteristics x and unobserved characteristics v , which are assumed to be external and temporally invariant. Initiation into homelessness may causally affect the duration C h through its transition i.

Similarly, initiation into daily use of cannabis may causally affect the duration H c through its hazard rate. Denote the hazard rate into daily use of cannabis at time t for an individual with characteristics as. Similarly the hazard rate into homelessness at time t for an individual with characteristics is. The unobservables and are from an unrestricted joint distribution in which the unobservables may have elements in common.

Both observables x and unobservables and capture ex ante heterogeneity, i. The inclusion of correlated unobserved heterogeneity is an important feature of bivariate duration models that allows them to account for time invariant characteristics that, in our application, may lead individuals to be simultaneously more prone to substance use and to homelessness. These shocks represent the randomness in the transition processes after conditioning on x , v and survival. Conditionally on observed characteristics and the distribution of unobserved heterogeneity, current hazards therefore depend only on past events and the transition processes evolve recursively.

Formally, for all : and for all. In our specific case, it requires that, conditionally on x and v , an individual does not alter her behaviour relevant to cannabis consumption because she knows that she will become homeless in a particular future year, and vice versa. We have already shown in Table 5 that the onset of homelessness is reportedly driven by a wide variety of factors, the most common of which involve actions by others e.


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Similarly, the timing of initiation into regular drug use is likely to depend on imperfectly predictable factors such as the degree to which occasional drug use leads to addiction, which seem equally unlikely to change behaviour with respect to homelessness in advance. In modelling the uptake of daily use of cannabis, we assume that potential exposure to drugs occurs from the age of 10 years.

We model transitions up to and including age 30 years to capture early onset of drug use and early onset of homelessness.

Individuals who have not started to use cannabis daily by age 25 years are very unlikely to do so later in their life Van Ours, a and, as discussed in the previous section, onsets of homelessness in later life appear to be driven by a set of factors that is different from earlier onsets. We specify 10 age dummies, seven of which are for individual ages age 12,…,18 years , whereas the first is for ages less than 12 years, the second last for ages between 19 and 21 years and the last interval is for ages from 22 years onwards up to 30 years.

As we know only the age at which each event first occurs and not the actual date, we cannot determine whether homelessness occurred first if both the onset of homelessness and substance use occurred at the same age. It is for this reason that we allow homelessness to impact on substance uptake if and only if it occurred in a previous period.

The potential correlation between the unobserved components in the hazard rates for substance uptake and homelessness is considered by specifying the joint density function for both durations of time until daily use of cannabis c and the duration of time until homelessness h conditional on x as 5 As is standard in recent applications of bivariate duration models, is assumed to be a flexible discrete distribution with an unknown number of points of support.

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We start by assuming that for every transition process its unobserved heterogeneity can be specified by a discrete distribution with two points of support. In combination this leads to four points of support: v h 1 , v c 1 , v h 1 , v c 2 , v h 2 , v c 1 and v h 2 , v c 2 , reflecting two types of individuals in the hazard rates for cannabis use high susceptibility and low susceptibility and two types in the hazard rate for homelessness high susceptibility and low susceptibility.

The four mass points imply that conditionally on observed characteristics there are four types of individuals.


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These probabilities are modelled by using a multinomial logit specification, i. The parameter estimates are obtained by using the method of maximum likelihood considering that our duration information relates to intervals rather than to exact durations. For example, an individual who indicated that they became homeless at age 16 years may have become homeless on his 16th birthday or on the day before his 17th birthday.

For this individual, we model that he did not yet start at age 15 years, but started before turning 17 years. A graphical explanation of this model is presented in Appendix A Figs 4 and 5. The control variables that are included in our model are listed in Tables 1 and 2.

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Alternatives, including dropping observations for which there are missing data, are explored in a sensitivity analysis that is discussed in Section 5. Including specific dummy variables for respondents with no male or female caregiver to distinguish between those two reference categories does not alter the results. Table 6 presents estimates of the bivariate model for initiation into daily use of cannabis and the onset of homelessness, allowing for causality in both directions. First we find evidence of the presence of unobserved heterogeneity.

We can identify four mass points of which the distribution is given in Table 7. Thus conditionally on observed characteristics and age we can distinguish four types of individual with different predispositions to daily use of cannabis and homelessness. Failing to take this into account would lead to a spurious effect of cannabis use on homelessness or vice versa. Now consider impacts on the onset of homelessness for young men. Taking up daily use of cannabis is associated with a higher hazard rate for onset of homelessness than that of otherwise equivalent men who do not use cannabis daily by a factor of 1.

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Under the assumptions that were set out in the previous section this can be plausibly interpreted as a causal effect. Possible causal mechanisms for such an effect include breakdown of family relationships and financial strain resulting from drug use qualitative evidence for both was presented by Johnson and Chamberlain These estimates provide the strongest quantitative evidence to date on the effect of use of cannabis on the onset of homelessness.

They also add evidence of a further negative social outcome to the literature on the causal effects of cannabis use. The strongest association with the onset of homelessness among this sample comes from not living with one's parents at age 14 years because of conflict, which almost quadruples the hazard rate for the onset of homelessness. This is consistent with the high proportion of young men who cited this as a reason for first becoming homeless as presented in Table 5.

We find little evidence of reverse effects—from onset of homelessness to initiating daily use of cannabis—for young men. We show below that in most robustness tests it is negative, similar or smaller in magnitude, and statistically insignificant. Other statistically significant factors include a male caregiver with substance abuse problems or who has spent time in prison. Data that enable a quantitative analysis of the effects of adverse childhood experiences such as these on cannabis use are rare, but existing studies have found a positive association between parental substance use and own drug use e.

The results for women are almost the polar opposite of those for men.

Early illicit drug use and the age of onset of homelessness

We see no evidence of an effect of daily use of cannabis on onset of homelessness, but clear evidence of a reverse effect from homelessness to daily use of cannabis the corresponding hazard ratio is 1. This gender contrast is to some extent visible in the raw data that were presented in Table 4 , where the onset of homelessness more often precedes drug use uptake for women whereas the opposite is the case for men.

Conflict with parents at age 14 years is again the variable with the strongest association with both outcomes. Note that reporting a male caregiver with a gambling problem again takes a negative sign. Experiencing sexual violence as a child is an additional factor that increases the hazard for both the onset of homelessness and daily use of cannabis for young women but not young men, as is missing data about the male caregiver.

Ours is not the first study to find evidence of stronger effects of cannabis use for men than for women on social outcomes. Other studies have also flagged potential gender differences specifically in the nature of the association between drug use and homelessness which are consistent with our results. This is consistent with the evidence from JH presented in Table 5. Instead women cite domestic violence much more frequently, both in the JH study and elsewhere e.

Kidd discussed whether young homeless women face greater adversity or perceive greater social stigma than young homeless men on average, which would be consistent with young homeless women disproportionately turning to drug use via one or both of the adaptation and coping mechanisms. Evidence that is suggestive of an effect of youth homelessness on drug use, both qualitative and quantitative, has been presented elsewhere in the homelessness literature e. None of the existing quantitative studies, however, satisfactorily deals with selection on unobservables.

Other common restrictions include bans on outdoor drinking and indoor smoking.