Catrin Evans

Eunice Wambui Ndirangu

Implementing Routine Provider Initiated HIV Testing in Public Healthcare Facilities in Kenya: A Qualitative Descriptive Study of Nurses' Experiences

Keywords: HIV, Nurses, Kenya, Provider initiated testing HIV, provider initiated testing, nurses, Kenya

published or not. The documents may come

 2007). PITC has significant implications for health care teams, requiring increased levels of engagement with HIV issues, higher work loads and/or the need to re-organise working patterns to incorporate HIV testing into routine care. In response to concerns about the protection of individual rights in resource limited clinical settings [START_REF] Gruskin | Provider-initiated HIV testing and counselling in health facilities: What does this mean for the health and human rights of pregnant women?[END_REF][START_REF] Rennie | Desperately Seeking Targets: The Ethics of Routine HIV Testing in Low Income Countries[END_REF], WHO/UNAIDS (2007) guidelines state that PITC should only be implemented in contexts where a minimum package of HIV care and the 3C's -informed (verbal) consent, confidentiality and counselling can be guaranteed (WHO/UNAIDS, 2007 p.30).

Kenyan Context

This paper examines PITC in Kenya where HIV prevalence is 7.1%; over 86% of the adult population has not had an HIV test and approximately 83% of people who are HIV positive are unaware of their diagnosis (Ministry of Health, 2008a). PITC has been progressively rolled out in Kenyan public sector health facilities (which comprise approximately 51% of health services) since 2005 [START_REF] Marum | Scale Up of Voluntary HIV Counselling and Testing in Kenya[END_REF]Ministry of Health, 2009). PITC scale up is supported by national guidelines (Ministry of Health, 2008b) and a national health worker training programme. In public sector health facilities, PITC is usually carried out using rapid tests and is primarily undertaken by nurses.

Literature Review

Research from across sub-Saharan Africa shows high levels of patient acceptance of PITC when measured quantitatively [START_REF] Obermeyer | The utilisation of testing and counselling for HIV: A review of the social and behavioural evidence[END_REF][START_REF] Wanyenze | Acceptability of routine HIV counselling and testing, and HIV seroprevalence in Ugandan hospitals[END_REF]. However, in Kenya (as elsewhere), considerable variation in testing uptake and return for follow up between different testing sites has been reported, indicating that specific site factors have an impact on the patient experience [START_REF] Anand | Site factors may be more important than participant factors in explaining HIV test acceptance in the prevention of mother to child HIV transmission programme in Kenya, 2005[END_REF]. A number of qualitative studies highlight that patients can feel pressured into testing, are mistrustful of healthcare staff or report poor quality care [START_REF] Delva | Quality and Quantity of Antenatal HIV Counselling in a PMTCT Programme in Mombasa, Kenya[END_REF][START_REF] Groves | The complexity of consent: women's experiences of testing for HIV at an antenatal clinic in Durban, South Africa[END_REF][START_REF] Hamilton | Potential for abuse in the VCT counselling room: service provider's perceptions in Kenya[END_REF][START_REF] Painter | Women's reasons for not participating in follow up visits before starting short course antiretroviral prophylaxis for prevention of mother to child transmission of HIV: a qualitative interview study[END_REF]. In Kenya, a 2005 national health worker survey found high levels of knowledge and support for the PITC programme (National AIDS and STD Control Programme, 2006). However, a recent evaluation of the PITC national training programme found that only 30% of health facilities were fully implementing PITC citing staff shortages, lack of space and low staff morale as associated factors [START_REF] Kathambana | Challenges of scaling up provider initiated testing and counselling in Kenya: Paper presented at XVII International AIDS Conference[END_REF]. Similar findings have been reported in a range of other countries (Evans & Ndirangu, 2009;Minnie, van der Walt, & Klopper, 2009).

To date, HIV testing research has focused upon out-patient settings (primarily antenatal or TB clinics).

Very little is known about PITC practice within in-patient contexts.

Research Aim

Given the critical role of nurses in ensuring high quality PITC implementation in Kenya, this paper reports on an exploratory study that aimed: (i) to investigate key challenges in PITC from a nursing perspective and, (ii) to explore ways in which the principle of the 3C's (consent, confidentiality and counselling) were being managed in every day practice.

Methods

The study adopted an interpretative qualitative methodology [START_REF] Rubin | Qualitative Interviewing: The Art of Hearing Data[END_REF]. A multi-method design was used, involving 2 focus groups (n=6 in each) and 13 semi-structured interviews [START_REF] Green | Qualitative Methods for Health Research[END_REF]. The focus groups were conducted to explore social/professional norms and discourses around HIV testing and of nurses' role in HIV care. These were followed by individual interviews to elicit accounts of actual HIV testing practices and experiences in particular workplace contexts [START_REF] Barbour | Mixing qualitative methods: quality assurance or qualitative quagmire?[END_REF].

Data were collected by the second author, a Kenyan nurse-researcher. The sampling strategy was deliberately broad in order to represent nurses from a range of workplaces. The inclusion criteria were that participants had a nursing qualification, worked in a public health sector facility in or around Nairobi and that they either delivered PITC directly or worked in a setting where PITC directly impacted upon their everyday nursing practice (e.g. having to care for in-patients who had just received a HIV diagnosis). There were a total of 25 nurse-participants, representing 11 different healthcare facilities; 13 worked in in-patient settings and 12 worked in out-patient settings and/or held managerial positions -see tables 1 and 2 for further details.

Data Analysis

All interviews/group discussions were digitally recorded, transcribed and checked for accuracy. Data were analysed manually using inductive thematic content analysis [START_REF] Boyatzis | Transforming qualitative data: thematic analysis and code development[END_REF], paying particular attention to atypical cases and to contextual variations [START_REF] Tobin | Methodological rigour within a qualitative framework[END_REF]. Initially, the interviews and focus groups were analysed separately but strikingly similar themes emerged from both data sets, so they were combined. To enhance rigour, transcripts were read by both authors and a common coding scheme and thematic framework was agreed. Three major categories were identified.

Findings

(1) The Contradictions of Routinisation All the nurse participants were highly knowledgeable about the PITC policy and supported its rationale. However, nurses identified two contradictions that PITC posed for their everyday practice.

The first was associated with trying to normalise a highly stigmatised disease. On the one hand, many nurses noted that the routine offer of a test made HIV seem "just like any other chronic disease", and that, in practice, routinisation made it easier for both staff and patients to talk about HIV. So, whereas previously, 'HIV-talk' had been conducted using coded forms of communication (e.g. oblique references by health-workers to "P-24 antigen") or by complicated guess work based Before, a patient will come -inside his heart wanting to do the test -but just asking you would be a problem for him, but now its all in the open (N13)

On the other hand, nurses recognised that in the public mind HIV was not yet a 'routine' illness due to the stigma that surrounded it. Indeed, many participants commented that some nurses themselves still stigmatised HIV and could exhibit a damaging judgementalism:

We talk as if it's a bad thing; we also discuss these patients despite saying that we are going to keep the confidentiality -so of course patients will not want to test (FGD1, P5)

The second contradiction was associated with trying to maintain a client centred philosophy of care within a routinised and target driven practice context. For example, many nurses were not convinced about the PITC guideline to minimise pre-test discussions in order to expedite client through-put. Their own experience was that in many cases (because of HIV-related stigma), patients did require in-depth pre-test discussions to help them to overcome their fears and to give consent:

Pre-test counselling is the most important thing because it prepares the patient to receive a positive result -if you just test -where do you start when the patient turns out to be positive? (FGD2, P3)

In such cases, nurses' narratives indicated that, where possible, they adapted the guidelines, tailoring their discussions to an in-depth understanding of the patients' situation:

With this patient, I knew I had to take longer. So I took her very slowly through everything.

She didn't want to test, but then, after some persuasion, she decided to let me go ahead (N12)

Many of the participants (particularly from out-patient settings) felt that routine testing had created target-rather than client-centred approach to HIV care and that this inevitably compromised quality of care: wondering where this 50 will come from. If we coerce these patients to be tested -then they won't come back. It won't be provider-initiated, it will be provider-coercion (FGD2, P1)

(2) Everyday Ethics

The data indicated that PITC sometimes created acute ethical dilemmas within nurses' everyday practice which were experienced as very stressful.

A commonly cited situation was where patients refused to have the HIV test. In dealing with such cases, nurses repeatedly returned to the principle of "do no harm" to justify their decision making.

So, for example, nurses noted that they would usually give the patient more time or simply have to accept the patient's choice (even if they did not agree with it). However, a number of nurses described situations where they had applied strong pressure to persuade patients to take the test. In principle, this runs counter to the PITC guidelines to elicit voluntary informed consent. In the examples given however, nurses clearly felt that not testing would have caused even greater harm:

Sometimes you find a patient where you know the spouse or a child has died because of AIDS and they refuse to be tested despite the counselling and all that. It is challenging because upon discharge you will lose that patient. So you find you might be aggressive for the sake of helping them, not because you want to create harm, but just because you want them to benefit, even though you have to use a cold and aggressive way of handling such a situation………….Like there was a girl on the ward and I told her -either you lose your life or comply with the protocols of the hospital………..then, you see………..it was like forcing……but at the end of it she accepted. But it was for her benefit (N2)

None of the participants mentioned the multi-disciplinary team as a source of advice in dealing with such situations. In fact, several interviewees (all from in-patient settings) described incidents where medical doctors or clinical officers had tested patients without consent, indicating that this was common practice:

It happens many times when the doctors are doing their rounds. Interestingly, all such narratives were recounted without comment or judgement. When the nurses were asked if they ever questioned the practice of a doctor, they indicated that their views would be dismissed:

Sometimes we do suggest about patient management with the doctor but then the doctors feel you are undermining them -you know -you are just a nurse (N5)

Another difficult situation was when HIV positive clients refused to disclose their status to others who were potentially at risk. Again, in most cases, nurses spoke of having to accept and respect a patient's choice. Nonetheless, in four interviews, nurses admitted to breaching confidentiality. In all cases, the situation involved a male patient refusing to inform a spouse and was rationalised in terms of acting in the public good:

You know, this whole issue is gender biased because the men, they keep it to themselves and the women perish. That part of the confidentiality -I think it's killing us. It should be mandatory that the spouse news is told to the other spouse. It is not opening up other people's issues, but it is just taking care of the others (FGD1, P4)

Nurses described a deep discomfort in dealing with a related scenario in which the family was anxious, was bearing a high financial and physical burden of care, and yet the patient would not disclose. Some nurses felt it was ethically wrong to keep such relatives in the dark:

See, the relative is the one paying the bill and they are asking all the time 'what has the doctor said'?…. As a nurse you are fixed because on the one hand there is confidentiality and on the other there is the relatives' vulnerability……….Mostly it is women, and you see that they will not be able to take care, so you just go ahead and give information to that person (N10)

Nurses also described becoming de-moralised at the sheer number of patients who tested positive and at their sense of powerlessness to help those in need: Working with HIV therefore exacted an emotional toll. In some institutions, specialist HIV counsellors received monthly clinical supervision, however, this was not available everywhere and did not include general clinic/ward nurses.

F
(3) Workplace Environment and Support A major source of stress and frustration for the participants related to their working environments.

Lack of staff, lack of resources and lack of time were the most common complaints leading to patients being kept waiting, being sent away un-tested or being dealt with abruptly.

Sometimes you find like in my ward you are alone…..you have all the clients for testing -so what we do is sketchy -you know -shallow, not deep Many nurses identified the over-crowded ward environment (where beds are shared or positioned close together, where there are no screens and where relatives may be present at all times) as a challenge to maintaining dignity and confidentiality:

We don't have cubicles….so it forces us to go bed by bed as we give a report….patients have come to realise the language we use and then you say "this immuno-suppressed patient or this is a p24 patient" and it just gives away the whole story to the others (N13)

In addition, nurses described how the need to involve relatives in patients' care also led to inadvertent breaches in confidentiality:

Like, when we remove the blood then it is taken to another facility for testing…..then….in most cases it is the relatives who bring the results back and some of the relatives know about the CD4 count and why it is done, so we actually breach confidentiality (FGD1, P5) Many participants expressed the view that the additional burden created by PITC had been insufficiently recognised in their workplaces, leading to de-motivation and a task-oriented mentality:

When it comes to doing PITC, if you are trained and the other nurse counsellor is not there, you are not much willing to do it -there is no recognition for it, so you just wait until she comes back (N8)

Indeed, a general perception that nurses were under-valued at the wider policy level was strongly expressed in the focus group discussions:

If you look at all the programme implementation -anything on HIV -it ends up with the nurse. If the nurse does not implement it, the whole programme falls back. But if you look at the people who are being rewarded for that particular programme, the nurse is at the back.

So there is a lot of de-motivation………..People are creating policy up there, they are not coming down (FG1, P2).

Discussion

Although small scale, our study findings are highly are consistent with related research in this area [START_REF] Mavhandu-Mudzusi | Nurse's experiences of delivering voluntary counselling and testing services for people living with HIV/AIDS in the Vhembe district, Limpopo province, South Africa[END_REF][START_REF] Mkhabela | Experiences of nurses working in voluntary counselling and testing services in Swaziland[END_REF][START_REF] Nuwagaba-Biribonwoha | Challenges Faced by Health Workers in Implementing the Prevention of Mother to Child HIV Transmission (PMTCT) Programme in Uganda[END_REF] and show that nurses face a number of challenges in implementing PITC.

The first relates to the routinisation of a stigmatised disease. The nurse participants agreed that PITC confronted HIV stigma and enabled a greater openness about the disease, but recognised that its implementation was hindered by existing stigmatised social norms around HIV (expressed by nurses as well as by patients). Nurses faced a contradiction in that addressing stigma required an individualised approach to patient care -but this was difficult to deliver because of routinised testing protocols with minimal pre-test discussion, a focus on meeting targets and lack of time and/or staff. Similar findings have been reported by [START_REF] Pope | South African TB nurses' experiences of provider-initiated HIV counseling and tesing in the Eastern Cape Province: a qualitative study[END_REF] and [START_REF] Rohleder | What I've noticed is that they need the stats": Lay HIV counsellor's reports of working in a task-oriented health care system[END_REF].

Second, the study indicates that PITC can be stressful -relating in part to the emotional labour of managing complex client situations, and, in part, to workplace resources and conditions. This study Finally, this study also identified particular challenges to maintaining the 3C's within in-patient settings. Although quantitative studies on PITC uptake have been published from in-patient care (e.g. [START_REF] Gichangi | The Acceptability of HIV Testing in Patients with Invasive Cervical Cancer in[END_REF][START_REF] Wanyenze | Acceptability of routine HIV counselling and testing, and HIV seroprevalence in Ugandan hospitals[END_REF], to our knowledge, there have been no in-depth qualitative studies examining the process of PITC implementation in hospital wards. There is an urgent need for more research on HIV testing practice within the in-patient context, and our findings suggests that such research must also include the practices of doctors and clinical officers.

Despite a strong national training programme and clear guidelines, the process of translating PITC policy into practice is invariably complex, shaped by client, provider and health system factors, and, as this study shows, by specific local interpretations of key ethical principles. Further understanding of the complexities of PITC implementation in different cultural contexts is hindered by the fact that most studies (including this one) have relied on self-reported recall of PITC experiences. We suggest that future research should include observation of actual HIV testing practice and a strong focus on the patient experience.

In conclusion, nurses are on the front lines of PITC implementation in Kenya and require continued support to negotiate the challenges and to fulfil their roles effectively. ) is done at the same level as the Registered Nurse but encompasses general nursing, community health nursing, midwifery and psychiatric nursing. KRCHNs, RNs and ENs all provide basic nursing care, however the RNs/KRCHNs are equipped with additional leadership and managerial skills which means that they often hold more senior leadership roles. However, this distinction is usually subject to availability of staff, for example, if a health centre in a rural area does not have a KRCHN nurse then the senior most EN will be the 'in charge'.

  Initiated HIV Testing in Public Healthcare Facilities in Kenya: A Qualitative Descriptive Study of Nurses' Experiences Dr. Catrin Evans (Ph.D.), Lecturer, School of Nursing, Nottingham University, B Floor, Queens Medical Centre, Nottingham, NG7 2UH, U.K. (catrin.evans@nottingham.ac.uk) Ms. Eunice Ndirangu (M.Sc.), Lecturer, Advanced Nursing Studies Programme, Aga Khan University, P.O. Box 39340, Parklands, Nairobi, Kenya, (Eunice.ndirangu@aku.edu) testing and counselling (PITC) is a key strategy in the global effort to increase HIV testing rates. Global PITC guidelines propose that all clients attending health services in high prevalence areas be offered an HIV test, regardless of their presenting complaint (WHO/UNAIDS,

  individual interviews used convenience sampling; the second author contacted health facilities (Hospitals A-D and Health Centre A) where she had contacts amongst senior nursing staff who, in turn, facilitated access to potential participants. The focus group participants likewise comprised a convenience sample in that they were drawn from a larger group of nurses who were attending a course (not connected to HIV) in a Nairobi School of Nursing. The interviews (lasting 45 -60 minutes) were held in a quiet room in the individual's workplace. The focus group discussions were held in the School of Nursing. Ethical permission to conduct the study was obtained from the Aga Khan University Research Ethics Committee, the Kenyan Ministry of Education Science and Technology and individual hospital ethics committees. All participants provided written informed consent.

  from patients (e.g. references to "weight loss"), nurses felt that routinisation now facilitated more open conversations:

7

  If you see the crowds at the clinic they [the supervisors] will be very happy……but they will not bother to find out the quality of work you did with each client….They are pressurizing the staff…… if you do not test this many numbers then you are a failure………and we are

  of areas where maintenance of the 3C's was problematic for nurses, including several examples where clients had been pressured to consent and where confidentiality had been breached. Nurses expressed ambivalence about PITC's focus on protection of individual rights in the face of safeguarding the public health and in a cultural context where women lack power and where health decision making is based on collective rather than purely individual interests (cf.[START_REF] Mulemi | Patients' perspectives on hospitalisation: experiences from a cancer ward in Kenya[END_REF]. A recent study in Malawi,[START_REF] Angotti | Working outside the box: how HIV counselors in sub-Saharan Africa adapt western HIV testing norms[END_REF] showed that, like the nurses in this sample, HIV counsellors learned to use their discretion to creatively manage difficult ethical situations. One way of addressing these dilemmas of everyday practice would be for nurses to receive greater opportunities for clinical supervision and group support in which they could formulate their own workplace-specific strategies for practice development. Any interventions to support PITC need to pay heed to the sense of disempowerment expressed by nurses in this study however, and should consider how to support nurses to secure a greater sense of autonomy and recognition in the workplace.

F

  specialist training on HIV counselling n=6 n=6 48% 1 Registered Nurses (RN) are mainly trained at diploma level (3 years of training) with a few having a BScN qualification (4 years of training). Enrolled Nurses (EN) are trained at a certificate level (2 years of training). The Kenya Registered Community Health Nurse (KRCHN) training (3.5 years

  next thing you know, the clinical officer is poking into this patient drawing blood and the patient doesn't know why. The patients are so innocent, they trust that whatever you are doing is for his own good…..…they do not demand to know (N6)

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Many are the times they don't inform the patients what is wrong with them. The doctor notes down the test and the

  You test them and then they tell you their history and you just don't know what to do next. They are poor and they can't afford food, and then you ask yourself 'what can I do to help this person'. It really affects me (N10)

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Table 1 :

 1 Sample Characteristics -Clinical Sites and Nursing Roles

	Clinical Sites	Interviews	Focus Groups	Total
	n=11, labelled A-K	n=13	n=12	n=25

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Acknowledgements

We are grateful for the support of a Boehringer Ingelheim Research Grant administered through the UK National HIV Nurses Association. We thank all the nurses who kindly agreed to participate in this study.

Government hospitals in


Johan Jarl
email: johan.jarl@med.lu.se

U-G Gerdtham

Does drinking affect long-term sickness absence? A sample selection approach correcting for employment and accounting for drinking history Running head: Alcohol and long-term sickness absence

Keywords: J21 -Labor Force and Employment, Size, and Structure < J2 -Time Allocation, Work Behavior, Nutrition, Mortality, Morbidity, Disability, etc

Does drinking affect long-term sickness absence? A sample selection approach correcting for employment and accounting for drinking history

Johan Jarl, Ulf-G.

I. Introduction

Sweden experienced a rapid increase in sickness-related absence 1 from 1998 to 2003, and although the trend shifted in 2004, Sweden continues to experience one of the highest absence rates in Western Europe. In fact, in 2004, the rate of absences was about twice as high in Sweden as compared to the EU-15 countries (4% versus 2%) (Försäkringskassan, 2005). This was costly to Swedish society and has attracted significant attention and study regarding its causes. From an international perspective, the causes of absence have received attention in the context of efforts to reduce these rates for the purposes of improving public health and decreasing health costs [START_REF] Hse | Managing sickness absence in the public sector[END_REF]. Several potential causes have been studied, including shift work [START_REF] Tüchsen | Shift work and sickness absence[END_REF], moral hazard [START_REF] Johansson | Moral hazard and sickness insurance[END_REF], contractual arrangements [START_REF] Barmby | Sickness absence in the UK 1984-2002[END_REF]), work stress [START_REF] Vasse | Associations between work stress, alcohol consumption and sickness absence[END_REF] and health-related behaviours [START_REF] Christensen | The impact of health behaviour on long-term sickness absence: Results from DWECS/DREAM[END_REF].

Focusing on health-related behaviours in general and alcohol consumption in particular is considered important as alcohol-related absence constitutes a significant part of the societal cost of alcohol. For example did a recent Swedish study estimate alcohol-related absence to SEK 4.3 billion for the year 2002, after subtracting reductions from beneficial health effects [START_REF] Jarl | The societal cost of alcohol consumption: an estimation of the economic and human cost including health effects in Sweden[END_REF]. This figure constitutes over 21% of the total cost to the Swedish society from alcohol. 73% of the burden of absence is due to long-term absence (defined as longer than 14 days). Alcohol-related absence is thus a substantial burden on the society which would explain policy makers' interest in ways to reduce the absence rates.

It has been difficult to arrive at any final conclusions about the effect of alcohol on absence rates in prior research. In a review regarding absence, psychiatric disorders and alcohol, 1 From here on only "absence". 3 [START_REF] Hensing | Chapter 7: Sickness absence and psychiatric disorders[END_REF] conclude that there is insufficient evidence that alcohol affects absence. The studies reviewed, however, showed that individuals diagnosed with alcohol dependence or abuse suffer more and/or longer periods of absence [START_REF] Hensing | Chapter 7: Sickness absence and psychiatric disorders[END_REF]. Studies focusing on high alcohol consumption did not show any conclusive results, probably due to different definitions of both high alcohol consumption and absence. Some studies reported that women who do not consume alcohol are at increased risk of absence [START_REF] Hensing | Chapter 7: Sickness absence and psychiatric disorders[END_REF]); this result is not surprising given the negative outcomes associated with abstention that are commonly found in studies on alcohol (e.g. [START_REF] Andréasson | Alcohol and J-shaped curves[END_REF][START_REF] Peters | Is there a wage bonus from drinking? Unobserved heterogeneity examined[END_REF].

In more recent studies, there is some evidence of the effect of alcohol on absence. For example, it has been shown that the risk of short-term absenteeism is increased the day after alcohol consumption [START_REF] Mcfarlin | Workplace absenteeism and alcohol use: A sequential analysis Psychology of[END_REF]. A Finnish study using micro-data found a positive association between the level of consumption and absence [START_REF] Johansson | Alcohol consumption and sickness absence: Evidence from micro data[END_REF]. [START_REF] Cunradi | Alcohol, stress-related factors, and short-term absenteeism among urban transit operators[END_REF] showed that short-term absenteeism was associated with several measures of problem drinking in a sample of urban transit operators, while [START_REF] Tómasson | Correlates of probable alcohol abuse among women working in nursing homes[END_REF] found no effect of problem drinking on sick leave in a female working sample. [START_REF] Roche | Workers' drinking patterns: the impact on absenteeism in the Australian work-place[END_REF] found that risky alcohol consumption (compared to low-risk), increases both selfreported alcohol-related absenteeism and overall illness/injury absenteeism. The prevalence of absenteeism was higher with higher risk consumption as well as more frequent, risky consumption. This is the only study that incorporates pattern as well as the level of consumption. Norström (2006), in a time series analysis of aggregated alcohol consumption on absence, found that a one litre increase in consumption is associated with a 13% increase in absence among men. No significant effects were found among women. These results were later repeated in a similar study in Norway [START_REF] Norström | Per capita alcohol consumption and sickness absence in Norway[END_REF]. Two recent studies have employed alcohol groups based on the level of consumption when studying the effect on absenteeism. Based on average weekly levels, [START_REF] Vahtera | Alcohol intake and sickness absence: a curvilinear relation[END_REF] found that, compared to light drinkers, there was an increased risk of absence for former drinkers, heavy drinkers, and those who abstain from drinking. They concluded that the Ushaped relationship could not be explained by confounding psychosocial factors or the "former drinker error" (i.e., including former drinkers in the abstainer group). A Danish study investigated the effect of health behaviours on long-term sickness [START_REF] Christensen | The impact of health behaviour on long-term sickness absence: Results from DWECS/DREAM[END_REF].

Two analyses were conducted wherein the alcohol variable was first divided into heavy versus non-heavy drinkers, and second into non-drinkers, moderate drinkers and heavy drinkers, defined by weekly level. No association between alcohol and long-term absence was found. It should be noted that although the authors controlled for former smoking in their regressions, they did not control for former drinking. This article analyses the effect of alcohol consumption on sickness absence. There are several significant contributions of the study. First, focus is on the rarely studied long-term absence, which is due to the fact that many of the detrimental health effects associated with alcohol are chronic and have relatively long recovery processes. Also, long-term absence was shown in the recent Swedish cost of alcohol study to amount to 73% of the total absence cost [START_REF] Jarl | The societal cost of alcohol consumption: an estimation of the economic and human cost including health effects in Sweden[END_REF]. Second, the effect of drinking history is controlled for, as it is expected to play a key role in long-term absenteeism, i.e. the long-term effect of alcohol consumption. Third, a sample selection model is used that correct for the effect of alcohol consumption on employment probability. In the study we focus attention on woman's absenteeism and the results for men are only reported briefly. The reasons for this are discussed below. The study indicates that long-term, light alcohol consumption has a protective effect on the probability of long-term absence, while abstention and heavy drinking have a detrimental effect. However, the detrimental effect is highest for women who have changed their consumption to and from abstention. Hence, controlling for drinking history (and thereby avoiding the former drinking and former abstainer errors) is important. We also find that controlling for the selection effect into employment is important and that a conventional probit model generally understates the effects of alcohol. In a simple model simulating changes in the prevalence of consumption, we find that although alcohol on average only explains a small part of individual long-term absence, the total societal effect is considerable.

The results for men are generally insignificant. Next, we address methods and data, followed by the results of the regressions and the simulation model in subsequent sections. The results will then be discussed and some concluding remarks will be shared.

II. Estimation Method

To model the effects of alcohol on absenteeism, we use the micro-economic data set described in Section 3 below. The basic idea of the analysis is that alcohol, by causing increased prevalence of certain diseases and injuries [START_REF] Dave | Alcohol taxes and labor market outcomes[END_REF][START_REF] Jarl | Medical net cost of low alcohol consumption: A cause to reconsider improved health as the link between alcohol and wage?[END_REF], increases the prevalence of absenteeism. It is expected that the level of consumption is more closely related to absence in the long run, while the pattern (e.g. binge drinking) is more closely related to absence in the short run [START_REF] Roche | Workers' drinking patterns: the impact on absenteeism in the Australian work-place[END_REF]. The short-term effects of alcohol (e.g. hangovers) are also thought to increase work absenteeism.

Methodological considerations

There are three key methodological issues that need to be considered in the modelling. 6 demonstrated that male abstainers have a reduced probability of employment, which is almost entirely due to abstainers being diagnosed as alcohol dependant [START_REF] Johansson | Abstaining from alcohol and labour market underperformance: Have we forgotten the 'dry' alcoholics?[END_REF].

Problem drinking has also been found to reduce the probability of employment [START_REF] Mullahy | Alcoholism, work, and income[END_REF][START_REF] Mullahy | Employment, unemployment, and problem drinking[END_REF][START_REF] Macdonald | Does problem drinking affect employment? Evidence from England[END_REF], while other studies have found no such relationship (e.g. [START_REF] Feng | The impact of problem drinking on employment[END_REF]. In a Russian sample, [START_REF] Tekin | Employment, wages, and alcohol consumption in Russia[END_REF] concludes that when controlling for unobserved heterogeneity, alcohol has no effect on employment for men and a small positive effect for women. Although previous studies have produced vastly different results, one hypothesis is that individual health status is a determinant in the employment equation, and that alcohol affects health status. This implies that we might face a selection effect, in other words, absenteeism might not be observed for those with sufficiently detrimental drinking. This is dealt with below by using a Heckman model, where the selection equation is the employment function, a method not previously employed in the alcoholabsence literature.

The second methodological issue is that alcohol affects health over both the short and long term; in other words, drinking history may be as important as current level of alcohol consumption. In addition, changes in alcohol consumption over time may be considered a proxy for (alcohol) problems. Earlier studies have shown that former drinkers who are now abstainers are, in many aspects, different from long-term abstainers [START_REF] Fillmore | Alcohol consumption and mortality. I. Characteristics of drinking groups[END_REF]. This is also true for other consumption groups such as former abstainers that are now light drinkers and long-term light drinkers [START_REF] Jarl | Wage penalty of abstinence and wage premium of drinking: A misclassification bias due to pooling of drinking groups?[END_REF]. Failure to control for past consumption may result in biased estimates (Sharper et al., 1988;[START_REF] Jarl | Wage penalty of abstinence and wage premium of drinking: A misclassification bias due to pooling of drinking groups?[END_REF]. It is interesting to note that, with the exception of one study that controls for the former drinker error [START_REF] Vahtera | Alcohol intake and sickness absence: a curvilinear relation[END_REF], no prior studies consider the possibility of bias due to individuals with the same current consumption level faces different outcomes based on their consumption Third, there is an alternate theory for explaining the relationship between alcohol and absenteeism: that absenteeism increases alcohol consumption through, for example, selfmedication or reduced social control when spending time at home (e.g., [START_REF] Aira | Drinking alcohol for medicinal purposes by people aged over 75: A community-based interview study[END_REF][START_REF] Suh | Selfmedication hypothesis: connecting affective experience and drug choice[END_REF]. The relationship between alcohol and absenteeism is difficult to disentangle and normally is only association estimated. The alcohol variables in this study, constituting both current and past consumption, can be interpreted as the change in consumption. As this change has taken place in between the waves, the causality is stronger than in most prior studies. However, it can be debated if the time between the change and the observation is long enough to control for reversed causality.

We model the effect of alcohol on the likelihood of an episode of absenteeism using a probit equation:

y 1i = r i β 1 + x i β 2 + u (1)
where y 1 is equal to 1 if absent from work for i th individual, 0 otherwise, r is a set of alcohol variables that incorporates both current and past consumption, x is a set of control variables including health and u is the error term. Our main hypothesis is that β 1 >0. If this holds, then productivity losses may be avoided if current and past alcohol consumption could be reduced.

However, information on absenteeism is limited to a sample of the working population. Thus, absence is observed contingent on the likelihood of employment, which may be modelled as: where y 2 is equal to 1 if employed for i th individual, 0 otherwise, z is a set of control variables, and v is the error term. It may be expected that γ 1 <0. If there is a non-zero correlation between u (1) and v (2), E[u|v] = ρv, the absenteeism model may be specified as:

y 2i = r i γ 1 + z i γ 2 + v (2)
y 1i = r i β 1 + x i β 2 + ρv (3)
Failure to allowance for non-random sampling when estimating (3) results in biased estimations. In this case, z in equation ( 2) must be a superset of x in equation (1) [START_REF] Baum | An introduction to modern econometrics using Stata[END_REF][START_REF] Wooldridge | Introductory Econometrics 2nd ed[END_REF]. We estimate β, γ and ρ jointly using a full maximum-likelihood procedure [START_REF] Baum | An introduction to modern econometrics using Stata[END_REF]. For this we use Stata software and the heckprob command (Stata Corp., 2005). We employ robust cluster estimation and to facilitate interpretation, and calculate average marginal effects using the Stata margeff command (Bartus, 2005, version 2.1.8). The possibility of unobserved heterogeneity in the absenteeism model is dealt with by including the health lag.

The estimated model is used to predict the probability of individuals experiencing long-term absenteeism, conditioned on them being both employed and non-employed, but had they been employed. We multiplied the predicted probability with the average number of long-term sick days for those who had at least one long-term spell of absence, which gives the expected number of long-term absence days per individual. By simulating a change in the prevalence of alcohol consumption and re-predicting the probability of absenteeism, we can calculate the difference in number of expected long-term sick days. These prevalence changes can be seen as effective interventions. Four such hypothetical interventions/prevalence changes will be simulated:

• To stop alcohol consumption among heavy drinkers and thereby turn them into former drinkers (short-term simulation);

Instruments

Variables included in x and z above are variables that are normally controlled for in estimates of labour market outcomes (see below). In order to identify the Heckman model in practical applications, we need z to be a superset of x; in other words, z should include the determinants of x but also some determinants specific to z, commonly termed instruments.

Unemployment rates affect the probability of being in paid employment. However, it has also been shown that it also affects sickness absence rates. Although some studies have shown this also for Sweden [START_REF] Knutsson | Occupation and unemployment rates as predictors of long term sickness absence in two Swedish counties[END_REF][START_REF] Berggren | Swedish sickness absenteeism in a European perspective[END_REF], the effect is uncertain. A common suggested explanation of the relationship between unemployment and absence rates is that reduced perceived job security that follows from economic slow downs with high unemployment reduces shirking and/or increases presenteeism (working while sick). It has indeed been shown that perceived job security affects sickness absence in Sweden, although this mostly affects short-term absence. Interestingly, there is only a weak effect on long-term absence (measured as longer than 7 days) [START_REF] Khan | Perceived job security and sickness absence: a study on moral hazard[END_REF]. Likewise has Olsson security of employees affected short-term much stronger than long-term absence. This is also connected to the issue of moral hazard which is expected to be more related to short-term than long-term absence as a medical certificate is required after the first 7 days. Considering that long-term absence in the current study is measured as longer than 28 days, we argue that the effect of perceived job security is negligible. Another Swedish study investigated the effect of unemployment rates and occupation as predictors for long term sickness absence defined as longer than 29 days [START_REF] Knutsson | Occupation and unemployment rates as predictors of long term sickness absence in two Swedish counties[END_REF]. They found, when controlling for occupation, no effect of unemployment rates for women and an inversed relationship for men.

Interesting to note is that without controlling for occupation, their results showed a positive relationship between unemployment rate and long-term sickness absence for both men and women. A suggested explanation for the gender differences in results is that a greater proportion of women compared to men are employed by public employers that are less sensitive to business cycles [START_REF] Knutsson | Occupation and unemployment rates as predictors of long term sickness absence in two Swedish counties[END_REF]. Information from comparable, neighbouring countries is conflicting. A study in Norway on one hand showed that increased job insecurity due to increased unemployment reduced long term sickness absence, measured as longer than 15 days [START_REF] Askildsen | Unemployment, labor force composition and sickness absence: a panel data study[END_REF]. On the other hand did a Finish study of the effect of alcohol consumption on sickness absence show a positive effect of regional unemployment on sickness absence, i.e. increased sickness absence in regions with high unemployment [START_REF] Johansson | Alcohol consumption and sickness absence: Evidence from micro data[END_REF]. [START_REF] Johansson | Assessing the effect of public policy on worker absenteeism[END_REF], studying policy changes in Sweden 1990-91 that coincided with rising unemployment levels found that it was the increased cost of being on sick leave following policy changes that pulled the absence rates down rather than the increasing unemployment rates. The conclusion for the current study based on prior research is that unemployment rates mainly affects short-term absence and potentially mostly men's sickness absence. Given that the current study investigates long- From a legislative perspective, the Swedish labour legislation (LAS 1982:80) strongly protects the employee from unreasonable discharge. Disease, sickness absence or parental leave are not reasonable grounds for dismissal. Even in the extreme cases where the disease makes it impossible for the employee to perform his/her work tasks in the long run, it falls on the employer to, if possible, find other assignments for the employee. The union to which the employee belongs has the same rights to be informed and to act instead of the employee to contest dismissals. All this can also be taken as an additional argument that the employee should not fear discharge due to sickness absence, no matter in what business cycle phase the country currently finds itself.

Two instruments connected to unemployment are tested in the current study, the yearly national unemployment rate and the yearly municipality unemployment rate. The former should capture the business-cycle effect beyond the pure time effect, thus affecting the probability of employment. The latter is expected to also capture differences in employment possibilities beyond the business-cycle effect, such as differences within the country at a certain time point. We will also try to capture this with a third instrument -homogeneous The forth instrument that will be employed is whether the individual has any small children.

Having a small child is considered to affect the probability of paid employment, especially among women as they take larger responsibility for children compared to men. However, it is not expected to affect the probability of sickness absence as absence due to care of a sick child is registered specifically as "temporary parental benefit". The temporary parental benefit is generally higher than sick pay/benefit why possible moral hazard issues could be expected to reduce sickness absence and increase absence due to a sick child. However, this should mostly affect short-term absence. All four instruments will be tested individually and in different combinations and their appropriateness will be discussed after the results have been presented.

III. Data

In terms of compensation, absence in Sweden is divided into two different periods. During the first period, the employee receives sick pay from the employer. In the second period, the employee receives sickness benefits from the Social Insurance Agency. Given this division of responsibility, no national register data exists for sick pay, while data on sickness benefits is of good quality. In this study, therefore, we define long-term absence as absenteeism long enough to be covered by sickness benefits.

Participants

We apply the model to data from the Swedish Survey of Living Conditions (the ULF survey) missing values for the lag of income).

Measures

An individual is considered employed if she works full-or part-time, runs a company or a farm, or works at least one hour per day in a family business/farm. As mentioned above, longterm absenteeism is defined as receiving sickness benefit from the Social Insurance Agency.

However, the length of the employer responsibility period has differed over the years. In 1997 (Försäkringskassan, 2005); as a result, the register data differs over the years. We have therefore defined long-term absence as absences longer than 28 days, which is the longest employer responsibility period covered by the study. In order for an individual to be categorized as having a long-term absence during a specific year, the individual must be employed and receive sickness benefit for at least one sickness spell longer than 28 days during that year.

We constructed alcohol variables that focus on changes in consumption from the survey data.

A question asking whether the respondent had consumed any kind of alcoholic beverage within the previous 12 months was used. In addition, questions on the level of weekly consumption were used to differentiate between low and heavy drinking, using the cut-off points suggested in [START_REF] Rehm | Comparative Quantification of Health Risks: Global and Regional Burden of Disease Attributable to Selected Major Risk Factors[END_REF] Although the exact level is expected to be measured with a bias, the change from, for example, consumption to abstention is considered to be more reliable.

<< Table 1 >>

The income variable is the lag of disposable income. It is converted to US dollars using the average monthly exchange rate for 2005 (SEK 7.47 for US $1). The prices were adjusted using the Swedish consumer price index (CPI) before conversion. Two variables were created to capture if the individual has smoked or been obese in the current wave or the lag.

The instrument variable homogeneous regions divides Sweden into 7 regions based on population. The three largest cities with surroundings are there own regions, one region is municipalities with more than 90,000 inhabitants within 30 kilometres from the municipalities centre. The fifth region is municipalities with 27-90,000 inhabitants within 30 kilometres from the municipality centre and 300,000 inhabitants within 100 kilometres. The sixth region is the same as the fifth but with less than 300,000 inhabitants. The last region used is for municipalities with less than 27,000 inhabitants within 30 kilometres (Statistics Sweden, 2003).

Most of the observations in the sample are long-term light drinkers while about 5-7% are found in each of the other alcohol consumption groups. A total of 84% of the sample is in good health, and about 13% of those employed have had a spell of long-term absenteeism (see Being employed is most common among current light drinkers (both long-term and formerly heavy drinkers), as seen in Table 3. The lowest employment rate is found among current abstainers, and former drinkers have somewhat lower rates than long-term abstainers. Based on these averages, we would expect negative associations on employment probability from being an abstainer compared to light drinkers, as has been seen in some earlier research (e.g., [START_REF] Johansson | Abstaining from alcohol and labour market underperformance: Have we forgotten the 'dry' alcoholics?[END_REF]. In examining the rate of long-term absenteeism for different alcohol consumption groups, we see that the lowest rates are found among long-term abstainers and long-term light drinkers. Former drinkers and former abstainers show the highest proportion of absenteeism. We would therefore expect that the latter two consumption groups show a positive association with absenteeism, compared to long-term light drinking, while no association is expected for long-term abstention.

<< Table 3 >>

IV. Estimation Results

This section reports the results of the estimations of probability of employment and long-term absenteeism. We demonstrate the results of the conventional probit estimations first, followed by the sample selection model. Estimates are considered significant at the 5% level.

Estimating the model without taking selection into account

The female probit model for having at least one spell of long-term absence shows few significant estimates (see Table 4). Only former drinkers and former abstainers are significant of the alcohol consumption groups, increasing their probability of long-term absenteeism.

Neither long-term abstention nor heavy drinking affects absenteeism, compared to long-term light drinking. The lag of health demonstrates that being in poor health is not significant, while being in between good and poor health increases the probability of long-term absenteeism. Higher education indicates some protective effect and having ever been obese

shows detrimental effects.

Estimating the selection into employment

Estimating the probability of being employed using a probit model results in a number of significant variables. All consumption groups are related to a decrease in employment probability for women-with the exception of the insignificant group of current light but formerly heavy drinkers-compared to long-term light drinkers (see Table 4). Wald tests show no differences between the different significant alcohol consumption groups. Other variables are as expected: age has an inversed U-shape, the lag of not being in good health reduces employment probability, and more education increases employment probability. Both the lag of unemployment and the national unemployment rate have negative effects with current employment probability, although the effect of the former is much stronger. The variable for ever having been obese has a negative relationship with employment probability.

<< Table 4 >>

Estimating the Heckman selection model

Empirical testing has indicated that there are several combinations of instruments that appear to work well. Here we will present the result using national unemployment rate and the variables also show more significance: age has a U-shaped relationship while women with a lag of poor health or in between good and poor health increases absenteeism probability compared to good health. More education reduces absence compared to no or only primarylevel education, although the negative effect of theoretical secondary school 2 is somewhat stronger than higher education. Having experienced unemployment in the former wave increases absence, which also ever having smoked or been obese does.

The average marginal effects of the selection model for women are shown in Table 5; this is the average of the marginal effects calculated for each individual in the sample. Of all the alcohol consumption groups, being a former drinker increases the probability of long-term absence the most (18%) compared to long-term light drinkers, followed by former abstainers (15%). Long-term abstainers and long-term heavy drinkers have about the same probability of absenteeism (10%) given employment. The variables for ever having smoked and been obese

increases the probability of long-term absenteeism of around 4 and 9% respectively.

<< Table 5 >>

There are few observations in many of the alcohol consumption groups for men who have at least one spell of long-term absence, 3 resulting in estimations that are sensitive to the data and estimation methods. The alcohol consumption groups show no relationship to long-term 2 Theoretical secondary school is in preparation for university studies as opposed to practical secondary school that is more focused on professional education. 3 The reason for this is unknown. One hypothesis is that men's life situation affects their alcohol consumption to a smaller extent then women's, and vice versa. Compared to long-term light drinkers, former drinkers, former abstainers and current light but formerly heavy drinkers are less likely to be employed. Age, the lag of health, smoking and the two variables for unemployment are also significant in the employment equation, with expected signs.

V. Simulation of productivity gains in terms of reduced sickness absenteeism

Given the estimations for women in the former section, it is interesting to predict and simulate the effect of assumed consumption changes on long-term absenteeism. The average probability of having at least one spell of long-term absence given employment is 0.135. The average predicted probability of one spell of long-term sickness for the non-employed subsample, had they been working, is 0.256. Table 6a and 6b outline the predictions following assumed population interventions (consumption changes). All average changes in expected long-term sick days between the original sample and after the assumed intervention are rather small-generally less than one day. However, considering the large population groups, the net societal effect is considerable, ranging between an increase in long-term sickness of 3'957 productive working years to a decrease of 7'000 years annually. The last row in Table 6 shows the potential productivity change in monetary terms, using the Human Capital

Approach. This gives a range from a productivity loss of 798 million SEK to a gain of 1'412 million annually, for the employed population.

<<

VI. Discussion

The focus of this article has been to analyse the effect of alcohol consumption on sickness absence. The results of the employment probability estimation indicate quite strong relationship between alcohol and employment. Compared to long-term light consumption, all other groups (except current light but formerly heavy consumption) have a negative effect on employment. There is no significant difference between long-term abstainers and former drinkers. Therefore, individuals who have regular, light alcohol consumption seem to have an advantage on the labour market when it comes to the probability of being employed. It is quite surprising that the negative effects on employment from the other alcohol consumption groups are about the same magnitude with variation in point estimates between 11% and 16%

(average marginal effect). All other variables have expected signs, although it should be noted that the variable for ever having smoked is not significant.

The probit model for long-term absenteeism reveal some remarkable results as, for example, we failed to separate this group from long-term light drinkers in this study (i.e., conducting the "former abstainer error"), the protective effect of long-term light drinkers would have been smaller. Thus, the increased risk of other alcohol consumption groups would also have been smaller, underestimating the negative outcome of non-regular non-light consumption.

It is also interesting to note that the increased risk of long-term absenteeism is larger for former drinkers (18%) than for long-term abstainers (11%). Failure to separate these two groups is known as the "former drinker error" and would result in an estimate of a 14% (not shown) probability reduction. That is, underestimating the risk from being a former drinker and overestimating the risk of being a long-term abstainer, in comparison to being a long-term light drinker.

As such, the result from the selection model indicates that long-term light alcohol consumption reduces the probability of long-term absenteeism. Given employment, being a long-term abstainer or heavy drinker increases the risk of absenteeism by around 10%.

Having changed consumption behaviour to or from abstention shows the highest increases in risk of long-term absenteeism.

Empirical testing, as mentioned above, showed different working combinations of instruments. Which of these combinations is used only affect the results marginally. The presented results are the estimations with yearly national unemployment rate and having a small child as instruments. The unemployment rate is a predictor of selection but insignificant in the absenteeism equation while having a small child does approach significance. The latter 22 is however included due to its theoretical validity although unemployment rate works on its own. Unemployment on a municipality level could be used instead of on a national level (significant at the 10% level), although it requires controlling for both having a small child and population homogeneous regions.

The most important instrument in these regressions is thus unemployment, either on a national or municipal level. It has been shown in prior research that business-cycle and unemployment rates are connected to absence rates, i.e. when unemployment increases absence rates decreases [START_REF] Berggren | Swedish sickness absenteeism in a European perspective[END_REF][START_REF] Askildsen | Unemployment, labor force composition and sickness absence: a panel data study[END_REF]. This is normally explained by insecurity regarding possible dismissal. The empirical testing done within the current study showed that unemployment rate is not connected to probability of long term absence for women in Sweden, when controlling for selection effects into employment. One reason for this might be the strong legal protection towards unreasonable dismissal (which dismissal due to sick leave is considered to be) and the strong positions of the unions. However, this result was not unexpected based on prior studies showing that the effect of unemployment on sickness absence mainly targets short-term absence [START_REF] Khan | Perceived job security and sickness absence: a study on moral hazard[END_REF]. In addition, women's long-term absence has been shown in a Swedish study not to be affected by unemployment rates [START_REF] Knutsson | Occupation and unemployment rates as predictors of long term sickness absence in two Swedish counties[END_REF]. With regard to the results of prior studies, it might not be odd that the results for men turned out as they did in the current study. It is likely that the employed instruments are most appropriate for Swedish women and that other instruments are needed in order to study the effect of alcohol consumption on long-term absence for Swedish men.

As we have discussed above, applying a sample selection model instead of a probit changes the results with stronger and more significant associations in the sample selection model. We 23 interpret this as that the probit model underestimates the probabilities of absenteeism due to the fact that non-employed who are sick are not absent. For example, the lag of being in poor health is not significant in the probit model, but strongly significant in the sample selection model. That is, individuals with a lag of poor health are more likely to be non-employed and thus do not experience absenteeism. When we control for this fact, the lag of poor health becomes important for explaining long-term absenteeism. This is further supported by the significant ρ which indicates that ignoring the selection effect would result in biased and inconsistent estimation of long-term absenteeism [START_REF] Baum | An introduction to modern econometrics using Stata[END_REF]. The fact that the ρ is negative indicates that employment and long-term absenteeism is negatively related [START_REF] Henneberger | Estimating wage functions and wage discrimination using data from the 1995 Swiss labour force survey: a double-selectivity approach[END_REF].

It is interesting to assess the results of this study in relation to the alcohol-wage literature that commonly finds a positive effect of alcohol on wages/earnings. For example, [START_REF] Peters | Is there a wage bonus from drinking? Unobserved heterogeneity examined[END_REF] and van Ours (2004) find a general wage premium from drinking while [START_REF] Lee | Wage effects of drinking in Australia[END_REF] and [START_REF] Barrett | The effect of alcohol consumption on earnings[END_REF] find a wage premium from moderate drinking, although none of these studies control for any of the former consumption errors discussed above. We would assume that increased absenteeism affects wages negatively, both directly as sickness benefits are lower than wages, and indirectly through reduced human capital accumulation. Increased long-term absenteeism is probably not enough to explain the reduction in wages/earnings as short-term absenteeism should also influence this. It is also possible (a suggested hypothesis in prior research) that current abstainers miss out on work-related social activities, and are thus "punished" for this by being discriminated against or by being overlooked for promotion opportunities. However, given the results of the current study, increasing the probability of long-term absenteeism in the 10-18% interval for non-long-term light drinkers, we expect intervention that turns heavy drinkers into light drinkers-thereby making them current light but formerly heavy drinkers-no effect is evident for the estimation conditioned on being employed. For those not employed, had they been working, the intervention would have reduced the average number of expected long-term absence days by one-half day. However, it could be argued that the original groups of former drinkers and current light but formerly heavy drinkers are different from heavy drinkers. The total number of sick days would then be overestimated by applying the β-coefficient from former drinkers (clfhd) on long-term heavy drinkers. A more pragmatic approach might be to assume an intervention that prevented the development of heavy drinkers and thus making them long-term light drinkers instead, which is done in column 4 of Table 6. The change per individual is rather small for those that are employed, although for the non-employed, had they been working, the reduction in the average absence is 0.7 days per year. Finally, an intervention that puts the whole population into the most beneficial consumption group (long-term light drinkers) would reduce expected sick days over a year by 0.7 days and 3.0 days, respectively (column 5 of Table 6). The remaining expected absence days of 12.6 (for those employed) and 22.3 (for the nonemployed had they been working) can be considered to be due to factors other than alcohol, such as other health-related behaviours, health status, income or bad luck. In other words, the effect of alcohol on long-term absenteeism is rather small compared to the combined effect of all other factors. However, if the entire female population were long-term light consumers, expected days lost per year due to long-term sickness would be reduced by 1.4 and 0.5 million days for employed and non-employed respectively. This is a substantial societal effect that translates into a productivity loss of SEK 1.4 and 0.5 billion in 2005 (US$189 and $67 million), using the Human Capital Approach. It should also be noted that the alcohol effect is much larger for the non-employed than the employed, giving reason to assume that alcoholrelated problems are more common in this group and that there is a selection effect from alcohol into (non-)employment. All estimates following the simulation are changes during a one year period in order to be comparable with other estimates (e.g. [START_REF] Jarl | The societal cost of alcohol consumption: an estimation of the economic and human cost including health effects in Sweden[END_REF].

Obviously are the societal productivity gain much higher measured over a person's life-cycle, and the gains are expected to differ at different periods of life.4

The discussion above assumes a causal effect between alcohol and being non-employed, and it therefore seems intuitive that societal production could be increased by changes in the prevalence of consumption. However, since the natural rate of unemployment is considered to be larger than zero, the full hypothetical productivity gain among the non-employed, had they been working, could not be realized in actual productivity. [START_REF] Koopmanschap | The friction cost method for measuring indirect costs of disease[END_REF]. This is also the case for replacing employees due to long-term absenteeism.

There are some limitations to this study. Although we have a rather large data set, the coding of the alcohol variable to account for prior consumption reduces the sample size considerably.

Defining long-term absence as longer than 28 days reduces the variation for each consumption group, which might be reflected in some insignificant estimates. Future studies should investigate the effects of alcohol on short-term absenteeism, something we did not do in the current study, although that would require other instruments. Due to data limitations, we were unable to account for patterns of consumption. This is unfortunate, as it has been

shown that the pattern of consumption-especially so-called binge drinking-affects outcomes [START_REF] Rehm | Comparative Quantification of Health Risks: Global and Regional Burden of Disease Attributable to Selected Major Risk Factors[END_REF]. Future studies should endeavour to include consumption patterns.

VII. Conclusions

This study again demonstrates the importance of avoiding the "former drinker error" and the "former abstainer error" as defined in [START_REF] Jarl | Wage penalty of abstinence and wage premium of drinking: A misclassification bias due to pooling of drinking groups?[END_REF] The commonly seen result of the protective effect of regular light consumption and the detrimental effect of abstention and heavy drinking is repeated in the current study, despite efforts to account for drinking history and selection effects. These results are along the lines of earlier studies such as [START_REF] Vahtera | Alcohol intake and sickness absence: a curvilinear relation[END_REF] and, regarding current abstainers, as reported in [START_REF] Hensing | Chapter 7: Sickness absence and psychiatric disorders[END_REF]

  First, there are individuals that, for different reasons, are not employed. Earlier research has

  address this by constructing alcohol variables that control for drinking history and any possible change (see Section 3 below).

•

  To reduce alcohol consumption among heavy drinkers and thereby turn them into current light but formerly heavy drinkers (short-term simulation);• To prevent heavy drinkers from becoming heavy drinkers, and thereby turn them into light drinkers (long-term simulation);• To prevent any individual from ending up in any of the drinking group save the group that is most beneficial based on the results of the model above (long-term simulation).These simulations indicate the attributable fraction of alcohol on long-term absence, and indicate the maximum productivity gains in value terms from the assumed interventions under different scenarios.

  shown that a change in the Swedish labour legislation in 2001 that reduced the job

  women (although the results for men also are presented), unemployment rate appears to be an appropriate instrument.

  28 days, in 2004 it was 21 days, and in 1996 and 2005 it was 14 days

  presences of a small child although other working combinations affect the estimates only marginally. The results changes dramatically when applying the sample selection model of long-term absenteeism where the selection equation is the employment probability model effect for former abstainers and former drinkers becomes stronger both economically and statistically. Long-term abstainers and long-term heavy drinkers both become significant at the 1% level and show positive relationship with absenteeism. The other

  in probit nor sample selection models which could be due to the instruments being more appropriate for women. The lag of health and whether the individual ever smoked or was obese are significant in the selection model, with expected signs.

  only former drinkers and former abstainers have a positive relationship with absenteeism and age is insignificant. These results are in line with what would be expected following results observed by Jarl and Gerdtham (2010) and Filmore et al. (1998)-that both former drinkers and former abstainers appear to be at a greater disadvantage than long-term abstainers and long-term light drinkers. The effect of health and education are along the lines of the Feng et al. (2001) study.The results of the effect of alcohol on long-term absenteeism change drastically when we control for selection into employment. When doing so, all consumption groups except current light but formerly heavy drinkers show a significant positive effect on long-term absenteeism compared to long-term light drinkers. There is, however, no statistical difference between the Wald tests. Being a former abstainer, which is commonly defined in studies as a light drinker, increases the risk of long-term absenteeism by close to 15%. Had

  a significant roll in the reduction in pay among abstainers and heavy drinkers, compared to light/moderate drinkers.The predicted probabilities of at least one long-term sickness spell among the individuals in the sample are higher among the non-employed compared to the full sample. That is, individuals who are not employed are more likely to experience long-term absenteeism had they been working, compared to employed individuals. The simulation model of the effect of changes in the prevalence of alcohol on the number of days of long-term absence show rather substantial effects from a population perspective. We start out by turning all heavy drinkers into former drinkers, as this is the logical step based on the modelling of alcohol consumption, which increases the number of expected absence days per year. If we instead assume an

  . Divergence from the most prevalent group of long-term light consumers increases the risk of long-term absenteeism among women in Sweden when we control for the selection into employment. Controlling for sample selection, and thus the non-independence of the error terms in the two equations, are important. It is shown that the probability of long-term absenteeism is higher among nonemployed, had they been working, compared to employed. A normal probit model cannot be considered as consistently estimated and generally understates the effects of alcohol on longterm absenteeism. The models for predicting expected long-term sick days per individual the effect of alcohol is rather marginal on an average individual basis, it has a large effect on society.

  and Labour Market Studies (LISA). Since 1975, Statistics Sweden has conducted annual systematic surveys of living conditions in the form of one-hour personal interviews with randomly selected 16-84 year olds. In this study we used data from 1988/89, 1996/97 and 2004/05, three two-year waves focusing on health-related issues, where the first wave is only used to control for drinking history and lags. The LISA material includes individual-specific information from the Social Insurance Agency, such as sickness benefits.The matching of survey and register data allows us to study the effect of health-related behaviours on actual labour market outcomes.

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from Statistics Sweden, matched to register data from the Longitudinal Integration Database The working sample constitutes of 6,109 individuals based upon 15,471 observations (3,253 individuals are followed over three waves and 2,853 individuals are followed over two waves). Of these, 2,449 are women with 6,144 observations (out of which 1,246 are followed over three waves and 1,203 over two waves). Due to the use of the lag when constructing the alcohol variable, we get 3,695 (1,246*2+1,203) observations available for the estimations. We lose 162 observations due to missing alcohol information, leaving a sample of 3,533 observations (2,294 women, out of which 1,239 are followed over three years). We correct for missing values in other variables by using Stata's impute command

[START_REF] Statacorp | Data management Stata Press[END_REF]

(two missing values for the lag of health, 11 for education, 54 for ever having been obese, and 47

  in 1988/89 but not in 1996/97). All other consumption categories were defined in the same manner (see Table1, where the proportions of observations for each consumption group also are shown). Measurement errors in the reporting of alcohol consumption are normally expected for several reasons, such as recall bias and fear of stigmatisation. The alcohol variable created in the current study is considered to reduce the negative effect of measurement errors, as it measures considerable changes (or non-changes) in consumption.

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. Hazardous and harmful consumption were combined into heavy consumption in order to avoid too few observations in each category. The panel information allowed us to construct six consumption groups based on current and past consumption. Long-term abstainers were defined as abstainers in two following waves: in 1988/89 and 1996/97, or 1996/97 and 2004/05. Former drinkers were defined as alcohol consumers during the first of two following waves and abstainers in the second wave (e.g. consumed

Table 2

 2

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	<< Table 2 >>

Table 6a

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  The important question is to what extent individuals that would have been a part of the natural unemployment rate replace individuals that leave employment due to alcohol. In any case, friction costs are expected to occur due to the recruitment and training costs involved in replacing an employee

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Table 1 .

 1 . Applying a larger sample in future research should be prioritized in order to statistically differentiate the detrimental effects between consumption groups as well as to incorporate patterns of consumption in the estimations. Alcohol consumption categories and the proportion of individuals in the employment (absenteeism) estimation

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Table 3 .

 3 Number of employed women and number with long-term absenteeism

		Employment	Long-term absence
		No	Yes	No	Yes
	Long-term abstainer	99	128	113	15
	Percent	43.61	56.39	88.28	11.72
	Former drinker	81	97	76	21
	Percent	45.51	54.49	78.35	21.65
	Former abstainer	81	135	110	25
	Percent	37.5	62.5	81.48	18.52
	Long-term light drinker	533	1,961	1,726	235
	Percent	21.37	78.63	88.02	11.98
	Current light but formerly heavy drinker	36	130	111	19
	Percent	21.69	78.31	85.38	14.62
	Long-term heavy drinker	82	170	149	21
	Percent	32.54	67.46	87.65	12.35
	Total	912	2,621	2,285	336
	Percent	25.81	74.19	87.18	12.82

Table 4 .

 4 Probability of long-term absence among women

		Probit	Heckprob
		Long-term sickness
	Long-term abstainer	-0.121	0.279 ***
	Former drinker	0.330 **	0.477 ***
	Former abstainer	0.302 **	0.384 ***
	Current light but formerly heavy drinker	0.125	0.080
	Long-term heavy drinker	0.025	0.260 ***
	Age0	-0.002	-0.178 ***
	Agesquare0	0.000	0.002 ***
	Income lag	4.16E-06	-2.50E-06
	In-between health lag	0.470 ***	0.464 ***
	Poor health lag	0.479 *	0.996 ***
	Education 2	-0.098	-0.275 ***
	Education 3	-0.308 **	-0.505 ***
	Education 4	-0.230 **	-0.416 ***
	Eversmoke	0.089	0.106 **
	Everobese	0.256 **	0.249 ***
	Unemployment lag	0.077	0.290 ***
	Constant	-1.276 ***	0.194 *
		Employment
	Long-term abstainer	-0.414 ***	-0.410 ***
	Former drinker	-0.461 ***	-0.466 ***
	Former abstainer	-0.334 ***	-0.335 ***
	Current light but formerly heavy drinker	-0.086	-0.087
	Long-term heavy drinker	-0.324 ***	-0.323 ***
	Age0	0.240 ***	0.244 ***
	Agesquare0	-0.003 ***	-0.003 ***
	Income lag	6.31E-06 *	6.60E-06 *
	In-between health lag	-0.332 ***	-0.341 ***
	Poor health lag	-1.046 ***	-1.072 ***
	Education 2	0.294 ***	0.302 ***
	Education 3	0.463 ***	0.484 ***
	Education 4	0.385 ***	0.374 ***
	Eversmoke	-0.090	-0.096 *
	Everobese	-0.191 **	-0.191 **
	Unemployment lag	-0.402 ***	-0.420 ***
	Small child	-0.001	-0.016
	Unemployment rate	-0.055 ***	-0.050 ***
	Constant	0.237	0.194
	Rho		-0.990 ***
	Significance is shown on 1(***), 5(**), and 10(*) per cent levels.

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Table 5 .

 5 Average marginal effects of the probability of long-term absence among women

		Long-term
		sickness
	Long-term abstainer	0.105 **
	Former drinker	0.181 ***
	Former abstainer	0.145 ***
	Current light but formerly heavy drinker	0.029
	Long-term heavy drinker	0.098 ***
	Age0	-0.059 ***
	Agesquare0	0.001 ***
	Income lag	-0.000
	In-between health lag	0.169 ***
	Poor health lag	0.360 ***
	Education 2	-0.095 ***
	Education 3	-0.178 ***
	Education 4	-0.140 ***
	Eversmoke	0.039 **
	Everobese	0.091 ***
	Unemployment lag	0.109 ***
		Employment
	Long-term abstainer	-0.139 ***
	Former drinker	-0.156 ***
	Former abstainer	-0.110 ***
	Current light but formerly heavy drinker	-0.027
	Long-term heavy drinker	-0.107 ***
	Age0	0.066 ***
	Agesquare0	-0.001 ***
	Income lag	0.000 *
	In-between health lag	-0.103 ***
	Poor health lag	-0.319 ***
	Education 2	0.083 ***
	Education 3	0.135 ***
	Education 4	0.106 ***
	Eversmoke	-0.028
	Everobese	-0.059 **
	Unemployment lag	-0.135 ***
	Small child	0.000
	Unemployment rate	-0.015 ***

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Table 6a .

 6a Simulation of an intervention abolishing heavy drinking, among the employed Labour Force Survey, Statistics Sweden (www.scb.se), figures for 2005. ** We use actual yearly working time in 2005 of 1,607 hours for Sweden (OECD, 2008). *** Based on a monthly average pay for women of SEK 22'100 and 22 working days per month.

		Original	FD	CLFHD	LLD	All light
		sample	(lhd=>fd)	(lhd=>clfhd)	(lhd=>lld)	drinkers
	Probability of
	long-term	0.135	0.139	0.135	0.134	0.128
	sickness spell
	Average sick days	98.87	98.87	98.87	98.87	98.87
	Expected sick
	days per	13.35	13.74	13.35	13.25	12.66
	individual
	Diff (original		0.39	0	-0.1	-0.69
	vs. change)		(2.92%)	(0%)	(-0.75%)	(-5.17%)
	Number employed *		2,038,000	2,038,000	2,038,000	2,038,000
	Potential days saved **		-794,820 (-3,957 yrs)	0	203,800 (1,015 yrs)	1,406,220 (7,000 yrs)
	Value of gained
	production ***		-798.4	0	204.7	1,412.6
	(million SEK)

*

Table 6b .

 6b Simulation of an intervention abolishing heavy drinking, among the unemployed

		Original	FD	CLFHD	LLD	All light
		sample	(lhd=>fd)	(lhd=>clfhd)	(lhd=>lld)	drinkers
	Probability of
	long-term	0.256	0.259	0.251	0.249	0.226
	sickness spell
	Average sickdays	98.87	98.87	98.87	98.87	98.87
	Expected
	sickdays per	25.31	25.61	24.82	24.62	22.34
	individual
	Diff (original vs		0.3	-0.49	-0.69	-2.97
	change)		(1.19%)	(-1.94%)	(-2.73%)	(-11.73%)
	Number unemployed *		167,500	167,500	167,500	167,500
	Potential days		-50,250	82,075	115,575	497,475
	saved **		(-250 yrs)	(409 yrs)	(575 yrs)	(2,477 yrs)
	Value of gained
	production ***		-50.5	82.4	116.1	499.7
	(million SEK)

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

This could be estimated by taking into account age effects on the probability of absence and age-adjusted average number of days absent, plus income.

Acknowledgement

Financial support from the Swedish Council for Working Life and Social Research (dnr 2006-1660) is gratefully acknowledged.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Conflict of interest

The authors declare that they have no competing interests.


Julien Delahaye
email: julien.delahaye@grenoble.cnrs.fr

Thierry Grenet

Ageing in granular aluminium insulating thin films

Keywords: Electron glass, ageing, disordered insulators PACS 72.80.Ng, 61.20.Lc

We present a new set of electrical field effect measurements on granular aluminium insulating thin films. We have explored how the conductance relaxations induced by gate voltage changes depend on the age of the system, namely the time elapsed since its quench at low temperature. A clear age dependence of the relaxations is seen, qualitatively similar to ageing effects seen in other well studied glassy systems such as spin glasses or polymers. We explain how our results differ from the previous ones obtained with different protocols in indium oxide and granular aluminium thin films. Our experimental findings bring new information on the dynamics of the system and put new constraints on the theoretical models that may explain slow conductance relaxations in disordered insulators.

Introduction

Among the electronic properties of disordered insulators, the slow relaxation of their electrical conductance is quite outstanding. This relaxation found up to now in a limited number of systems has been studied in many details in indium oxide (InOx) [1,2] and granular aluminium (Al) [3] thin films. The main features are the following. When the samples are quenched to liquid helium temperature, their conductance subsequently decreases like a logarithm of time for weeks without any tendency to saturation. Moreover, it was shown in MOSFET devices that a change of the gate voltage induces a fast conductance increase followed by a new slow and logarithmic decrease. Fast gate voltage sweeps G(V g ) performed after a long stay under a fixed gate voltage V g1 display a dip centred on V g1 , the so called anomalous field effect [1]. The amplitude of the conductance decrease under a fixed gate voltage and the corresponding growth of the G(V g ) dip depend on the temperature and on the resistance per square of the samples, a few % being typical for measurable samples.

These slow relaxation phenomena have aroused a broad interest since they may be the first direct experimental signature of the Coulomb glass, a glassy state resulting from the coexistence of disorder and electron-electron interactions and predicted more then 20 years ago [4]. But in spite of important theoretical developments [5][6][7][8], their detailed understanding is still unachieved.

In this article, we present new experiments in which we study the age dependence of the gate voltage induced conductance relaxations. According to the usual definition in other glasses, we call the age of the samples the time elapsed since their quench at low temperature. In order to clarify what is new compared with previous measurements, we first review some older protocols which were also claimed to demonstrate ageing effects. We then expose our new ageing protocols and what results we indeed get from them. And finally, we discuss the possible physical meaning of our findings.

Experimental

The samples used in this study are granular aluminium thin films, 20 nm thick, made by e-gun evaporation of Al under a partial pressure of oxygen. The substrates are either highly doped silicon wafers or sapphire single crystals covered with an Al layer. A gate insulator 100nm thick (silicon dioxide or alumina) enables us to measure the conductance of the films as a function of a gate voltage. All the films are insulating, with an exponential-like divergence of the resistance at low temperature. The electronic transport in the film is believed to occur through electron tunneling between nanometric Al grains. Resistances per square range between 10GΩ and 1M Ω at liquid helium temperature. Fuller details of samples preparation, characterization and measurements techniques are given elsewhere [3]. All the measurements presented here were performed at 4.2K.

Previous protocols

Different protocols have been built on in order to explore the response of InOx and granular Al thin films to gate voltage changes. But they are generally performed a long time after the quench of the samples. By long, we mean that the samples are kept under a fixed gate voltage V g1 until the conductance relaxation of the system is negligible over the time scale of the experiments (quasi-equilibrium state). This first waiting time (t w1 ) at V g1 that we will call later "the age of the system", is typically of a few days or more.

The simplest protocol (protocol 1) consists in changing after a waiting time t w1 the gate voltage to a new value V g2 . The conductance increases rapidly to an off-equilibrium value and then starts to decrease as a logarithm of time. Fast G(V g ) sweeps around V g2 at constant time intervals reveal a corresponding log(t) growth of the conductance dip centred on V g2 (dip 2). This is illustrated in Fig. 1, where the log(t) increase of dip 2 amplitude ∆G 2 is observed over 3 orders of magnitude in time (deviations from a perfect log(t) are indeed visible at the longest times, as will be discussed below). A more complex protocol (protocol 2) called the 2 dips measurement was introduced by Zvi Ovadyahu et al in InOx films [9]. In this protocol, the gate voltage is changed after t w1 to a new value V g2 , kept there during a time t w2 and then switched back to V g1 (time t = 0 in Fig. 2). Just before V g is switched back to V g1 , a new dip has formed at V g2 while the old one at V g1 has been partly erased (see the upper curve of Fig. 2). By repeating fast G(V g ) scans, we can then follow as a function of time how the conductance dip at V g1 goes back to its quasi-equilibrium value (recovery of dip 1) or look how the dip at V g2 is erased (erasure of dip 2). This is illustrated in Fig. 2 and3. Both lead to the same result, namely the longer t w2 is, the longer it takes for the system to come back to its quasi-equilibrium state. More precisely, the relaxation curves to quasi-equilibrium (see Fig. 3) are well described by a unique function of t/t w2 (full scaling). It was this t w2 dependence of the relaxation which was called ageing and even simple ageing as long as the t/t w2 scaling is obeyed [3,9]. It is also noteworthy that the extrapolation of the logarithmic part of the curves visible at short times indicates that the quasi-equilibrium state is recovered after a characteristic time t w2 (extrapolated amplitude of dip 2 equal to 0).

It was shown in [3] that the full scaling obtained with the protocol 2 can be well understood simply by assuming that the conductance relaxations result from the additive contributions of independent and reversible degrees of freedom having a 1/τ distribution of relaxation times. Similar ideas were recently develop within the Coulomb glass picture frame [11,12]. The full scaling of Fig. 3 may thus be understood without assuming any change in the dynamics of the system, contrary to the usual definition of ageing in glasses [START_REF] Biroli | [END_REF].

New protocols

In a new set of measurement, we have tested how the conductance relaxation depends on the age t w1 of the system. More precisely, we have measured how the results of protocols 1 and 2 are modified when the time t w1 is of the order and smaller than t w2 and the time scale of the measurements. This procedure is very similar to pioneer ageing experiments done in polymers [START_REF] Struik | Physical Aging in Amorphous Polymers and Other Materials[END_REF].

By repeating the protocol 1 for different t w1 s, we now clearly see (Fig. 4) that the increase of a new conductance dip does not follow a pure log(t) dependence. The G(t) curves are s-shape, with a faster dip amplitude increase around t = t w1 . By repeating the protocol 2 for different t w1 s, we have found two interesting features. First, the larger t w1 is, the longer it takes to erase the conductance dip at V g2 for a fixed t w2 (Fig. 5). The extrapolation of the logarithmic part of the relaxation gives a time larger than t w2 as the typical erasure time, t w2 being the t w1 infinite limit. Thus the erasure "master function" is modified for "young" samples and the form shown in Fig. 3 is only the limiting case of very "old" samples (t w1 ≫ t w2 ). However, even for t w1 close to 0, the full scaling as a function of t/t w2 is conserved within our experimental accuracy (not shown here).

Discussion

The results above are in qualitative agreement with what is found in other glassy systems [START_REF] Struik | Physical Aging in Amorphous Polymers and Other Materials[END_REF][START_REF] Vincent | Ageing and the Glass Transition (Lecture Notes in Physics)[END_REF]. The s-shape visible in Fig. 4 was also found in spin glasses [START_REF] Vincent | Ageing and the Glass Transition (Lecture Notes in Physics)[END_REF] where it was interpreted as a maximum in the log distribution of relaxation times. A consequence of Fig. 4 is that the longer one waits after the quench, the longer it will take to dig a new conductance dip of a given amplitude, in qualitative agreement with a hardening of the system with its age. The extrapolation of the logarithm relaxation part to times larger than t w2 visible in Fig. 5 indicates a symmetry breaking between the digging of the dip at V g2 and its erasure under V g1 . Such symmetry breaking is also in agreement with a slower response as the system ages: it takes a longer time to erase the dip after t w1 + t w2 than it took to dig it between t w1 and t w1 + t w2 . The fact that the t/t w2 scaling is conserved is more puzzling and deserves further theoretical analysis.

Clearly and contrary to previous results, our ageing effects cannot anymore be described by the linear contribution of independent degrees of freedom relaxing back and forth with the same relaxation times. More involved models, e.g. with relaxation time distributions differing from pure 1/τ and depending on the system's age may be needed. Whereas it is possible to propose an interpretation in agreement with the Coulomb glass theoretical picture still needs to be clarified. Finally, we would like to point out that a similar symmetry breaking was also observed in InOx thin films [2,[START_REF] Ovadyahu | [END_REF]17]. Starting from the pseudoequilibrium state (t w1 ≫ t w2 ), the conductance relaxation at V g1 was followed after large V g or bias voltage changes maintained during t w2 . As long as these changes are not too large (small loss of memory) the symmetry is broken (the extrapolation of the logarithmic part of the relaxation gives characteristic times larger than t w2 ) but the full scaling is conserved. This is fully consistent with our results and simply indicates that such modified erasure functions are obtained for "young" systems and that we have different ways to rejuvenated the systems.

Conclusion

In conclusion, we have observed for the first time that the conductance relaxation in granular aluminium thin films depends on the age of the samples, i.e. the time elapsed since their quench at low temperature. These ageing effects are in qualitative agreement with what was found in other glassy systems, such as Copyright line will be provided by the publisher polymers or spin glasses. It would now be interesting to see if they are also present in InOx films and if they can be explained within the frame of the Coulomb glass. Our observations also open new issues, such as memory and rejuvenation experiments as a function of temperature.

Fig. 1

 1 Fig. 1 Amplitude of a new conductance dip a time t after the gate voltage was changed from Vg1 = 0V to Vg2 = -30V . The sample was kept 5 days at 4.2K under Vg1 before changing Vg (tw1 = 5days). R✷ = 30M Ω.

Fig. 2 G

 2 Fig.2G(Vg) curves during a two dips measurement (see text for details). The sample was maintained 20h under Vg1 = 0V and then 1h under Vg2 = 10V . The first G(Vg) scan was taken just before Vg was switched back to Vg1 (t = 0). G(Vg) scans 80s long are taken every 400s to follow the erasure of the new dip at 10V and the recovery of the old one at 0V . Small mesoscopic reproducible conductance fluctuations are superimposed on the conductance dips relaxations (see[10] for more details). R✷ = 15M Ω. The Vg2 dip is almost completely erased after 20h. The curves have been shifted for clarity.

Fig. 3

 3 Fig. 3 Erasure of the conductance dip 2 dug during tw2 at Vg2 after Vg is switched back to Vg1 (2 dips experiment). (a) Amplitude of the dip as a function of time t. (b) Amplitude of the dip as a function of the reduced time t/tw2. The extrapolation of the short times logarithmic part is shown with intersect of the doted line (see text for details). R✷ = 480 M Ω.

Fig. 4

 4 Fig. 4 Growth of the conductance dip amplitude after a gate voltage change for different tw1s. R✷ = 5GΩ. The results should be compared with that of Fig. 1.

Fig. 5 :

 5 Fig.5: Erasure of the conductance dip 2 in a 2 dips experiment for different ages tw1s (see text for details). The time tw2 is fixed to 1000s. The erasure characteristic times are given by the intersect of the doted lines. R✷ = 480M Ω.

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Acknowledgements We acknowledge financial support from the "Jeunes Chercheurs" program of the French National Research Agency ANR (contract N o JC05-44044).