THE CHALLENGES HRM MUST FACE UNDER FLEXIBLE WORK ARRANGEMENTS (CASE OF THE SLOVAK REPUBLIC)

The research seeks to examine the background to the growing importance of this theme in Europe, the views and strategies of the parties involved (employers, employees, and governments), the impact of the new legislation and the application of labour flexibility in new market economies. The rese arch finds that it is unfortunate that only incomplete and disparate statistics and analyses are current Iyavailable. An international comparison in this area can thus be only of a quality nature. The regula tion of working time in Western Europe followed a number of rules which steadily became general throughout the continent, The application of the new forms (functional flexibility, financial/wage flexibility, labour mobility flexible patterns and organisation of work) is gradually introduced, map ping the employment developments of the EU Member States. However, the application of the poli cies in practice is mostly more difficult than expected and the implementation problems differ from one form to another. The problems identified in the Slovak Republic can be summarized as follows: gaps in legislation, insufficient managerial competencies to master new flexible forms, rigidness of working habits of both managers and employees, cultural barriers.

Introduction
Labour fleXIbility is prominent in employment policies across the European Union and beyond. The research seeks to examine the background to the growing importance of this theme in Europe, the views and strategies of the parties involved (employers, employees, and governments), the impact of the new legislation and the application of labour flexibility in new market economies.
Given the scope of the changes which have occurred in the area of labour market over recent years, the research finds that it is unfortunate that only incomplete and disparate statistics and analyses are currently available. An international comparison in this area can thus be only of a quality nature.
The EU Guidelines for Member States' employment policies (1998 and further documents) underline the importance of work flexibility in employment creation/preservation.
Over the quarter of a century of the rapid growth with almost full employment which followed World War n, the regulation of working time in Western Europe followed a number of rules that steadily became general throughout the continent. These basic rules were as follows: • for full-time workers, the law set maximum and normal durations for hours worked and companies adopted stable collective work timetables. The margins for flexibility were provided by the use of overtime working and temporary unemployment (lay-offs and short-time working); • the only role for collective agreements was to improve on the statutory provisions, mainly by reducing the length of the working week and increasing the length of paid holidays; • the reduction of working time was seen as part of social progress. It was one way, along with pay increases, of sharing productivity gains; and • atypical working hours were used only to solve specific problems. First, night and weekend work fulfilled certain technical needs related to production, or the needs to keep some public services open at all times. Second, part-time work, which accounted for an increasingly large proportion of the workforce, especially in northern Europe, fit a widespread social model of women's economic activity, and it was the same logic which brought about, at the end of this period, some experiments with flexible working hours ("flexitime") for office workers.
More or less the above mentioned principles were applied in the Slovak Republic as well. The application of new forms (functional fle-8 Xlbility, financiaJ/wage flexibility, labour mobility flexible patterns and organisation of work) is gradually introduced, mapping the employment developments of the EU Member States. However, the application of the policies in practice is mostly more difficult than expected and the implementation problems differ from one form to another. The identified problems can be summarized as follows: • gaps in legislation • insufficient managerial competencies to master the new fleXlble forms • rigidness of working habits of both managers and employees • cultural barriers.
The most common fleXlbility form appears to be flexi-time. The other forms (part-time and temporary contracts) are mostly used for peripheral groups of various categories of employees, primarily in services and media. They include well-paid positions as well as less glamorous ones. In addition, part-time and temporary contracts are used in the probation period as well. The managers argue that these forms of flexibility facilitate the termination of the employment relationship and prevent from the potential conflicts as well as they cut administrative procedures and costs necessary for an appropriate termination of the employment contract. Telework as a flexible form has not been introduced massively by any of the contacted organisations.
The research utilises structured questionnaires and semi-structured interviews covering the application of various types of flexibilities as well as the willingness of the employers and employees to participate in these schemes, as well as barriers.
Within the research there were 1423 questionnaires sent out to 67 organisations of different sizes and different industries; besides,

Introduction
The theorists have tried not only to identify the most appropriate forms of work arrangements, but also to class the layers of employees concerned.
Thus, any survey of non-standard working from the employer's perspective must start with a description of the now classical work of John Atkinson (1984) and, in particular, his model of the "fleXible firm". Its main feature is the suggestion that a fleXible firm (by which Atkinson means one that is competitive in the modern business environment) is composed of three basic groups of employees: core workers, peripheral workers and a third group who are employed only on some kind of subcontracted basis. The basic model is illustrated in Figure l.
Central to the model are two distinct types of flexibility: functional and numerical. The former is applied specifically to the core workers -that is, people who are employed on standard, permanent, full-time contracts and who undertake the tasks that are central to the success of the organisation. They are functionally flexible, in that they do not work to rigid job descriptions but carry out a broad range of duties. Moreover, they do not restrict their activities to work of a particular level. Instead, they carry out complex tasks associated with managerial or professional jobs as well as more mundane activities, depending on the dayto-day needs of the organisation.
The peripheral group can also be functionally flexible, but in the model it is more strongly associated with the term "numerical flexibility and temporal flexibility". J. Atkinson divided peripheral workers into primary and secondary categories, the first forming part of the firm's internal labour market. These people work mainly full-time and have a certain degree of permanence, but tend to have lower skills than colleagues who enjoy the status of core employees. As individuals they are less central to the organisation's success, because their skills are more widely available in the labour market. They therefore face a lower job security than the core workers and will be among the first to have their hours cut or to be laid off when business downturns are experienced. The secondary peripheral group members are in an even more precarious position, because they are brought in mainly to help cover peaks in business or short-term needs resulting from the absence of other staff. They are employed either on a part-time or temporary basis.
The final group, located beyond the periphery, consists of people who are not employees of the firm but who are hired on a subcontractual basis to undertake a particular task or set of tasks. In the vast majority of cases this will be temporary, and hence insecure, although it is possible for a series of fixed-term contracts to follow one after another. Some may be professionally qualified people working on a self-employed basis; others may work for an agency or some other service provider. In both cases they are perceived by the other groups as being external to the organisation and thus readily replaceable by a competitor should their work prove to be unsatisfactory or more cheaply provided elsewhere.
Over recent years others have proposed similar models (e.g., Loveridge and Mok 1979, Handy 1989). In The Empty Raincoat Charles Handy (1994) suggests that employers will increasingly wish to buy a specific service from a worker rather than that person's time. The result will be a situation in which, for most people, there will be little opportunity to enjoy the security of a long-term, full-time job. Instead, Ch. Handy believes, people will have to develop portfolio careers in which they earn money by "looking for customers, not bosses". Employers will be both far less willing and ab-10 le to employ people (especially professionals or "knowledge workers") to come to their premises for a fixed number of hours each week. Rather, they will say, "Do this by this date; how you do it is up to you, but get it done on time and up to standard." The term "job" will thus revert to its original meaning of a specific task or project rather than an occupation or profession, while individual ambitions will focus more on the achievement of employability than the status of being an employee. The same kind of analysis also underlies other influential publications concerned with the future of work, some writers going further than Ch. Handy in respect of the speed with which and the extent to which they believe these developments will occur (e.g., Bridges 1995, Rifkin 1995, Davison and Rees Mogg 1997).
A number of others have come out in opposition to some of these ideas, and particularly to Atkinson's model, such as Anna Pollert who has argued in a series of books and articles that there is nothing particularly new about flexibility as it is described by J. Atkinson. Firms have always had to slim down their workforces when faced with difficult business circumstances, and they have always shed subcontractors and peripheral workers first. What is new, according to Pollert (1987Pollert ( ,1988, is the promotion of flexibility in the form of a model intended to guide management actions. In other words, it is the idea that organisations should deliberately develop core and peripheral structures as part of a considered strategy that represents a departure from past practice. However, she goes on to argue that there is little evidence that managers are in fact adopting such strategies. Her point ofview appears to be backed up by the swvey evidence, which has persistently shown that while the extent of self-employment, temporary and part-time work has increased in recent years, this results from managers' reacting on an ad hoc basis to specific needs (Hakim 1990, McGregor and Sproull1992), reflecting a continued demand for part-timers in retailing, catering and publishing. Since 1994 we have in fact seen the creation of substantially more permanent jobs than temporary ones (Donkin 1997).
Moreover, we can see that trends in different kinds of non-standard working affect different industries unevenly. For example, there is relatively little part-time working in manufacturing, but there is a good deal of subcontracting. By contrast, the use of fixed-term contracts has grown most in the public services, where funding to undertake specific projects is limited in terms of time. Such contracts are also used extensively by employers whose workload increases and decreases on a seasonal basis (e.g., in tourism and agriculture), and have necessarily become highly significant in sectors where most employees are female, as a result of the greater take-up of the right to maternity leave in recent years.
Back in 1998, the European Commission's Green Paper on Partnership for a new organisation of work devoted considerable space to the question of a new approach to working time, examining both reorganisation and reduction. The EU Guidelines for Member States' employment policies 1998 underlined the importance of work fleXIbility, and the social partners' role in achieving it, in employment creation/preservation. The guidelines invited the social partners "to negotiate, at the appropriate levels, in particular at sectoral and enterprise levels, agreements to modernise the organisation of work, including flexible working arrangements, with the aim of making undertakings productive and competitive and achieving the required balance between flexi-bility and security". However, it was still too early, according to the Commission's May 1998 review of the National Action Plans developed by EU Member States in response to the guidelines, for the social partners' response to be fully developed.

Categories of Flexible Organisation of Work
Working time flexibility may be defined as permanently variable and adjustable working time in terms of structure and length. Working time fleXIbility is closely associated with the notions of the flexible firm on the employer's side and time sovereignty on the employee's side.
Working time in an employment relationship concerns two dimensions, the length (e.g., in hours) and the structure (e.g., working in shifts or on demand) of individual working time. Points of reference may be daily, weekly, monthly, annual or life working time. Means to achieve working time flexibility in an employment relationship are as follows: • variable working time regarding length and structure; • flexi-time; • working time accounts; • overtime; • working time corridors, which gives companies the possibility, within a certain limit, to reduce or to extend working time; • job sharing; • sabbatical leave; • early and partial retirement; • weekend work; • part-time work; • temporary work; • parentaVmaternity leave; • homeworking; • telework.

Part-time Contracts
Part-time working is by far the most common form of fleXIble working. The biggest period of growth in part-time work was during the 196Os, when the proportion of the total workforce that worked part-time almost doubled. Since then it has continued to rise steadily, along with the overall female participation rate.
In past decades there were clear incentives for organisations to employ two part-timers instead of one full-timer. This resulted from an inequality of treatment in legal tenns, whereby part-time could be denied pension scheme membership and other fringe benefits.
Creating part-time jobs can bring considerable advantages to an organisation. It can reduce costs dramatically by making sure that people are present only when required and can also attract well-qualified people who, because of childcare or other commitments, are looking for less than full-time work each week. Other parts of the labour market to which employers can look include retired people and students in full-time education. Another possible advantage in some situations is the apparent lack of interest among part-timers for trade union activity.
There are of course potential disadvantages too. First, there is the possibility that part-timers, because of other obligations and the fact that theirs is often not the main family income, will show less commitment to their work than their full-time colleagues. The problem is potentially compounded by the lack of promotion opportunities open to them. Part-timers can also be infleXIble in tenns of the hours they work because of the need to honour their other commitments. They are often attracted to the job in the first place because they need to be guaranteed fixed weekly hours (e.g., 12.00-2.00, Wednesdays and Thursdays) and will thus be either unwilling or unable to change these too much.

Term-time Working
A variation of traditional part-time working which has many attractions in principle is the employment of staff to work only during school tenns. Such arrangements allow employees with childcare obligations to maximise their earnings over the course of a year while being free for their children during school holidays. Such approaches have long been used in the education sector itself, where the need for teaching and support staff is, of course, lower outside term time. There is, however, no reason why other sectors should not also adopt such arrangements, especially when troughs in business coincide with school holidays. The approach is particularly applicable where longtenn project work is being undertaken with no particular requirement for work to proceed at the same pace all the year round. However, one must take into consideration the real hours a part-timer works (Thble 1). This may vary across countries considerably and thus part-time work arrangement can have various statuses, impacts on entire employment in the country etc. which obviously influences the choice of employers/employees to decide for such a form of employment.

Temporary Contracts
We use the term "temporary worker" to cover a variety of situations. On the one hand, there are staff who are employed for a fixed term on a seasonal basis to carry out a specific job or task. This category includes well-paid or senior people such as football players or public officials, as well as individuals brought in to undertake more ordinary work on a fixed-term basis. A second group are people who are employed temporarily but for an indefinite period. Their contracts thus state that they will be employed until such time as a particular project or body of work is completed. Again, this category can encompass well-paid individuals such as 1V presenters and actors, in addition to those occupying less glamorous positions. A third category includes temporary agency staff who are employed via a third party to cover short-term needs.
Work on a temporary or fixed-term basis can rise during summer months as a result of seasonal work in the tourism and agricultural sectors. The number of temporary workers also tends to fluctuate with economic conditions, so we saw a rise in the early 1980s, followed by a slight reduction, before the figure rose steeply again in the early 1990s. From the employer's perspective there is thus a number of compelling reasons to consider offering fixed-term contracts to certain groups of staff. They are particularly useful when the future is uncertain, because they avoid raising the employee's expectations. It is far easier, when departments close or businesses begin to fold, not to renew a fixed-term contract than to make permanent employees redundant. During the run-up to redundancies it is also useful to be able to draw on the services of temporary staff to cover basic tasks, freeing permanent employees who are under threat of redundancy to spend time seeking new jobs.
According to the 2000 Eurostat labour force survey, 13.4% of employees in the EU had an employment contract of limited duration (see Thble 2). Compared with 1983, this represented a significant increase in fixed-term employment over the 1980s and 1990s (though Denmark, Greece and Ireland saw fixed-term employment to fall over this period).
In all countries, the share of women with a fixed-term contract is higher than the share of men. Considering all forms of non-permanent employment, the gender difference is even clearer: EU women were 30% more likely to work on a fixed-term!temporary/casual basis than men in 1999.
By age groups, the rate of fixed-term employment is high among people aged between 15-24 and 25-49. While the rate for men and women aged 15-24 is the same, the rate is higher for women in the 25-49 age group, perhaps because this is the age when many women are having children. Non-permanent employment occurs across all levels of qualification.
There has been a trend towards a greater use of non-permanent employment across a variety of sectors, but this is particularly evident 14 in the expanding service sector. In the EU, over 66% of all fixed-term contracts are in services, covering retail, catering, transport, finance and the public sector.

Flexible hours contracts
Another form of fleXIble working arrangement that, evidence suggests, is becoming more common involves a move away from setting specific hours of work. While such contracts come in several different forms, all help in some way to match the presence of employees With peaks and troughs in demand. They thus help ensure that people are not being paid for being at work when there is little to do, while at the same time avoiding paying premium overtime rates to help cover the busiest periods.
The most common, and least radical, departure from standard employment practices is the flexi-time scheme. Precise rules vary from organisation to organisation, but they usually involve employees' clocking in and out of work or recording the hours they work each day. lYpically, such schemes work on a monthly basis, requiring employees to be present for a specific number of hours over the month, but permitting them and their managers to vary the precise times in which they are at work in order to meet business needs and, where possible, their own wishes. In such schemes many identify core hours when everyone must be at work (e.g., 10.00-12.00 and 2.00-4.00 each day), but allow flexibility outside these times. It is then possible for individuals who build up a bank of hours to take a "flexi-day" or halfday off at a quiet time.
The number of situations in which flexi-time can operate and in which it is appropriate to do so is quite limited. Clearly, it is not a good idea where the presence of a whole team throughout the working day is important. It would thus not be used for roles where there is a direct contact with customers or where a manufacturing process requires a large number of employees to be present at the same time. It is also inappropriate where organisational objectives and culture focus heavily on the maximisation of effort and the completion of specific tasks.
However, flexi-time remains in manyorganisations, particularly where large numbers of clerical and secretarial workers are employed, to look after a range of different bodies of work. Where deadlines are relatively unimportant, where individuals have responsibility for carrying out a prescribed range of tasks and where there is no requirement to be available to members of the public all day long, there is a good case for using flexi-time to maximise organisational efficiency.
A more radical form of flexi-time is the annual hours contract. The principle is the same, only here the amount of time worked can vary from month to month or season to season as much as from day to day. It varies from typical flexi-time systems not least, because variations in hours are decided by the employer without much choice being given to the employee. Each year all employees are required to work a set number of hours, but to come in for much longer periods at some times than others. Pay levels, however, remain constant throughout the year. Again, from the employer's point of view, the aim is to match the demand for labour to its supply and thus avoid employing people at slack times and paying overtime in busier periods. Variations can occur seasonally, monthly or can follow no predictable pattern at all At the other end of the scale is the zero hours contract, which organisations use in the case of casual employees who work on a regular basis. They are most suitable for situations in which there are frequent and substantial sur-ges in demand for employees on particular days or weeks of the year, but where their instance is unpredictable. An example is the employment of couriers in the travel industry. A company needs to have a body of trained courier staff it can call on to look after clients, but is unable to predict exactly how many it will need and on what dates. It therefore hires people on a casual basis, gives them training and then calls on their services as required during the holiday season.

Subcontractors
Aside from the use of temporary agency workers, subcontracting comes in two basic forms. First, there is the use by employers of consultants and other self-employed people to undertake specific, specialised work. Such arrangements can be long-term in nature, but more frequently involve hiring someone on a one-off basis to work on a single project. The second form occurs when a substantial body of work, such as the provision of catering, cleaning or security services, is subcontracted to a separate company. Both varieties have becollie more common in recent years, leading to a rise in the number of agency employees and self-employed people. Self-employment is focused on the fields of technical and professional services, the majority of self-employed workers being relatively well-paid. Most of the traditional professions provide opportunities for self-employment, but the highest concentrations are in the fields of draughting, design engineering, computing and business services.
According to the ELUS survey described above, the main reasons given for using selfemployed subcontractors were as follows: • to provide specialist skills (60%) • to match staffing levels to peaks in demand (29%) • because workers prefer to be self-employed (28%) • to reduce wage costs (9%) • because the self-employed are more productive (8%) • to reduce non-wage costs (6%) • to reduce overheads (4%) • other reasons (11 %) (Source: McGregor and Sproull 1992: 227) As with temporary workers, it is interesting how cost-cutting opportunities appear to be so much less significant than the need to bring in specialists. This may be because, hour for hour, the employment of a self-employed contractor is often a good deal more expensive than hiring a temporary employee. Aside from cost considerations, there are also other potential disadvantages from the employer's perspective. First, it is often suggested that self-employed people, like agency workers, inevitably have less reason to show a high level of commitment. They have no long-term interest in the organisation and are thus less likely than conventional employees to go beyond the letter of their contracts. In turn this leads to suspicions about the quality and reliability of the services they provide. Only where there is a clear possibility of an on-going relationship in the form of further work does the contractor have a serious economic incentive to overservice the client.
Another possibility to consider, which is relatively common now, is the rehiring of retired employees on a self-employed basis. Both parties stand to gain from such arrangements where the retired person has a reasonable income from his or her pension.

Teleworking
Thleworking is defined as "a form of organising and for performing work, using informa-16 tion technology, in the context of an employment contract/relationship, where work, which could also be performed at the employer's premises, is carried out away from those premises on regular basis" (EU Framework Agreement on Telework 2002).
We must differentiate this form from selfemployed people or casual workers. The extent to which this kind of arrangement currently occurs is not easy to state with certainty, because many people work outside their jobsite only for a proportion of their time. However, there is a clear, now considerable potential for growth with the expansion of computerised communication technology and improvements in telecommunications. According to Brewster et aL (1993: 46-50), full-time teleworkers fall into two camps: the up-market teleworker and the more traditional manual variety. The latter are heavily concentrated in the industries where part of the manufacturing process c~ be carried out by people working alone away from the shop floor. However, some routine office tasks, such as the preparation of mailshots, can also be performed at home.
For the employer, the main advantage is a reduction in the size of premises required. Savings are thus made in terms of office rents business rates, heating and lighting. The ma~ disadvantages relate to the low morale that teleworkers often suffer as a result of their isolation from co-workers. A different kind of supervision is thus required, along with control systems that assess performance on the basis of the quantity and quality of each batch of work undertaken. Since it is clearly not possible to oversee each individual's work, there is no opportunity either to encourage or correct when mistakes are made or when the pace of work slackens.
Thlework has been increasing across Europe in recent years -the European Commission estimates that there are currently 4.5 million employed teleworkers (and 10 million teleworkers in total) in the EU. Over the past 18 months, it has been the subject of two European-level sectoral agreements in the form of guidelines, the first signed in February 2001 in the telecommunications sector (EmObserver 2/01 p.4) and the second in April 2001 in the commerce sector.
The biggest problem in managing a teleworkforce is the maintenance of effective communication -a particularly important issue where members of the "core" workforce are employed on a teleworking basis. IT such arrangements are to work, more is needed than simple electronic communication. There is also a need to hold regular team meetings, as well as face-to-face sessions between supervisors and staff. In practice, as has been pointed out, most teleworking of this kind is carried out part time, the employee performing some work at the office and some at home. When managed well, this can be the best of both worlds, in that effective communication is retained while savings in terms of office space and energy use are also achieved. Of course, this can occur only if employees forgo the privilege of having their own office or desk at work and accept "hot-desking" arrangements, whereby they occupy whichever workstation or computer terminal is free when they are not working at home.

Employer Perspective: The Flexible Firm
The idea of the flexible firm suggests that the firm is flexible in terms of its adaptability to expansion, contraction or change in the pro-duct markets. Among others, flexibility serves as a means to improve productivity and to cut unit labour costs, to adjust to unpredictable fluctuations, and to allow for the introduction of new manning practices to match new technologies. The flexible firm involves the notions of financial ( and pay) flexibility, functional flexibility (e.g., by multi-skilled employees), subcontracting, outsourcing and distancing strategies (employment relationships are replaced by commercial ones). and numerical flexibility.
The numerical flexibility of the firm concerns the firm's ability to adjust the level of labour inputs, employment and the wage bill to meet fluctuations. The practices include: 1) the use of additional or supplementary labour resources such as part timers, temporary workers or casual workers; 2) the alternation of working time patterns of existing labour resources.

The Future
It is necessary briefly to consider what the effects will be if the management gurus who have predicted a sweeping change in work organisation turn out to be right. What will the effects be in employee-resourcing terms if nonstandard working becomes the norm and people too seriously cease to expect, or even to seek, long-term, full-time employment with a single employer, preferring instead to work on a self-employed consultancy basis for a number of clients? The straightforward answer is that there will be a need for employee-resourcing specialists to find ways of managing through or round some of the disadvantages associated with atypical working described above. However, there are other potential consequences too -some of which can already be observed in industries where there are lucrative freelancing opportunities for people with particular skills. Examples include computer programming, some branches of engineering and the provision of some specialised business service.
The most obvious result is the increasing difficulty in finding people to undertake work at the rates of pay currently being offered. The organisation is thus faced with three options: • to accept that it is necessary to employ freelancers at whatever cost • to hire untrained staff and then to invest substantial amounts in training them • to compete more effectively in a tighter labour market, giving particular attention to the retention of valued staff.
For many organisations this will require fundamental changes in the approach taken towards employee resourcing. It will no longer be possible simply to assume that, if someone leaves, they can readily be replaced by another person with similar skills. In other words, it will be necessary for managers to accept, to a far greater extent than is often the case today, that competitive labour markets exist, and that they need to develop effective strategies for competing in those that are vital to the success and survival of their organisations. Secondly, there is a need to redefine the psychological contract that is developed with employees by fostering relationships that facilitate high trust but that are not expected by either side to last for a long period of time. This involves acknowledging that employees will have different expectations from employers. Instead of seeking furtherance of a career inside an organisation, they will be looking for opportunities to increase their employability. Th attract and then to motivate the best, more 18 attention will thus have to be given to skills acquisition and to finding opportunities for employees to deepen their experience.
A third possibility that arises if key labour markets become much tighter than they are at present, could be the need to alter the perspective from which strategic business planning currently takes place. Instead of looking for product market opportunities and then devising employee-resourcing policies to permit their realisation, there will increasingly be a need to start the process by assessing the organisation's labour market position.

Methodology
The research utilises structured questionnaires and semi-structured interviews covering the application of various types of fleXlbilities as well as the willingness of the employers and employees to participate in these schemes.
Within the research there were 1423 questionnaires sent out to 67 organisations of different sizes, different industries and different ownership as well as managers of 46 companies were interviewed. The returned questionnaires accounted for 62%.
The only flexible form of work arrangements which is consistently recorded and reported proved to be flexi-time. The other forms were commented on in the interviews as being applied or planned to be implemented, however, no relevant recording was offered to provide a reliable evidence on their implementation in the view of the ratios of such flexible arrangements versus regular traditional work arrangements. Thus, only qualitative evaluation of the research could be provided.

The Findings
The most common flexibility fonn appears to be flexi-time. The other forms (part-time and temporary con tracts) are mostly used for peripheral groups of various categories of employees, primarily in services and media. They, as is mentioned above, include well-paid positions as well as less glamorous ones.
In addition, part-time and temporary contracts are used in the probation period as well The managers have argued that these forms of flexibility facilitate the termination of the employment relationship and prevent from the potential conflicts, as well as cut administrative procedures and costs necessary for appropriate termination of the employment contract.
Telework as a flexible fonn has not been introduced by any of the contacted organisations.

Flexi time
In Slovakia, the framework for utilising flexitime is set by the Labour Code. It assumes that both the beginning and the end of the work shift is set by an employee within the so-called daily, weekly or four-week working cycles while the obligatory daily spell of presence at work (minimum 5 hours) is established. The presence at work is at the employee's discretion. In the case of daily working cycle, the employee is obliged to work for a preset number of hours within a day (the same every day) and flexibility relates just to the beginning and end of the working block. The weekly variation presets the number of hours to be worked weekly, but the number of working hours can vary daily. If the four-week working cycles are applied, the number of hours to be worked is based on the weekly figure multiplied by four. Here, a number of hours to work can be shifted also from one week to another.
The employer here benefits primarily from the fact that all out-of-work commitments of the employee can be covered outside the working hours.
While numerous employees use mass transportation to get to work, the general benefit of flexi-time can be seen also from the perspective of transportation organisation in large cities. On the other hand, if commuting depends on particular lines (buses, trains) and the employees cannot get to work otherwise, the employer will not have chance to introduce flexi-time.
As mentioned above, flexi-time is difficult to implement in some industries, e.g., manufacturing. If it is introduced, it mostly applies to the back offices in companies. Nowadays, flexi-time is used in less than 10 companies ( approx. 5.000 employees) in metal industries, mostly owned by the German capital.
The implementation of flexi-time on the part of the employer relates mostly to the industries with a predictable or unpredictable fluctuation of work loads.
The predictable fluctuation of work load occurs in agriculture, forestry, construction and the like. The Labour Code allows for flexi-time arrangement in a longer horizon, i.e. fourweek or yearly arrangement. It means that in the busy season the employees work longer hours or more days a week while in the troughs they work less hours or even less days.
An unpredictable fluctuation occurs when the employer is forced to react to unpredictable demands of the environment, e.g., loss of orders or a large number of new ones. This is mostly the case of subcontractors. Such cases are not covered by the Labour Code in force at present and therefore the situation can be solved partially just through flexi-time arrangement. In Slovakia, the German model of flexi-time application is used, mostly in the subcontracting companies of large automobile producers. Here, if the employee does not work the full number of working hours within a particular month, a bank of working hours is created with either plus or minus balance. The employees are paid as if they worked full monthly time in either case. If the employee worked more, as a compensation they can utilise time off in the future when the work load is lower and vice versa. The zero balance must usually be reached within a year. Of course, the implementation of the model must observe the general provisions of the Labour Code, such as the maximum length of the work shift, rest between two shifts, obligatory days for rest, etc.
The disadvantage here is that the implementation of such a model cannot be covered by a general agreement (e.g., collective agreement), but is always part of the employer~mployee contract/relationship. Thus, the relationship is not neutral. The employer is usually more powerful While the employer lowers the costs related to overtime, the employee may experience even raise of the costs, e.g., for transportation or childcare. In addition, a conflict can emerge if the employer needs the employee to be at work at the same time when the employee is forced to take time off because of extemal commitments. Again, the infrastructure can also have its say in the introduction of this model in some regions.

Part-time Work
The part-timer, if not working more than 20 hours per week, exercises the position as that of a full-timer under the terms and conditions of the current Labour Code of the Slovak Republic. It relates primarily to the contributions to the social funds (e.g., pension scheme, health insurance, etc.). The only disadvantage seems to be job insecurity, 20 as the employer can terminate the contract without any notice.

Temporary Work
The implementation of a temporary contract cannot exceed 3 years. The employer, even if he decides to terminate the contract earlier, is obliged to pay the agreed-upon reward fully. This contract's disadvantage is that termporary workers are not considered as potentials in terms of training and career: development.
Another form of temporary work covers the contracts limited by 300 hours per year. In that case, the temporary worker is paid just for work actually carried out. This form is frequently utilised as there are no contributions to the funds and thus labour costs are substantially lower.
There is no obligatory recording and reporting of such contracts and therefore they are frequently misused, e.g., by the unemployed who may acquire regular pay along social welfare, or by employers who are able to dovetail several temporary worker positions to cover a full-time position and simultaneously cut the obligatory payments.

Conclusions
As mentioned above, the most often used flexible work organisation is fIexi-time, part-time and temporary contracts are used primarily because of economic reasons, such as cutting costs, no need for contributions to social funds, no need for redundancy payments in the case of closing jobs/positions; remuneration includes only base pay, frequently it means just the minimum pay.
From the cultural point of view, there is no surprise that telework has not been introduced yet. Moreover, the low mobility of work-force, the usage of mass transportation and its availability can influence the introduction of this or that flexible form in spite ofthe wish of


extfieldsofstudy: Physics Economics Mathematics

text:
Levy distribution and long correlation times in supermarket sales

Sales data in a commodity market (supermarket sales to consumers) has been analysed by studying the fluctuation spectrum and noise correlations. Three related products (ketchup, mayonnaise and curry sauce) have been analysed. Most noise in sales is caused by promotions, but here we focus on the fluctuations in baseline sales. These characterise the dynamics of the market. Four hitherto unnoticed effects have been found that are difficult to explain from simple econometric models. These effects are: (1) the noise level in baseline sales is much higher than can be expected for uncorrelated sales events; (2) weekly baseline sales differences are distributed according to a broad non-Gaussian function with fat tails; (3) these fluctuations follow a Levy distribution of exponent alpha = 1.4, similar to financial exchange markets and in stock markets; and (4) this noise is correlated over a period of 10 to 11 weeks, or shows an apparent power law spectrum. The similarity to stock markets suggests that models developed to describe these markets may be applied to describe the collective behaviour of consumers.

Introduction
The search for general trends in markets has a long history. Nevertheless, some 70% of new products put in the market fails. In marketing science the adoption of new technologies is traditionally studied using the Bass model [1], which was first posed in 1969, and which relates the fraction of consumers adopting a new technology per unit of time, to the fraction present at that time. This model ignores the variation among consumers and it ignores their network of social relations. One important recent insight in the description of human economic behaviour is that these networks may be very important for the success or failure of new products. Arthur [2] argued that the amount of information humans typically have deal with is too large to handle, and moreover individuals usually have to base their decisions on partial information. Therefore they turn to rules of thumb, or strategies, to determine their actions. These strategies are often just copied from peers; this is the first reason why social networks are important.
The second reason why networks are important, is that part of the perceived value (or utility) of a product depends on its acceptance in the social network of the consumer. The utility of a product represents more than its direct application; its value in use can be increased because the consumer feels that it attributes to his/her social status [3]. For example, clothing can be valuable to express the membership of a peer-group, or otherwise expensive cars may cue status to the peer-group. This social effect is not limited to products like cars, but may also hold for commodity markets.
Recently Stauffer [4], Weisbuch and Solomon have studied the impact of social networks and percolation phenomena to the adoption of new products. Solomon et al. [5] discuss the possibility of observing self-organised criticality. The question addressed is: why does one observe that some newly launched products are doomed to failure while others become great hits, rather than a featureless distribution of partial success? The general explanation for such a bimodal distribution is discussed in terms of bounded rationality. Decisions are not taken upon complete information, but consumers copy the behaviour of their peers [6]. Thus, the spread of a new technology is often compared to the spread of a virus over the population, and is determined by a percolation transition. Goldenberg et al. [7] bring these ideas further and compare them to marketing of consumer goods, namely the introduction of cars and LCD color television sets.
However, the models mentioned are all based on theoretical ideas of how consumers choose, the link to empirical data is weak or missing. Before attempting to describe the RD Groot, Lévy distribution and long correlation times in supermarket sales 3 dynamics of new market introductions, one should at least be able to describe the dynamics of a stationary market. The first step to develop a realistic model of the collective behaviour of consumers, which takes into account psychological and social factors, should be to collect empirical facts that can be used as a standard to test the models. The development of models for financial and stock markets has benefited greatly from the analysis of price fluctuations [8,9]. Since this was the case for our understanding of stock markets, the obvious first step towards building a model of consumer sales, is to analyse the fluctuations in this market. This should unearth the empirical -stylised -facts of consumer sales. Such an analysis seems to be missing in this field. Once the stylised facts are established we can analyse their causes, and finally build models based on these insights. As a first attempt in this direction the fluctuations in actual sales data of a number of consumer goods are analysed. Here we restrict to presenting the empirical data and its implications for modelling.

The consumer goods market
The available observations are actual sales data of products in supermarkets. Time series of sales can be obtained from ACNielsen [10]. The longest series available is over a period of 120 weeks. As an example of sales in a commodity market, the sales data of ketchup in the Netherlands will be discussed first. In the Netherlands there are about 16x10 6 consumers, divided over some 7x10 6 households. These households shop at some 5200 supermarkets.
The raw sales data for Calvé, Gouda's Glorie, Heinz and Remia are shown in Figure 1a.
Most of the noise in the sales data shown in Figure 1a can be attributed to promotional actions. ACNielsen also provides a baseline for the sales of each product, which is the total sales not conducted under promotion. For the shops where a promotion is on, baseline sales from the previous eight weeks are used to extrapolate to the value one would have had if there would not have been a promotion in that week. Basically it comes down to subtracting the excess sales that is attributed to promotion. The output of this analysis is known as the baseline sales. The noise in the baseline sales is shown in Figure 1b, this is the underlying fluctuation of the market.
The principal parameter to characterise the sales data is the market share of the various brands. In this case these are 52.7%, 19.6%, 14.8% and 12.9% respectively in order of size.
As a first method of analysis the baseline sales data in Figure 1b were fitted to parabolas, and the variations from the trends were studied. The root mean square fluctuations thus found vary from 7.6% of sales for the product of highest market share to 13.2% of sales for the product of lowest market share. RD Groot, Lévy distribution and long correlation times in supermarket sales 4 The relative noise is an indication of the number of uncorrelated sales events. If we have N independent events the relative noise is given by 1/√N. Hence, from the relative noise in sales we find in turn the number of independent sales events. The remarkable result is that out of 37000 bottles of Heinz ketchup sold per week, apparently only 173 events are independent, and out of 9000 bottles of Remia sold per week only 57 events are uncorrelated. This difference cannot be explained on the basis of the size of the sample taken by ACNielsen. The sample is allegedly based on some 1100 shops (out of 5161), which represents 40% of all sales in the Netherlands; the statistical variation is estimated as 2% [11]. Nor can it be explained by assuming that the data reflects sales to the retailer in larger quantities. The data is actual point of sales data to the consumer [11]. Even if we assume that the number of 1100 shops is overstated (some say that the size of the sample is only 350 shops) then still the noise level does not fit the number of independent buying events.
Hence, merely by studying the variance in baseline sales fluctuations we arrive at the conclusion that the buying behaviour of thousands of consumers is correlated. Whereas this may be an obvious social effect for fashionable products like cloths, it is less obvious why this would be the case for a commodity like ketchup. Therefore we will study the data in more detail in the next sections to obtain the noise spectrum and correlation functions.

The Noise Distribution
To analyse the data set further, the noise distribution of sales is studied. Mantegna and Stanley introduced a method to analyse the fluctuations in the S&P 500 index of stock markets, by studying the price difference of a stock at two successive points in time (the price return) [8]. In stock markets, this time difference can be as small as one minute, but it can also be days. They found that the distribution of price differences follows a characteristic shape, the Lévy distribution. The width of the distribution obviously depends on the time interval studied, but the shape of the distribution remains the same. For stock markets it is given by where α takes on the value α = 1.4 in real markets. For α = 2 this equation generates a Gaussian distribution, but for the lower value α = 1.4 pertinent to the market, the distribution has fat tails. For large values of the price return the distribution crosses over to a characteristic power law with α = 3, thus following a truncated Lévy distribution [12,13]. RD Groot, Lévy distribution and long correlation times in supermarket sales 5 For ketchup sales data we can use the same method of analysis; the distribution of the change of sales from one week to the next is studied, i.e. the distribution of ∆s(t) = s(t+1) − s(t). Because we have only limited data, the mean value of ∆s was first determined for each series, which was subsequently subtracted from the data. Next the spread in ∆s was determined, and ∆s was normalised to its spread for each series. This gives four series of zero mean and spread one, with a total of 468 observations (some data points corresponding to Xmas sales were removed). For this data set a distribution has been determined, which is shown in Figure 2.
This figure shows that the distribution of sales fluctuations is not a Gaussian distribution. In fact the Lévy distribution taken at the power α = 1.4 seen in stock markets [8] makes a very good fit to the ketchup data, whereas the Gaussian distribution of the same width makes a poor fit. The remarkable take out is that for the ketchup market, daily supermarket sales corrected for promotional actions, follows roughly the pattern of price return fluctuations of stock markets. This suggests a similar underlying cause. Naively one would expect a Gaussian distribution, as the sales are the result of many independent buying events. When a distribution is not Gaussian, this implies that there are strong correlations in the signal. In other words, the buying events are not independent.
One may wonder if the effect shown here is an artefact, caused by the procedure followed by ACNielsen to obtain the baseline. This is not the case. If we simply subtract all sales in shops where promotional actions are on and then study the fluctuations, we find the same distribution. Further, one may wonder if the broad noise spectrum may be a remnant of promotional sales. Perhaps a small residual error in subtracting the promotional sales has led to the Lévy noise. If this would be the case the effect should disappear when we take out all high frequency modes, since the promotions are spiky one-week events. To this end the data was Fourier transformed, and all modes of frequency ω > 1 were removed from the sales data (i.e. all frequencies with a period smaller than 6.3 weeks are taken away). The back-transform for each brand is now a smooth curve running through the baseline sales.
When a distribution of sales differences from one week to the next is calculated from this smooth curve and scaled relative to the noise amplitude, we find again a Lévy distribution (see Figure 3), and within the statistical accuracy this is indistinguishable from the previous distribution. This shows that the broad distribution and its fat tails are not caused by high frequency noise, since everything with a period less than 6 weeks has been taken away.
This implies that the shape of this distribution is not caused by promotions, not caused by weather variations and not caused by isolated sale bursts at bank holidays. RD Groot, Lévy distribution and long correlation times in supermarket sales 6 Finally, if this effect is no coincidence, one should be able to reproduce it for other markets.
Products deemed to be similar to ketchup are mayonnaise and curry sauce, in that they are all sauces, and not bought very frequently. We studied the baseline sales of Calvé, Gouda's Glorie and Remia mayonnaise, and of Calvé, Gouda's Glorie, Hela, Heinz, Remia and AO curry sauce over the same time interval as the ketchup data. Baseline sales in these markets indeed look as noisy as that of ketchup.
For the mayonnaise and curry baseline sales data, again the weekly sales differences were determined. For each brand and product, the sales differences were then normalised to the mean spread over the 118 week period (again Xmas 2000 sales was excluded from the statistics). When the mayonnaise and curry sauce markets are studied separately the same distribution is obtained as for ketchup. All three markets are therefore statistically the same as far as the noise distribution is concerned. Because each data series is normalised to unit variance, all ketchup, mayonnaise and curry data can be collected into one distribution. This distribution matches the Lévy distribution close to exactly, see Figure 4. Again, the Lévy exponent 1.4 -copied from financial markets -fits the data.

Correlation functions
One may argue that the shape of the distribution and the high noise level could be caused by a cross correlation effect between promotions of one brand and the sales of another. The idea behind this is that baseline sales data of a brand has been corrected for promotions of that same brand, but not for promotions of other brands. If brand 1 has a promotion leading to sales increase of brand 1, then brands 2, 3 and 4 might suffer as a result. Thus, one might expect a negative cross correlation between the sales of one brand and the baseline sales of another. If this is true, the noise level observed in the previous section may not be caused by the dynamics of the market, but could still be a remnant of promotion effects. To check this hypothesis the auto-correlation and cross-correlation functions were studied.
If the weekly sales of brand i is given by s i (t), the sales correlation is given by where  stands for a time average. Since the variance should be proportional to the number of sales events, C ij (t) should be independent of the size of the brand. This is checked for all sauces (ketchup, mayonnaise and curry cause) and indeed found to be the case. We first RD Groot, Lévy distribution and long correlation times in supermarket sales 7 concentrate on the baseline sales auto-correlation, and then study cross correlations. The value of the auto-correlation at t = 0 is the number of sales events that are correlated. To see this, let mean sales be given by <s> = Ns 0 where N is the number of independent events, and s 0 the average amount sold in such an event. The variance in the mean is σ 2 = Ns 0 2 , hence C(0) = σ 2 /<s> = s 0 .
If the broad noise distribution is a remnant of promotions, one would expect a sharp peak at t = 0 and no signal after the first week, since promotions only run for one week. To calculate the sales correlation functions, the data can be detrended or not. Detrending means that the mean trend over the 118-week period is subtracted from the sales curves, such that the mean slope will vanish [14]. This obviously takes away fluctuations on the time scale of two years or more, but it would correct for a continually rising or declining market. For ketchup, detrending or not detrending has little influence on the result, for curry sauce and mayonnaise the differences are larger. Taking the mean and half difference of the detrended and non-detrended correlation functions as our estimate and its error bar, the results for all three markets are within the uncertainty of the others. Thus, within a first approximation the three markets show the same sales auto-correlation function, which is shown in Figure 5.
The small dots in Figure  which are shown in Figure 5.
Indeed, the auto-correlation function in t = 0 is higher than the value extrapolated from the correlation at t > 0. This excess can be attributed to be a remnant of the promotions, but this represents only 37% of the variance. Other effects like weather variations or holidays may have also an influence on this term. Most of the variance is related to fluctuations of the baseline, and is thus caused by intrinsic market moves. As can be seen from Figure 5, these fluctuations have a very long correlation time as compared to the typical 4 minutes seen in RD Groot, Lévy distribution and long correlation times in supermarket sales 8 stock markets [12]. The mean correlation function averaged over all brands and markets for t > 0 is given by where t is in weeks. The slow correlation time points at an internal dynamical process, this could be customer loyalty and repeat buys, but certainly cannot be due to promotions.
We now discuss the cross correlations, and focus upon the cross-correlations between ketchup brands. When the top brand has a large peak due to a promotional action one might expect the other brands to have a (small) sales decrease. This, however, is not seen.
Whether we correlate the full sales with baseline sales, or take the correlation between baseline sales does not matter significantly for the result. The cross correlation function between top brand and the others vanishes within the noise, although close to t = 0 a small positive correlation might be present, see Figure 6. This observation again confirms that because the cross correlation is zero, the noise in the baseline cannot be a remnant of the promotional noise. To gain further insight into the nature of the processes that determine the baseline sales dynamics, the Fourier transform of the baseline sales data, s(ω) = 2/T 0 ∫ T s(t) exp(iωt) dt is studied. If indeed there are two processes, one of which is much faster than the other, this should show up as a signal at high frequency. Thus we could separate the high frequency noise from the noise spectrum of the slow process. The baseline sales correlation is readily obtained as is actually the Fourier transform of the function C ii (t) defined above, and is an average over all brands. There is a subtle difference though. By taking the Fourier transform the convolution is calculated, implicitly assuming that the function s is periodic in T, whereas in Eq 2 the time average is restricted to the interval where t+t' < T, and no periodicity is assumed. The error bars are the estimated error in the mean, based on the spread in the RD Groot, Lévy distribution and long correlation times in supermarket sales 9 data for each point. The autocorrelation functions of the baseline sales have been determined for 11 brands and products. Two curry brands had long running new product introductions, which were counted as promotions by ACNielsen. This seriously affects the baseline for these brands and therefore these were left out of the statistics. If we average over all 11 products and assume that there is a unique mean value at each frequency, we obtain the function shown in Figure 7. The points are averaged over two to four successive frequencies to reduce noise. The logarithm of the correlation function is averaged over all brands. The full curve shown in Figure 7 is a fit to a single Maxwell mode and a constant noise term, G(ω) = a/(1+(ωτ) 2 )+c, the dashed curve is a fit to a power law plus a constant, G(ω) = 1/(ωτ) α +c. Within the uncertainty of the data the two fit functions are equally valid.
Hence, over about a decade in frequency the correlation function scales with an apparent power law G(ω) ∝ ω −α with power α = 1.5±0.1.

Discussion
The analysis of baseline sales of three different products (ketchup, mayonnaise and curry) has led to four new observations, namely: 1. the sales noise level is much higher than can be expected for uncorrelated buying events 2. weekly sales differences show a broad non-Gaussian distribution with fat tails 3. this sales distribution is similar to the price return distribution of stock markets 4. the baseline auto-correlation shows a long correlation time or an apparent power law behaviour at low frequency.
A trivial explanation for the first observation might be that the sample upon which the sales data is based is actually smaller than claimed. However, this explanation can be ruled out by the data. The correlation function averaged over all products extrapolates to zero at a mean value of about 160. This means that the intrinsic variance in the baseline sales is 160 times larger than actual sales. If this is to be explained on the basis is the sample size, the data must be based on only 32 shops. This is not realistic. Moreover, this trivial explanation would imply that the noise level is based on fewer sales events that are all independent. Such a model of independent consumers, going through independent buying decisions, would directly lead to Gaussian fluctuations. This again is falsified by the data: the fluctuation spectrum resembles that of a (truncated) Lévy flight. This points at strong correlations between the behaviour of consumers. With other words, the notion of independent consumers who take independent decisions is false. RD Groot, Lévy distribution and long correlation times in supermarket sales 10 The explanation that the noise is a remnant of promotions is also ruled out by the data.
Indeed the extrapolated value of the auto-correlation function is lower than the actual value at t = 0. The difference can be attributed to short time effects like promotions, weather etc, but this can only explain some 37% of the variance. The major part of the fluctuations is related to an intrinsic process on a time scale of some 10 weeks.
Lévy distributions have been observed recently in commodity markets [15], but unlike the earlier result by Mandelbrot for the cotton market [16], these studies showed higher exponents of distributions that are not Lévy stable. The reason for this is that the market crosses over from Lévy stable behaviour with α ≈ 1.4, to power law behaviour with α ≈ 3.
The crossover point is located near an absolute return of roughly 3 standard deviations [9,12,15]. Mandelbrot did not have enough data to see this crossover. The present analysis of sales to consumers also lacks the amount of data to see this limiting law. However, the result in Figure 4 is consistent with a truncated Lévy distribution that crosses over by 3 standard deviations. It should be mentioned here that weekly sales returns of soups have also been analysed, and added to the distribution. For this combined data set we do start to see a crossover. However, soup consumption is very season dependent. Hence, to analyse this data the yearly variation had to be subtracted by detrending against periodic functions.
This also led to spurious oscillations in the auto-correlation function. For this reason we cannot say whether this crossover in the combined data set is fortuitous or not, hence the data was left out of There are basically two different explanations for the occurrence of fat tails in markets. The first is that the system is in a self-organised critical state [19], and that "avalanches" occur regularly. The second explanation is that actions are correlated because agents are linked in a social network. The first explanation is closely related to the theory of avalanche dynamics.
In this theory 1/f-noise is related to anomalous random walks of the underlying process [20].
A class of deterministic models introduced by Olami, Feder and Christensen exhibits 1/fnoise with an exponent that depends on the degree of conservation [21]. In a similar model of artificial societies a cellular automaton evolves towards a critical state, with avalanches obeying finite size scaling [22]. This principle of self-organized criticality has been applied to financial market modelling by Ponzi and Aizawa [23]. Their model describes an evolving network of traders, subject to Darwinian evolution. It produces a Lévy distribution of the correct exponent for the price returns, and it reproduces clustered volatility. The simplest market model exhibiting self-organised criticality is the Minority Game. This has been applied to market simulation with different species of traders with finite capital [24].
Wealth is accumulated in the course of the simulation, and the richer agents have more influence on the market. As in the standard Minority Game, a phase transition is found, depending on the ratio of the information complexity and the number of agents. The emergent picture is that when agents are few, the market is rich of profitable opportunities.
These attract others to the market. As the number of agents increases, the opportunities are eliminated and the market is driven towards its critical point. This suggests why real markets operate close to the critical point where profitable trade opportunities are barely detectable.
Challet et al [24] state that the process by which the market self-organises is likely to be of evolutionary nature, and hence takes place on longer time-scales.
There is an obvious competition amongst the producers, which may give rise to an evolutionary effect (including "avalanches"), but whether or not this can explain the fast sales variations on a weekly basis is questionable. Evolution is related to product improvements, and their fitness to the market. Indeed the market is very dynamic, and new products are introduced regularly, but the typical time scale involved is months rather than weeks. One may speculate that this corresponds to the 10-11 week time scale seen in the sales autocorrelation function. On the other hand, in the examples studied here only three to six leading brands are competing, which is a small number for such complex behaviour, even if each brand actually holds six or more different items in their product portfolio.
The second explanation for stylised fact in markets is that the behaviour of agents is correlated because they are linked in a social network. If they tend to follow the decisions of their peers, sales becomes correlated which gives rise to larger sales fluctuations. A simulation model that incorporates this effect must contain a large number of consumer groups, that have mutual interactions and that drive the market system to a critical point. In marketing language, these groups may correspond to the particular segmentation of the market. The critical point should then correspond to a consumer segment distribution that is given by Zipf's law [13]. The archetypal model to describe such correlated behaviour due to social networks is the Cont-Bouchaud percolation model [25]. This model is based on a random communication structure between agents, which gives rise to power-laws in price fluctuations and herding behaviour. The model assumes that agents form coalitions, where all agents in one coalition take the same (random) decision to buy, sell, or do nothing. The coalitions are formed through a stochastic process, where each agent is linked to any other one with a given probability. At a critical probability, the system shows a percolation transition, where a very broad distribution of cluster sizes appears. Since the cluster size distribution has an algebraic decay, so does the distribution of price variations because the price variation follows the excess demand. Hence, the correct stylised facts are found when the correct cluster size distribution is put in by hand [13,26], or when the random clusters are formed by simulating the Ising model at its critical point [27]. Lux and Marchesi describe a multi-agent model of financial markets which supports the idea that scaling arises from mutual interactions of participants. Their model contains a news arrival processes that lacks power-law scaling and time dependence in volatility, yet it generates such behaviour as a result of interactions between agents [28]. Finally, social networks are key in the analysis of Sornette et al of endogenous and exogenous shocks in book sales [17,18].
In reality both the competitive evolution of brand fitness and the network structure of the consumers may be pertinent. However, there are two arguments that point to the latter effect as being dominant. Firstly, the avalanches seen in evolution theory describe the correlated extinction of many species. Translated to the market this would mean many brands going bust at the same time, rather than many consumers buying the same product at the same time. This is not in line with observations. Secondly, 58% of the long time variance in ketchup sales is cross-correlated between brands, and the time scales for the autocorrelation and cross-correlation functions are the same. This points at a cause for the fluctuations that is common to all brands, rather than to the brand management strategy and evolution of brands. The question thus arising is how these clusters of correlated consumer behaviour are formed. Why do all consumers simultaneously decide to buy mayonnaise? It is speculated that advertisements play a crucial role in forming such correlation, and in generating the non-Gaussian distribution of sales returns, as this may create a broad distribution of consumers who have and who have not been influenced.