Victoria Buesch
email: victoria.buesch@otahochschule.de

Svenn-Aage Dahl
email: svennaage.dahl@snf.noc

Dennis A V Dittrich
email: dennis.dittrich@uni-erfurt.de

Victoria Büsch

Svenn-Åge Dahl

An Empirical Study

Keywords: hiring decisions, older workers, demographic change hiring decisions, older workers, demographic change JEL-Classification: J14, J23, J71

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Introduction

In this article we present the results of a questionnaire study that we conducted to investigate whether applicants with same qualifications are treated differently in the selection process just on the grounds of age, and address age discrimination in hiring decisions in Germany and Norway. Are there differences in age discrimination between the two countries, and if such differences exist, can we explain them? Discrimination is a situation in which individuals identical in regard to their productive ability are treated differently because of certain of their nonproductive characteristics. In perfectly competitive labor markets discrimination cannot persist. Labor markets seem, however, to be monopsonistic (Manning, 2003). The labor supply to the individual firm is not infinitely elastic. Workers have limited mobility and entry costs hinder other firms from competing for the labor pool in question. This imperfection in competition allows the monopsony to discriminate without being forced out of the market.

Age discrimination in labor markets is consequently defined as fewer opportunities of older workers not due to lower productivity but only due to their age (Cain, 1986). Though age discrimination was already observed more than 50 years ago (see, e. g. Tuckman and Lorge, 1952) it is still one of the most difficult research questions to investigate in labor market research (Johnson and Neumark, 1997;OECD, 1998). The reason is that it is difficult to establish whether differences between groups in relation to unemployment and wages are a result of discrimination, or of real differences in productivity or labor market ambitions. Incomplete contracts, hiring and training costs lead to an improved position of 'insiders' when it comes to rent sharing (see, e. g. Solow, 1985). Wage differentials then no longer reflect productivity differentials alone. and classifications based on them harms many productive older workers (Neumark, 2001).

A result of age discrimination is that older workers are often over-represented among the long-term unemployed, and have longer unemployment spells compared with their younger colleagues (Laczko and Phillipson, 1991;McDonald and Chen, 1993;OECD, 1998). The employer might use the unemployment spell as a signal for lower productivity of the applicant pool as a whole. Such statistical discrimination can, of course, be totally rational, if the cost of testing the individuals exceeds the potential expected gains from finding the most productive individual.

In Germany, it has become more difficult to find a new job already from the age of 45 and onwards (Frerichs and Naegele, 1998). Büsch, Dittrich and Königstein (2006) have shown that age discrimination in hiring decisions is rather common. The most-named reasons for the high proportion of long-term unemployed persons among older job seekers in Germany are perceived higher health risks and insufficient skills (Bogai, Hess, Schröder and Smid, 1994;Naegele, 1992). Furthermore, wage costs for older workers generally are considered to be too high because of the seniority principle in many wage systems, and the prospective employment period is seen to be too short. In Norway, the empirical evidence is much more anecdotal in character, and, as in most other countries, research on discrimination has focused on race and gender rather than on age. But, it has been found that age together with ethnic background, and long-term unemployment are the most important barriers for the unemployed in the labor market (Rogstad and Raaum, 1997). A recent survey shows that 13 % of interviewed managers did not hire an applicant or promoted employees because of their age (Senter for Seniorpolitikk, 2002).

The remainder of this article is organized as follows: In the next section, we briefly review the relevant literature on age discrimination and position ourselves relative to the various perspectives. Then we describe institutional features of the two countries. This is followed by hypotheses concerning what we expect to find and a description of the sample(s) together with research methods. In the subsequent section, we comment on the results from our empirical analysis, and finally provide a conclusion and discussion in the last section. There are, in principle, two approaches to explain discrimination. One is the taste-based approach of Becker (1957). According to him, the different treatment results from the dislike of a person who belongs to a certain group. The other approach deals with statistical discrimination (see Phelps, 1972). Here, Aigner and Cain (1977) distinguish between group discrimination and individual discrimination. Group discrimination occurs whenever the average remuneration of a group is not proportional to its average productivity. Individual discrimination happens as soon as workers with the same true abilities are not receiving the same wage (see Büsch, 2004, for further implications).

Consequently, empirical research on discrimination in the labor market has, for the most part, focused on race and gender wage differentials by estimating wage equations (see, e.g., Hinks, 2002;Ward, 2001). In their recent overview of the mainly American literature, Altonji and Blank (1999) and Darity and Mason (1998) conclude that these differentials have been persistent over time, but that the nature and magnitude of the differences have changed. Yet, estimating wage equations posses serious problems. The problem of omitted variables, which invariably exists, leads to the conclusion that the obtained results always overestimate discrimination. If, on the other hand, discrimination has an impact on explanatory variables the obtained results may underestimate discrimination. Other research methods that try to overcome these problems and assess discrimination directly include paired-audit studies in which two applicants for a job are matched who differ only in one characteristic, such as race (for a summary presentation of relevant works, see Darity and Mason, 1998;Riach and Rich, 2002), the comparison of productivity and wage differences (e. g. Hellerstein, Neumark and Troske, 1999;Kahn, 2000), and, less common but increasingly popular, field (Harrison and List, 2004) 2001). Our approach is similar to field studies using the correspondence testing technique where fake letters of applications of individuals with identical human capital but different demographics are sent out to companies (e. g. Bertrand and Mullainathan, 2004;Riach and Rich, 2004;Weichselbaumer, 2003).

The empirical literature on age discrimination in the selection process is to a large degree dominated by psychologists. Empirical research has found mixed evidence for the role of applicant age in selection decisions. While some studies found a significant effect of the applicant's age, e.g., Rosen and Jerdee (1976b) and Avolio and Barrett (1987), who show that younger applicants are evaluated more favorably than older applicants, others found little or no effect of age (Fusilier and Hitt, 1983;Locke-Connor and Walsh, 1980).

There are several themes regarding age discrimination in the empirically oriented literature, and among these are negative stereotypes, employers' attitudes, employers' / interviewers' age, job type/status, and the recruitment process. Negative stereotyping is usually suggested as a reason for age discrimination (Perry and Bourhis, 1998). Stereotypes in the relevant literature are typically defined as ". . . cognitive structures that consist of associations between attributes or features (e.g., personality traits, overt behaviors) and social categories (e.g., occupations, age)" (Perry andBourhis, 1998, p. 1673). When an individual is identified as a member of a social category, the attributes associated with this category are applied to this individual (Kalin and Hodgins, 1984). Age stereotypes are defined by Rosen and Jerdee (1976a, p.180) as "widely held beliefs regarding the characteristics of persons in various age categories." Typically negative stereotypes of older workers are that they are less motivated, not up to date regarding their occupational skills, have a lower performance capacity, have less potential for development, are more risk averse, more resistant to change, and less creative (Maloney and Paul, 1989;Rosen andJerdee, 1976a,b, 1977;Warr, 1994) (Itzin and Phillipson, 1993;Laczko and Phillipson, 1991;McEwan, 1990;Taylor and Walker, 1991;Walker and Taylor, 1993). Ginn and Arber (1996) found that 64 % of the women and 66 % of the men over the age of 40 reported that age was the most important barrier for getting a better job in Great Britain. Lewis and McLaverty (1991) found in a survey among managers and professionals aged 40 to 55 that 36 % reported age as being a barrier for internal promotion in their organization, and 45 % had not had any possibility for development during the last five years. Johnson and Neumark (1997) found that employees who reported age discrimination (self-reported -no promotion, demotion, laid off, not hired, etc. because of age) had a higher probability of leaving their employer and a lower probability of being employed (even if controlled for personal characteristics and other variables) than workers who did not report discrimination.

The age of the person conducting the job interview might also influence the hiring decision.

Perry, Kulik and Bourhis (1996), based on their research, argue that those who evaluate older workers are strongly influenced by their attitude toward older persons in job selection processes.

A potentially greater number of years in the firm, "paper qualifications", and more adaptability are some of the reasons employers give for their preference for younger workers even though older workers are looked upon as more reliable. Many older workers felt that the only jobs that were available for them were part-time work and/or jobs with low wages (Taylor, 1998). This can be exemplified by the study of Chiu andNgan (1996) andHeywood, Ho andWei (1999) both of whom studied older employees' possibilities on the labor market in Hong Kong. Among employers it is common to hire older persons only reluctantly, and age limits exist for a lot of jobs, especially for women. The suitable age for women is set lower than for men in spite of a higher life expectancy of women compared to men. Finkelstein and Burke (1998) find that the age of the managers have an effect on how they rated hypothetical applicants, and older managers are found to disfavor older workers. According to the authors this finding indicates that older people 7 F o r P e e r R e v i e w may actually be more likely than younger to hold economic stereotypes of older workers. On the other hand, Slater and Kingsley (1976) found that younger employers reported less advantageous attitudes towards older employees than older employees, and that employers in companies with many elderly had more advantageous attitudes towards this group.

Previous research and theory suggest that jobs have age norms or are age-typed (e.g., youngtyped, old-typed, or age-neutral) and that young applicants and employees will be evaluated more favorably for young-typed jobs, and vice versa for older applicants (Cleveland, Festa and Montgomery, 1988;Cleveland and Hollman, 1991;Cleveland andLandy, 1983, 1987;Gordon and Arvey, 1986;Perry and Bourhis, 1998;Perry et al., 1996). The job status has also been found to be of importance, as old candidates are favored for low-status jobs and young candidates for higher-status jobs (Triandis, 1963). Taylor and Walker (1994) find that age is an important factor in recruitment processes in such a way that several companies have official and unofficial upper age limits (see also Loretto, Duncan and White, 2000). In advertisements of vacancies, age is often seen as a barrier for applying when an age interval is specified. Yet other information in job advertisements can also discriminate older job seekers as specifications of education, demands for qualifications, type of experience, etc. may convey that a younger person suits the job or company better than an older one (McGoldrick and Arrowsmith, 1992).

Our study uses the method developed by Büsch et al. (2006) and differs from most of the studies cited above in the following aspects: First, in our questionnaire study we use four different age groups where age is randomized so that we have 24 different questionnaires and a total of 12 different age specifications for each of the three male applicants. The introduction of four different age groups improves the setting of other studies as the notion of being old varies with the occupation and can apply to a wide range, i. e. between 25-60 years (see Büsch, 2004). It allows to yield more robust results and to test an alternative explanation for age dependent hiring probabilities. Second, a real job advertisement from a German newspaper is used; we developed the CVs of the three applicants together with the personnel manager of the respective company that had published the advertisement. Though the decision remains hypothetical, the decision 8 F o r P e e r R e v i e w frame becomes more realistic than in most earlier studies by psychologists. Third, our study is comparative, i.e., we examine whether different institutional arrangements in countries like Germany and Norway produce different results on age discrimination outcomes. To our knowledge, there have been no other comparative studies of age discrimination using such a questionnaire so far.

Background information on Norway and Germany

Based on historical and institutional differences between countries, Esping-Andersen (1990,1999) distinguishes between different welfare regimes. Norway is classified as a social democratic welfare regime together with the other Nordic countries. They are characterized by universalism, comprehensive risk coverage, generous benefit levels and egalitarianism. Germany on the other hand is classified as a conservative welfare regime. The essence of such a regime lies in its blend of status segmentation (occupational) of pension and health schemes, and reliance on the family as a welfare provider. Early retirement policies have in continental Europe become the main means to facilitate industrial restructuring (Kohli, Rein and Guillemard, 1993), and the employment management policies have been passive. The Nordic approach has been 'productivistic' in the way that the focus is on re-employment through retraining and reactivation programmes. The result is low levels of early retirement and high rates of participation in particular among women and older workers, and high average retirement age. Classifying countries according to their degree of labour market regulation Esping-Andersen (1999) argues that Norway has medium regulation while Germany has strong regulation. On the other hand the employment protection is considered by OECD ( 2004) as somewhat stricter in Norway than in Germany. Such differences make it interesting and relevant to compare the two countries, and below we will go more in detail describing differences between the countries which are good examples of social democratic and conservative welfare regimes.

The standard retirement age in Norway is 67 years, while the compulsory retirement age is 70. However, some professions and occupations have a lower retirement age, and law fixes some 9 F o r P e e r R e v i e w of these. There is no public early retirement scheme in Norway, but as in several other countries, institutional arrangements that were originally made for other purposes, notably unemployment benefits and disability pensions have been used as pathways to early retirement. By the end of 2004 as many as 311.000 persons received disability pension, i.e. 13.1 % of the work force. Older persons are entitled to unemployment insurance for an extended period. Persons who become unemployed when they are 60.5 years old can receive unemployment benefits until they reach the standard pension age of 67 years. The most important non-public early retirement scheme in Norway is Avtalefestet pensjon (AFP, "Early Retirement Pension Agreement"). This scheme came into effect as from the 1st of January 1989. The pension age in the scheme has been gradually reduced over the years, and has been set at 62 as of 1st of March 1998. The replacement rate is different for the various types of retirement schemes. This may lead to different economic incentives for the retirement pathway that is used. As there is no public early retirement system, the above mentioned schemes have been extensively used by Norwegian companies and employees, especially disability pension and AFP (Dahl and Nesheim, 1998).

Our brief description of the German retirement system is focused on West Germany since, due to the transition, many temporary regulations were introduced. Even though the standard retirement age in Germany is 65, the actual retirement age is lower, i.e., on average around 60 in West Germany. One reason has been, and for a certain age group still is, the possibility to go into early retirement by the pathway of unemployment by the age of 58. Nowadays -due to the Social Security Reform of 1992 -only persons born before 1982 are still entitled to receive this kind of retirement pension. Since, in Germany, the social security system was still facing serious financial problems, a law was implemented in 1996, which prescribed a higher retirement age for older workers receiving unemployment benefits. In the same year, a partial retirement for older workers was introduced to give persons an incentive to postpone retirement. Another important pathway to retirement is the disability pension. In 1981, 68 % of male workers retired via this pathway (Börsch-Supan, 1998) in 2001 only 15.9 % of all new pensions for workers in West Germany were due to reduction in earnings capacity [START_REF] Vdr | VDR Statistik Rentenzugang des Jahres 2001 einschließlich Rentenwegfall, Rentenänderung/Änderung des Teilrentenanteils[END_REF].

An additional notable background feature for the comparison of the two countries is the unemployment and labor force participation rates of older workers. The unemployment rate directly influences the opportunity to discriminate in the hiring process. If there is no queue there is little room for discrimination.

Older workers in Norway have a lower unemployment rate than other age groups: 1.6 % for the 55-64 age group compared to 2.6 % for the 25-54 age group in 2001. This is one of the lowest unemployment rates in the age group 55 and older in all OECD countries. In 2004, 16.7 % of all unemployed aged 55+ had been out of work for more than one year. The corresponding percentage for unemployed aged 25-54 years is 7.7 %. The average length of an unemployment spell increases with age. For the oldest group it is 30.4 weeks. In contrast, the unemployment rate of older workers in the reunited Germany is almost the highest rate in the OECD countries.

In 2001 it was 11.2 % compared to 7.5 % for the 25-54 age group. The labor force participation rate in the 55-64 age group is 41.5 % in Germany and 68.5 % in Norway in 2001 (OECD, 2002).

In September 2001 39.2 % of all older unemployed in Germany were long-term unemployed, i. e. two years and longer (Bundesanstalt für Arbeit, 2001).

Finally, the dismissal protection laws that may also influence hiring decisions (see, e. g., OECD, 1999) are rather similar in both countries as the legal dismissal period increases with tenure from one month up to 6 month in Norway, and 7 month in Germany (see table 1).

However, the maximal dismissal period is age-dependent in Norway but not in Germany. Contrariwise, in Germany employers have to follow determined social criteria for redundancy that include among other things the age of the employee. These criteria are, however, not explicitly specified but are subject to firm internal negotiations. This aims to guarantee socially acceptable selection processes for redundancy.

Hypotheses and methods

In this section we set up our hypotheses and describe the methods used to generate the data.

Furthermore we explain briefly the concept of young, age-neutral and old job positions.

The above description of the situation of older workers shows that in Norway, there are a higher retirement age and a higher participation rate of older workers in the labor market. In Norway the labor market situation in recent time has been stable and employees remain in their working positions. Older workers in Norway have a lower unemployment rate than other age groups. In Germany, however, the opposite is true. The unemployment rate is not only higher for older workers than for younger age groups but it is in general considerably higher.

Therefore, we expect that the degree of age discrimination will differ between the two countries with Norway being the country where the applicant's age has less influence on the hiring decision:

H 1 More age discrimination regarding the hiring decision will be observed in Germany than in Norway.

Since we also assess subjective expected productivity measures in our questionnaire study 12 (1957). Therefore, in line with our fist hypothesis, if there are any differences in the assessment of applicants' productivities:

F
H 2 The differences in the expected productivities between young, middle-aged, and older applicants will be larger in Germany than in Norway.

An alternative explanation for age dependent hiring probabilities is the prospective time to recoup human capital investments. The longer the prospective employment term the higher is the potential return on human capital investments. If this argument drives our subjects' decisions the disparity in hiring probabilities should increase with the average age of the applicant pool: Let the relative advantage of one applicant over another be defined as the ratio of the prospective employment terms. As we keep the age gap (14 years) in the applicant pool constant and only manipulate the average age, the relative advantage of the youngest over the oldest applicant in the group increases with the average age of the group.

H 3 The hiring probabilities depend on the age group of the whole applicant pool.

The higher the average age the less likely is the hiring of the oldest applicant.

As mentioned previously, we want to identify whether older applicants with the same qualifications are treated differently as compared to younger applicants. Since there is some evidence that certain jobs or positions have age norms, or are more appropriate for particular ages, it is important to identify an age-neutral position in a first step. By using an age-neutral position, we avoid identifying job discrimination, i. e. the job is seen as not suitable for the applicant (Perry et al., 1996), instead of applicant discrimination.

One method to identify age-neutral positions was developed by Cleveland and Landy (1987).

In their study, managers were asked to complete either a frequency grid questionnaire or a 13 We used this method in a pre-study in both countries. In contrast to Cleveland and Landy (1987), we provided the participating students not only with job titles but they also received some background information of the respective positions: They were supplied with real job advertisements of 20 jobs selected from the German newspaper Frankfurter Allgemeine Zeitung. 1 . We concentrated on white-collar positions that are not physically demanding because there is some evidence in the literature that it is possible that physical strength decreases with age. Further, all vacancies were for permanent positions, since younger workers are overrepresented in fixed term positions (see, e. g. Schömann and Kruppe, 1994), and we want to avoid such unduly biases. In both countries we used the same descriptions of jobs and the corresponding companies.

F
In Norway, we made some minor adjustments to allow for a more representative picture. The adjustments concern only the largest companies since Norwegian companies are rather small on average. They have a smaller number of employees and lower annual turnovers.

After having identified a position that was age neutral both in Germany and Norway, we continued with the main questionnaire study. This consisted of four different tasks: In the introduction, students were asked to assume they were assistants of a personnel manager. The items. The third task was to mark the adequate wage level for each applicant. Participants were explicitly requested to use the wage level as a measure for productivity. In the questionnaire we also indicated the real wage range for this kind of position as a support. Last but not least, they had to decide whom of the three applicants they would hire given that all applicants would receive the same salary. Thus, the effects of the seniority principle in remuneration schemes should be ruled out.

In order to identify the degree of age discrimination in the hiring process the age of the applicants was the only systematically manipulated variable. We used four different age groups (see table 2). In total we had 24 distinct questionnaires since the various ages where assigned in all possible permutations within one age group to the three different applicants leading to 12 age specifications for each candidate. (1996) who described only two applicants with an age gap of 25 years to their subjects, an age gap of only 14 years is considerably less salient. This is important since in the questionnaire the real purpose of our study was hidden. Such knowledge obviously would affect the answers of the respondents, and most likely in a way that would reduce the study's potential for detecting age discrimination.

Empirical results

We ran the pre-study in Germany and Norway to make sure that the position used in the the main questionnaire study was seen as age neutral in both countries. In Norway, 28 and 26 students from the economics department at the University of Bergen, respectively, filled in the two questionnaires types. In Germany, 26 students of the economics and business department of the Humboldt-University of Berlin filled in the first and 35 the second questionnaire type.

In total, six positions in Norway and seven in Germany were identified as age neutral (see appendix, table 10 and11). The overall evaluation of eight positions differed between Germany and Norway. In six of these eight cases, the answers differ in only one of the two questionnaires.

However, no job associated with young persons in Germany was seen as an old person's job in Norway. The position used in the main study, Project-Engineer in Total Quality Management, was seen as age neutral in both countries.

In Norway, 91 students filled in the main questionnaire (35 female, 44 male, and 12 not reported), and in Germany 174 students (87 female, 78 male, and 9 not reported) participated.

The students were enrolled at the same departments as in the pre-study. But, no student participated in both studies. In April 2002, we mailed the questionnaire to 294 Norwegian personnel managers of large industrial companies. These are companies with 200 or more employees according to "Norges største bedrifter 2001" (Norway's largest companies). Two reminders were sent out, and in total 66 analyzable questionnaires were received, yielding a response rate of 22 %.

In East Germany, we excluded this part of the country. We received 87 answers, yielding a response rate of 11 %.

In Norway, 45 male and 21 female managers and in Germany 58 male and 29 female managers filled out the main questionnaire. In Norway, the mean age of respondents was 47, in Germany it was only 40. This difference is significant according to a one-sided Wilcoxon test (p < 0.001).

A first result is that in the student sample wages for all three age types (young, middle-aged, old) did not differ much (see table 3). 2 This may indicate that they chose wages according to expected productivity as it was asked in the questionnaire. Personnel managers seemed, however, to rely on a seniority-base remuneration scheme. They offered to the oldest applicant a slightly higher wage than to the two younger applicants.

In order to calculate a measure for the perceived expected productivity, we multiply the percentage of how important the participants evaluated each of the twelve capability items by the value they gave each applicant regarding the corresponding item. Expected productivity for all three age types is very similar in both countries. There is no significant pattern as one can see in table 4. This indicates that age stereotypes have at most only little influence on the overall productivity assessment in both countries and the students and personnel managers subsample. Thus, we can exclude statistical discrimination as the main source of age discrimination in our study.

A closer look at the individual items (see tables 5 and 6) reveals that in Norway younger applicants received a significantly higher evaluation than older ones for only one item by the students (flexibility). German students, however, rated younger applicants significantly higher for two items (ability to learn and flexibility). Additionally, they assessed older applicants more highly in terms of organizational ability. While in Norway personnel managers did not show any significant pattern over all items, German managers evaluated in the same way as German students, i.e., they gave younger applicants a higher score for the items ability to learn and flexibility. So, there is some evidence that age stereotypes affect decisions in Germany but not or 18 reported in table 9.

Note, that we model the hiring decision not as a multinomial choice model since the alternatives are correlated and thus the crucial assumption of independence of irrelevant alternatives is violated. We also do not rely on a nested logit model that can overcome this problem since some respondents chose not to hire only one but two applicants. We therefore rely on a random effects logit regression where the decision maker decides for each applicant whether he is hired or not.

By using this approach we control for the repeated measurement. the random effects and thus the effect sizes are slightly larger than in the corresponding marginal model. The order of significance is, however, not affected. The model is specified by

y ij =        1 if y ij > 0 0 otherwise (1)
y ij = βX ij + γ i + ij ( 2
)
where i is the index over the respondents and j over the three applicants. If y ij = 1, respondent i decided to hire applicant j. The matrix X denotes the explanatory variables including the constant, β is the vector of corresponding coefficients. For the residuals γ and ,

E[γ] = 0, E[γγ ] = 0, E[ |γ] = 0 and E[ |γ] = 0
, with E being the expectation operator, hold.

For the regressions, we used the complete data set of all 418 questionnaires comprising German and Norwegian students and personnel managers. The first model already reveals that there is indeed age discrimination in our questionnaire data to be found: The coefficient of the variable Age Rank (coded 1, 2, 3 for youngest, middle-aged, oldest applicant) is significantly negative, indicating that older applicants have a lower probability of being hired. Furthermore, the subjective expected productivity has a significant positive influence on the hiring probability, i.e., the higher the subjectively perceived productivity of an applicant the higher is the hiring probability.

The same is true for wage that was supposed to be a measure for expected productivity, too. Since we observe that applicant "Koch" with everything else remaining constant is hired significantly less often, indicating that his vita is perceived as being inferior to that of the two other applicants, we also included an appropriate dummy variable to account for this (see also Büsch et al., 2006).

Since one may have doubts whether the influence of Productivity Rank and Wage Rank on the hiring decision is linear a second model is estimated where dummy variables for each level of the two rank variables are included instead. Subsequently, we tested which dummy variables are significantly different from each other and from zero. By this procedure the set of variables that need to be included to account for perceived productivity differences is reduced. In model 3, we add a variable denoting a country and student interaction with Age Rank to assess differences between Germany and Norway and between students and personnel managers.

In general, we observe the same results as before but, strikingly, age discrimination is significantly less pronounced in Norway. This is indicated by the significantly negative coefficient of the variable Age Rank and the significantly positive coefficient of the interaction effect between Norway and Age Rank. Here Norway is a dummy that equals 1 if the respondent is Norwegian. The total effect of Age Rank in the Norwegian subsample is still negative, but the size in absolute terms is significantly smaller than in the German subsample. There seems to be no significant difference between the student subsample and the personnel manager subsample. As is indicated by the nonsignificant coefficient of the interaction effect between Student and Age Rank, whereby

Student is a dummy that equals 1 if the participant is a student. Indeed, removing the Student variables improves the AIC slightly (down to 1050) which is then on par with model 2.

Conclusion and discussion

The aim of this article has been to get a better understanding of the role of workers' age in the labor market. In contrast to many other studies regarding older workers this study has concentrated on the hiring process and not on promotions or the end of the career.

In a first step we have applied a method developed by Cleveland and Landy (1987) to identify an age-neutral job position. We improved their method by giving participants not only job titles for their evaluation but also actual job descriptions from a newspaper. Identifying an age-neutral job position was important to avoid the identification of job discrimination instead of applicant discrimination.

The main questionnaire consisted of an age-neutral job position including the job descrip- wage floor, alternative and complementary measures on the supply side that come to mind are for example wage subsidies for otherwise unemployed old workers, and a reduction of unemployment and early retirement benefits. Such measures are already implemented or are being discussed to be adopted in, e.g., France (see OECD, 2005) so that their effects can be studied in the near future.

Thinking about future research aspects one could vary the questionnaire in different ways.

Some adjustments like the following may be interesting. It could be worthwhile to find out whether the picture will change if age discrimination for a blue-collar instead of a white-collar position is investigated. Another point of interest could be to find out how the results change if -instead of an age-neutral position -an age-specific position is described. It might be equally

important to analyze whether or not the results will change if age becomes more salient. Further, the use of female applicants could be of interest. Finally, an obvious future project is an extension to other countries like, for example, France and Italy. Due to their generous public pension systems and the expected sharp increase in the dependency ratio over the next decades these countries would suffer considerably from age discrimination in hiring decisions. 1. Please weight the importance you attach to the criteria given below to fulfil the specific job requirements. Please indicate in the second column which weight you would give to these criteria. Please keep in mind that the sum of the percentages has to be 100. 2. Please evaluate now each applicant regarding the above mentioned items by making a cross (between "extremely low" (1) and "extremely high"( 9)). Please use a separate table for each applicang and make sure that there is only one cross in each row. 5, which wage you would offer the candidate in the case he would be hired. The wage level should reflect your evaluation of the applicant's productivity. The typical wage in the sector -including benefits like Christmas bonus -lies between 38,000 ¤ and 46,000 ¤. Please take these limits into account for your answer.

  Such measurement problems, the unobserved heterogeneity of individuals and firms, have lim-

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  PageEconomic research on discrimination tries to explain the different treatment of individuals on the grounds of their nonproductive characteristics. So far these were mainly gender or ethnic background.

  and laboratory experiments (though not labor market specific see, e. g.Büchner and Dittrich, 2002; Fershtman and Gneezy,

  . On the 1st of January 2001, a new law came into effect that distinguishes between a complete or partial reduction in one's earnings capacity. As a consequence,

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  The untranslated advertisements are provided in the appendix of the working paper version of this article 14

  Given the individual random effects, the residuals are uncorrelated. The estimated coefficients are consequently conditional on 22

  . Negative age stereotypes depict older persons as being potentially less employable, particularly for highly demanding and challenging positions. These characteristics such as age to "statistically discriminate" among workers. Several studies of employers' attitudes toward older workers in the labor market indicate that older persons seeking work are heavily discriminated by employers

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	stereotypes are used by employers when they have limited information about applicants and
	project onto individuals certain perceived group characteristics, i.e., they use easily observable
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Table 1 :

 1 Dismissal Periods in Germany and Norway Till the 15th or the end of the month. The legal dismissal period becomes only effective after six month of tenure. All other dismissal periods are till the end of the month.

	Length of	Dismissal Period in Months
	Tenure	Germany Norway If older than
	in Years			50 55 60
	below 2	1 a	1
	2	1	1
	5	2	2
	8	3	2
	10	4	3	4	5	6
	12	5	3	4	5	6
	15	6	3	4	5	6
	20	7	3	4	5	6
	a

  we are able to identify and control for different age stereotypes in the two countries that may lead to statistical discrimination. Any discrimination that can not be explained by perceived productivity differences can be attributed to a dislike of older persons in the sense of Becker

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	v i e
	w

  graphic rating scale. In the frequency grid questionnaire, students had to express their subjective assessment regarding the age distribution in each job. They had to indicate how many of one hundred persons they thought were in each age category(<20, 20-29, 30-39, 40-49, 50question. A job was defined as a younger person's position if 60 % of responses from each questionnaire type fell in the first three rating categories. A job was characterized as an older person's position if 60 % of the responses fell in the last four rating categories. And, a job was classified as age neutral if in each of the two questionnaires less than 60 % of the responses of both questionnaires were concentrated either in the first three or the last four response categories.

	59, 60-69, >70). In the graphic rating scale questionnaire, they had to state which of seven age
	categories (1=young, 2, 3, 4=middle-aged, 5, 6, 7=old) they thought would be predominant for
	the position in
	o r
	P
	e
	e
	r
	R
	e
	v i e
	w

Table 2 :

 2 Age assigned to applicants in the questionnaire asked to answer the questionnaire. Then they were given the description of the age-neutral position and the CVs of three hypothetical applicants. The first task was to state for twelve capability items -regarding different types of ability (see the appendix A.1.1)weights (expressed in per cent) of the importance they attach to the criteria for filling the position. Second, they had to indicate on a 9-point bipolar rating scale, i. e. a discrete scale from one (extremely low) to nine (extremely high), how capable each applicant was with respect to all

			Applicant
	Age Group Young Middle-aged Old
	I	27	34	41
	II	31	38	45
	III	35	42	49
	IV	39	46	53
	managers were just

  The use of several age groups allows us to identify whether age discrimination is based on relative age within a group or whether it is also dependent on the absolute age. The age gap between the youngest and oldest applicant in each age group was only 14 years. Consequently,

	to e. g. Bendick, Jackson and Romero
	F o r
	P
	e
	e
	r
	R
	e
	v i e
	w
	the applicant pool itself was characterized by a relatively homogeneous age structure. Compared
	15

  Non-parametric Kruskal-Wallis test. b One-factorial analysis of variance with correction for repeated measurement.

		Submitted Manuscript		Page 16 of 38
			Table 3: Wage in Euro
			Applicant		p-value
		Young Middle-aged	Old	KW test a ANOVA b
	Students
	Norway	42472	42101	43153	<0.001	0.495
		(9050)	(3027)	(4364)
	Germany 41698	41587	41703	0.890	0.880
		(2515)	(2433)	(2320)
	Personnel managers
	Norway	40637	43011	43254	<0.001	0.005
		(5300)	(2091)	(2162)
	r o Germany 40756 F (2797)	41721 (2655)	42471 (2884)	<0.001	0.001
		P
		e
			e
			r
			R
				e
				v i e
					w
	February and May 2002, we sent a total of 761 questionnaires to companies with more than
	200 employees in West Germany. To avoid a bias due to the special situation of older workers in
			16

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Note: Numbers in parentheses denote standard deviations. a

Table 4 :

 4 Expected productivity on a 9-point scale Non-parametric Kruskal-Wallis test. b One-factorial analysis of variance with correction for repeated measurement.

			Applicant		p-value
		Young Middle-aged	Old	KW test a ANOVA b
	Students
	Norway	5.91	5.78	5.93	0.232	0.503
		(0.94)	(0.88)	(0.89)
	Germany	5.84	5.82	5.78	0.565	0.872
		(1.11)	(1.01)	(0.98)
	Personnel managers
	Norway	5.53	5.64	5.57	0.922	0.732
		(0.65)	(0.83)	(0.84)
	Germany	5.59	5.76	5.57	0.704	0.595
		(1.30)	(1.43)	(1.27)

Note: Numbers in parentheses denote standard deviations. a

Table 5 :

 5 Students' evaluation of the different capability items

		Applicant		p-value
		Young Middle-aged Older	KW a ANOVA b
	Norway:
	1. Technological know-how	5.44	5.40	5.80	0.112	0.177
	2. Computer skills	5.89	5.75	5.98	0.529	0.482
	3. Organization capability	6.02	6.03	6.25	0.264	0.405
	4. Foreign language skills	5.66	5.35	5.29	0.394	0.184
	5. Capability to learn	5.84	5.90	5.80	0.740	0.827
	6. Flexibility	5.99	5.53	5.55	0.010	0.015
	7. Conscientiousness	5.74	5.68	5.81	0.488	0.745
	8. Reliability	5.74	5.65	5.66	0.461	0.859
	9. Capacity for teamwork	5.98	6.02	6.31	0.105	0.253
	10. Communication capability	6.09	5.80	5.99	0.115	0.391
	11. Persuasive power	5.35	5.53	5.61	0.210	0.321
	12. Commitment	5.85	5.73	5.68	0.736	0.680
	Germany:
	1. Technological know-how	5.93	5.87	5.86	0.879	0.884
	2. Computer skills	5.88	5.86	5.79	0.807	0.825
	3. Organization capability	6.20	6.33	6.54	0.038	0.048
	4. Foreign language skills	5.65	5.87	5.67	0.747	0.525
	5. Capability to learn	6.25	5.72	5.40 <0.001	<0.001
	6. Flexibility	6.34	6.14	5.60 <0.001	<0.001
	7. Conscientiousness	5.87	5.89	6.02	0.457	0.374
	8. Reliability	5.96	5.98	6.17	0.286	0.169
	9. Capacity for teamwork	6.40	6.24	6.26	0.689	0.512
	10. Communication capability	6.26	6.23	6.29	0.828	0.923
	11. Persuasive power	5.73	5.91	5.99	0.183	0.200
	12. Commitment	6.32	6.22	6.10	0.314	0.285
	a Non-parametric Kruskal-Wallis test.
	b One-factorial analysis of variance with correction for repeated measurement.
		19

Table 6 :

 6 Personnel managers' evaluation of the different capability items considerably less in Norway. This confirms our second hypothesis. Yet, due to the weighting these differences are equalized in the aggregate productivity measure.The close agreement between students and personnel managers is expected as, for instance, Gordon,Rozelle and Baxter (1988) already observed that the evaluations of students and employer interviewers are very similar.Concerning actual hiring decisions we observe for the German subsample a considerable favoritism of younger applicants (see table7) that cannot be found in the Norwegian subsample according to a non-parametric test for trend in proportions (seeArmitage, 1955). If we pool all data and stratify for the two countries we can test whether the four different age groups have an influence on the hiring decisions. First, the Woolf test shows that the assumption of homogeneous conditional odds ratios is not violated (p = 0.832). Therefore, we can use the

			Applicant	p-value
		Young Middle-aged Older KW a ANOVA b
	Norway:
	1. Technological know-how	5.84	6.12	5.98 0.601	0.476
	2. Computer skills	5.83	5.85	5.94 0.914	0.840
	3. Organization capability	5.60	5.84	5.81 0.446	0.375
	4. Foreign language skills	5.58	5.88	5.59 0.207	0.346
	5. Capability to learn	5.84	5.82	5.73 0.841	0.815
	6. Flexibility	5.63	5.39	5.44 0.286	0.274
	7. Conscientiousness	5.28	5.62	5.66 0.447	0.089
	8. Reliability	5.17	5.67	5.59 0.109	0.017
	9. Capacity for teamwork	5.95	6.02	6.03 0.986	0.913
	10. Communication capability	5.64	5.81	5.72 0.789	0.631
	11. Persuasive power	5.15	5.39	5.47 0.564	0.194
	12. Commitment	5.59	5.63	5.31 0.159	0.221
	Germany:
	1. Technological know how	5.37	5.60	5.79 0.114	0.239
	2. Computer skills	6.08	6.05	5.87 0.331	0.442
	3. Organization capability	6.01	6.21	5.81 0.234	0.142
	4. Foreign language skills	5.98	6.63	5.60 0.300	0.371
	5. Capability to learn	5.84	5.84	5.28 0.001	0.006
	6. Flexibility	6.03	6.01	5.54 0.009	0.014
	7. Conscientiousness	5.47	5.72	5.75 0.104	0.249
	8. Reliability	5.57	5.81	5.73 0.242	0.441
	9. Capacity for teamwork	6.11	6.26	6.05 0.444	0.456
	10. Communication capability	6.19	6.30	6.06 0.340	0.402
	11. Persuasive power	5.58	6.01	5.71 0.026	0.055
	12. Commitment	5.95	6.06	5.81 0.523	0.423
	a Non-parametric Kruskal-Wallis test.
	b One-factorial analysis of variance with correction for repeated measurement.
		20

Cochran-Mantel-Haenszel test for count data

(Agresti, 1990)

. The test indicates that there is no association between hiring decisions and age groups when adjusted for country (χ 2 = 5.173, df = 6, p = 0.522). Consequently, any discriminating behavior applies in the same way to all age groups, i. e. age discrimination in our study is as severe in the applicant age group 27-41 as in the age group 39-53. We cannot support the hypothesis derived from the recouping human capital investments argument.

If the stated wage offer is a measure for productivity the hiring probability of the applicant with the highest wage offer should be higher than the corresponding unconditional hiring probabilities given that all applicants will obtain the same wage if they are hired. As table

8

shows, this can be confirmed. Additionally, this table reveals that by controlling for perceived productivity measured as (highest) wage rank age discrimination can be found in all subsamples. Though, it is less pronounced in Norway.

Table 7 :

 7 Unconditional hiring probability Applicant p-value Young Middle-aged Old χ 2 test a Trend test b Non-parametric χ 2 test for count data. b Non-parametric χ 2 test for trend in proportions (see Armitage, 1955).

	Students
	Norway	35.16	27.47	37.36	0.331	0.753
	Germany 46.26	29.89	23.85 <0.001	<0.001
	Personnel managers
	Norway	28.03	43.18	28.79	0.115	0.926
	Germany 39.08	35.63	25.29	0.133	0.054
	a

Table 8 :

 8 Conditional hiring probability with respect to wage Applicant with highest wage p-value Young Middle-aged Old χ 2 test a Trend test b

	Students
	Norway	86.36	65.38	63.04	0.133	0.069
	Germany 77.27	67.19	54.10	0.022	0.006
	Personnel managers
	Norway	81.82	83.33	54.84	0.047	0.031
	Germany 73.68	76.67	47.62	0.023	0.019

a Non-parametric χ 2 test for count data. b Non-parametric χ 2 test for trend in proportions (see

Armitage, 1955)

.

Table 9 :

 9 Random effects logit regression on hiring decisions model is presented in table 9 as model 2. Concerning the Productivity Rank only when the applicant is ranked highest (rank = 3) or jointly highest with a second applicant (rank = 2.5) the hiring probability increases. Comparably, having at least rank 2 on the wage scale also increases the hiring probability.

	The resulting

  Since respondents in the Norwegian subsample are older than in the German subsample, this may drive the above result. We introduce five age groups. The first group of participants is aged 24 years and younger, the second is aged 25-34 years, the third is aged[START_REF] H | Production function and wage equation estimation with heteregeneous labor: Evidence from a new matched employer-employee data set[END_REF][START_REF] N | Zwischen Arbeit und Rente: Gesellschaftliche Chancen und Risiken älterer Arbeitnehmer[END_REF][START_REF] S | Insiders and outsiders in wage determination[END_REF][38][39][40][41][42][43][44] years, the fourth is aged 45-54 years, and the fifth is aged 55 years and older. All age groups show the same discriminatory behavior as indicated by nonsignificant coefficients on the Age Group : significant coefficients either. Using a continuous specification of the respondents' age leads to the same result. Discriminatory behavior is not age dependent in either Germany or Norway.Consequently, both German and Norwegian participants, regardless of their age, exhibited on average age-discriminatory behavior. The Norwegian participants, however, did show significantly less discriminatory behavior on average. Finally, we also observe that students do not behave significantly different from personnel managers as is indicated by the coefficient of the interaction effect between Student and Age Rank in model 3, which does not significantly deviate from zero.To test for an influence of the four different age groups used in the questionnaire we introduce the appropriate interaction terms: age rank of the applicant within an age group and a dummy for each of three of the four different age groups. The remaining age group serves as the base condition. None of these interactions is significant at the 5 % level. This confirms the result of the earlier Cochran-Mantel-Haenszel test. The age group of the applicants has no significant influence on the hiring decisions when we control for perceived productivity. Consequently, the prospective term of employment seems not be an issue here. A possible term of employment of 24 years (time until the oldest applicant in the youngest age group reaches the age of 65) does

	F o r F o r
	P P
	e e
	e e r r	3 Since
	the residual deviance of this revised model 3 is, however, lower (1028) than that of model 2 it is preferred to model 2. R not lead to a higher hiring probability than a term of employment of 12 years (oldest applicant in the oldest age group). R
	Finally, in model 4 we examine the influence of the participants' age group on discrimina-e To illustrate the different age-discriminatory behavior, we finally compute the conditional e
	v i e hiring probability of an applicant perceived as being the most productive according to expected productivity and offered wage, using the revised model 3. According to this, in Germany the probabilities in Norway are 91.50 %, 86.64 % and 79.61 %, respectively. v i e tory behavior. Age Rank variables. Including corresponding dummies for the Norwegian subsample yields no w youngest applicant is hired with a probability of 93.70 %, the middle-aged applicant with a prob-ability of 85.78 %, and the oldest applicant with a probability of 71.00 %. The analogous hiring w
	26

  tion and three short CVs, one for each applicant. In contrast to many other studies -mostly done by psychologists -age has not been a salient variable here. In our questionnaire we have four different age groups for the three applicants. The age gap between the youngest and the oldest applicant is always 14 years. In total we have 12 different age specifications for the same applicant.that even if the qualifications and perceived productivities are the same the applicants are not treated the same way just on the grounds of age. Statistical discrimination plays -if any -only a minor role. However, we observe a considerable difference in discriminatory behavior between Germany and Norway. In Norway there is significantly less age discrimination. Additionally, we found no significant difference between students and personnel managers and no dependence on the respondent's own age. Therefore, the results are probably influenced by the different working situation of older workers in the two countries. Norway has less unemployment and a higher participation rate of older workers. Consequently, there is more experience with working with older workers in Norway. One could also suspect that different norms and the institutional design have been of importance for the results. Anyhow, in Germany there is a strong tendency to discriminated against older workers in the hiring process. To meet the demographic challenges, it is necessary to reduce age discrimirequired by the European Directive 78, the policy maker should exercise great caution as such a law can also have harmful effects. And, on the other hand, there is no clear evidence that suggests older workers are more likely to be hired as a result of such legislation (seeAdams, 2004, for a study on age discrimination legislation and employment).

	F o r F o r
	P P
	e e
	e e
	As it is almost impossible to assess one individual's true productivity, as Börsch-Supan r r
	(2001) asserts, the perceived productivity of the candidate becomes an important determinant R R
	of the hiring decision. If the perceived productivity depends on non-productive characteristics e e
	of the candidate, as for example age, i. e. if the decision maker uses age stereotypes to adjust the individual assessment, he statistically discriminates the candidate. To identify statistical dis-v i e v i e crimination and control for it, the questionnaire also asks for the evaluation of twelve capability items and their relative importance for the position in question. Discrimination that cannot w w
	be explained by perceived productivity differences results from a dislike in the sense of Becker
	(1957).
	In this study, we have focused only on the demand side for 'old labor' . As the generosity of
	Even though age has not been a salient parameter the older applicant has a significantly lower
	social welfare systems in Germany and Norway may also induce too high wage expectation of
	hiring probability than the younger one independent of the actual age group. Regarding the
	older workers given their productivity and as social benefits or early retirement pensions set a
	expected productivity the evaluation has not differed much with varying age. We can conclude
	27 28

nation. So that applicants with the same expected productivity are treated equally -regardless of their age. The reason for the "dislike" of older persons in Germany could be that, in contrast to Norway, an employee's age in Germany seems to be closely connected with hierarchical principles. In that case an employer in Germany might try to avoid hiring an older applicant for a low status position. Additionally, (though ruled out in our study) the seniority principle in remuneration schemes puts a higher price tag on an older employee's job performance. Changing these customs is only possible if the general norms of the society are altered -a very slow process that would last for some generations. Yet, when introducing a law against age discrimination, as it is

Table 1 :

 1 Criteria and their weights

	Criterion	Weight in %
	Technological know-how
	Computer skills
	Organization ability
	Foreign language skills
	Ability to learn
	Flexibility
	Conscientiousness
	Reliability
	Capacity for teamwork
	Communication ability
	Persuasive power
	Commitment
	Sum	100%

Table 2 :

 2 Name of the applicant: Mr. Müller

	Page 31 of 38		Submitted Manuscript
		1	2	3	4	5	6	7	8	9
		extremely very	pretty middle pretty		very	extremely
	Criterion	low	low	low	low	rate	high	high high	high
	Technological know-how
	Computer skills
	Organization ability
	Foreign language skills
	Ability to learn
	Flexibility
	Conscientiousness
	Reliability
	Capacity for teamwork
	Communication ability
	Persuasive power
	Commitment
				31

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

Table 3 :

 3 Name of the applicant: Mr. Schmidt

		1	2	3	4	5	6	7	8	9
		extremely very		pretty middle pretty		very	extremely
	Criterion	low	low	low	low	rate	high	high high	high
	Technological know-how
	Computer skills
	Organization ability
	Foreign language skills
	Ability to learn
	Flexibility
	Conscientiousness
	Reliability
	Capacity for teamwork
	Communication ability
	Persuasive power
	Commitment

Table 4 :

 4 Name of the applicant: Mr. Koch

		1	2	3	4	5	6	7	8	9
		extremely very		pretty middle pretty		very	extremely
	Criterion	low	low	low	low	rate	high	high high	high
	Technological know-how
	Computer skills
	Organization ability
	Foreign language skills
	Ability to learn
	Flexibility
	Conscientiousness
	Reliability
	Capacity for teamwork
	Communication ability
	Persuasive power
	Commitment
	3. Please indicate in table

Table 5 :

 5 Applicants and their wages Name of the applicant Annual salary in ¤ (gross) Please write now the name of the applicant you would hire, under the assumption that all applicants would receive the same salary.Please comment shortly on your decision: [about 12 lines of empty space]Finally we would like to ask you the following questions: In how many hiring decisions (approx.) have you been involved so far?Here is now space for your additional remarks: [about 12 lines of empty space]

	Mr. Müller
	Mr. Schmidt
	Mr. Koch
	4. Name of the applicant:
	32

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

The significant Kruskal-Wallis test result for Norwegian students is due to the high variance of wages for 'young' applicants. The means are not significantly different.

The Akaike Information Criterion is a model selection criterion that discounts the model fit by the number of explanatory variables. A smaller AIC statistic is preferred. It selects the model with the best fit while still being parsimonious.

Acknowledgements

We greatly benefited from helpful comments by Bengt-Arne Wickström, Alf Erling Risa, David Neumark, one anonymous referee, and the participants of the 2004 EEA meeting in Madrid. We gratefully acknowledge financial support from the Ruhrgas Foundation and the Swiss National Bank.

38

A. Appendix

A.1. Material for the main study A.1.1. Questionnaire This questionnaire describes a hypothetical employment decision: In the enterprise of the XY group they have to decide whom they would hire and which wage the applicants should receive. On the next page you receive the description of the according job position and a short profile of the three applicants. Afterwards you are asked to evaluate the three applicants regarding 12 items as well as to make suggestions for the level of the salaries. Please do not forget to indicate whom you would hire.

The job description can be seen in the following job advertisement: Project Engineer in Total-Quality Management We are an enterprise of the group XY which is in the European market leader in the industrial metrology. 5700 employees in more than 50 high tech enterprises worldwide make a turnover of more than 1 billion Mark per year. Among our customers are top enterprises from telecommunication, satellite technology, medical technology and the automobile industry. In the area of circuits boards we are one of the best producers worldwide. Tasks:

• Extension and improvement of quality management • Management and implementation of quality improvement projects • Analysis of processes and statistical summaries • Cooperation in problem-solving teams coming from different departments • Support of ideas of co-workers All three applicants fulfill the necessary hiring requirements. They have an engineer diploma and two years of sector specific job experience. Below there are further details about the three candidates:


Eduardo Acosta-González

Fernando Fernández-Rodríguez
email: ffernandez@dmc.ulpgc.es

Julián Andrada-Félix

Estimating

Eduardo Acosta-Gonzalez

Julian Andrada-Felix

Fernando Fernandez-Rodriguez

ESTIMATING TIME-VARYING VARIANCES AND COVARIANCES VIA NEAREST NEIGHBOUR MULTIVARIATE PREDICTIONS: APPLICATIONS TO THE NYSE AND THE MADRID STOCK EXCHANGE INDEX

Keywords: Nonparametric estimation, Stock market indexes, Variance and covariance prediction Nonparametric estimation, Stock Market Indexes, Time-varying variance and covariance prediction. JEL classification: C13, C14, G15

HAL is

I. Introduction

Cross-country covariances of asset returns play a key role in international risk management and portfolio diversification. So, potential benefits from international diversification from domestic investors are significant if crosscountry covariances are small. However, investors may not be able to diversify away much domestic risk if the cross-country covariances are large.

Since the market crash of 1987, a wide range of literature has emerged investigating the contagion phenomenon and the fundamental factors which are affecting the cross-country stock return correlations. A determining paper was [START_REF] Roll | Price volatility, International Market Links and their Implications for Regulatory Policies[END_REF] which presents a survey on the link of international stock markets, signalling that international correlations of returns increased dramatically during crash periods. Several seminal papers focused their attention on analyzing how news from one international market influences other markets` volatility processes (see Engle et al., 1990;[START_REF] Hamao | Correlations in price changes and volatility across international stock markets[END_REF]King andWadhawani, 1990, among others).

Other papers have established that correlations across the indexes, like their unconditional sample counterparts, are typically nonnegative (e.g. [START_REF] Koch | Evolution in dynamic linkages across daily national stock indexes[END_REF][START_REF] Koch | Evolution in dynamic linkages across daily national stock indexes[END_REF][START_REF] Engle | Autoregressive conditional heterocesdasticity with estimates of the variance of United Kingdom inflation[END_REF][START_REF] Engle | Common volatility in international equity markets[END_REF]. This empirical fact has also been corroborated by papers such as [START_REF] King | Volatility and links between national stock markets[END_REF] or [START_REF] Darbar | Co-Movements in international equity markets[END_REF]. More recently, literature asks if the spread contagion is due to economic and/or financial links between the base country and secondary country, determining which channels of financial (see Collins and Gavron, 2004 and other papers enclosed).

The methodology employed for estimating variances and covariances of asset returns are also crucial. As [START_REF] Darbar | Co-Movements in international equity markets[END_REF] point out, if the correlations are time varying, examining sample correlations may be inadequate because the time path of conditional correlations reveals information that cannot be obtained by simply computing the sample correlation statistic. The sample correlation coefficient may also be a misleading measure of independence between two markets. For instance, a large value of a sample correlation may be driven by an episode of unusually high conditional correlation.

ARCH family models (see [START_REF] Engle | Autoregressive conditional heterocesdasticity with estimates of the variance of United Kingdom inflation[END_REF] have been one of the most popular frameworks for modelling time-varying variances of asset returns.

The ARMA-ARCH model rests on the assumption that the time series are linear in mean but nonlinear in variance. Nevertheless, several nonlinear and no parametrical alternative models have been considered recently. If we consider the hypothesis that the financial series have a nonlinear structure in mean, a very well-known model for predicting the returns are the Nearest Neighbour (NN from now on) prediction method.. In this paper we propose a way of estimating time-varying variances and covariances when the nonparametric NN multivariate estimator method is used to predict returns.

In ARCH approach literature it is very common to use a multivariate framework for modelling time-varying covariances among international financial markets. In this case, there is a high number of parameters which has to be estimated. With N series, N(N+1)/2 processes, which characterize 4 the variance covariance matrix, need to be estimated. So, the imposition of restrictions is necessary to reduce the number of parameters of the model to be estimated (see [START_REF] Engle | Common volatility in international equity markets[END_REF].

The aim of the paper is to propose a different approach for estimating the time-varying covariance matrix using nonparametric local linear models. In our methodology the volatility of an observation is associated with the risk of an NN in-sample prediction. In some extensions, the NN procedure involves regression by ordinary least squares (OLS) of the future evolution of the k nearest neighbours chosen on their preceding histories. However, OLS is efficient only when the contemporaneous correlation of the OLS residuals do not exist, otherwise the estimators are inefficient. In this paper we use the seemingly unrelated regression (SUR) estimation methods to estimate the model [START_REF] Zellner | An efficient method of estimating seemingly unrelated regression equations and tests of aggregation bias[END_REF]. In this context we call this technique the locally-adjusted seemingly unrelated regression (LASUR) model. This will not only be able to obtain the predictions of the series but also the time-varying variances and covariances. So, future volatility and co-variability, one-step ahead of two series, is associated with the prediction error covariance matrix of an NN-LASUR prediction. To illustrate the use of this technique we analyse the time-varying variances and correlations between the daily returns on two equity stock market indices, the NYSE and the MSEI in the context of in-sample prediction.

Following [START_REF] Härdle | Applied Nonparametric Regression[END_REF], the nonparametric approach to estimating a regression curve has four main purposes. First, it provides a versatile method of exploring a general relationship between variables. Second, it gives predictions of observations yet to be made without reference to a fixed Besides, we add three additional purposes related to the specific covariances of stocks correlation problems:

• Our non-parametric method is robust to extreme values estimating volatilities and correlations guaranteeing that these measures are not affected by the stock market slumps. Given the dramatic changes in the stocks co-movement patterns around market crashes we used a nonparametric method in order to develop a precise study of stock indexes correlation in these periods as well as guaranteeing that the volatility and correlation will be not affected by the extreme values.

• As opposed to parametric models for estimating the volatility (like ARCH family models), our non-parametric model produces normal standardized residues or standardized residues very close to normality • Our non-parametric model is not affected by the possible existence of structural changes.

The plan of the paper is as follows. In section 2 the technique is developed. Section 3 describes an illustrative example of the LASUR procedure that uses real data sets, namely the New York Stock Exchange (NYSE) and the Madrid Stock Exchange Index (MSEI). In section 4 we show the conclusions. and predicting time series (see [START_REF] Härdle | Applied Nonparametric Regression[END_REF][START_REF] Green | Nonparametric Regression and Generalized Linear Models[END_REF][START_REF] Hastie | The Elements of Statistical Learning[END_REF].

F

In order to predict an observation 1 Then we can model the data locally as

+ t x ,
d d d d t t t t Y X = + (3)
where d t is a perturbations vector of size k, d t X is a matrix of size (k,d+1) formed from the nearest neighbors row-vectors selected from d Z , plus a column of ones to take into account the constant in the model: ( )

1 1 1 2 2 2 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) 1 ... 1 ... . . . ... . 1 ... k k k t t t d t t t d d t t t t d x x x x x x X x x x = , (4)
1 , ( ) ˆ( ) '( ) ( ) '( ) d OLS d d d d t t t t t X X X Y = . (6)
For the predictions of 1

+ t
x , the observations of the vector d t x are used as explanatory variables, so , ( ) 1

d d OLS t t t x x + = ) . (7)
This procedure may be generalized to the case of several simultaneous time series. In this case, we use the cross information of several time series in forming a predictive vector. There have been several practical attempts in finance, such as [START_REF] Mizrach | Multivariate Nearest-Neighbor Forecasts of the EMS exchange Rates[END_REF] Following (3), ( 4) and ( 5) we can model the data locally with two equations:

1, 1, 1, 1, 2, 2, 2, 2, d d d d t t t t d d d d t t t t Y X Y X = + = + . ( 9
)
Observe that the equations in (9) are seemingly unrelated although the information for selecting 1,

d t X and 2, d t
X are obtained in (8) using the simultaneous histories. The purpose of model ( 9) is to collect the multivariant information of both series and, at the same time, to have a minimum number of parameters to be estimated with the end of avoiding the curse of dimensionality.

The OLS estimation of ( 9) is efficient only if the contemporaneous correlation of the OLS residuals do not exist, otherwise OLS is inefficient.

When the contemporaneous correlation between 11 be more efficient to estimate the two equations jointly, rather than to estimate each one separately using OLS. The appropriate joint estimation technique is known as seemingly unrelated regression estimation (SURE), [START_REF] Zellner | An efficient method of estimating seemingly unrelated regression equations and tests of aggregation bias[END_REF], that in this context we shall call the locally-adjusted seemingly unrelated regression (LASUR).

We can rewrite (9) as

+ = X Y ( 10
)
where

= d t d t X X X , 2 , 1 0 0 , 1, 2, d t d t Y Y Y = , = d t d t , 2 , 1 , 1, 2, d t d t = . (11)
The

d d i t j t ij k E I =
for i,j=1,2. The identity matrix I k is of dimension k and is the Kronecker product. In this case cannot be written as a scalar multiplied by a 2k-dimensional identity matrix. It follows that the locally adjusted generalized least squares estimator: 6) is then equal to (13). The second condition is when all the explanatory variables in each equation are identical in name, ( )

( ) ( ) 1 , ( ) 1 1 ˆˆ' ' d LASUR X I X X I Y = ( 13
1, 2, d d t t X X =
what it is no possible in the procedure described in this section.

The aim of the paper is to propose a different approach for estimating the conditional covariance matrix using nonparametric local linear models. In finance, volatility is associated with the risk of a specific prediction. In the ARCH [START_REF] Engle | Autoregressive conditional heterocesdasticity with estimates of the variance of United Kingdom inflation[END_REF] and GARCH (Bollerslev, 1986) approximations, time series volatility is measured by means of the conditional variance of its unexpected component, that is, with the risk of an ARMA-ARCH prediction. In this paper, the volatility of an observation is associated with the risk of an NN in-sample prediction. Future volatility and co-variability, one-step ahead of two series, is associated with the prediction error covariance matrix of a NN-LASUR prediction.

+ + + = + + = ( ) ( ) 1 ' 1 ˆ' t t P X I X P + . ( 19
)
Note that ( 19) is the covariance matrix ˆplus a positive definite matrix. Thus, the future volatility and co-variability one-step ahead of both series depends not only on the stochastic element in the system ˆ, but is also a function of t P and matrix X. The t P matrix contains the vectors 1,

d t
x and 2, d t

x that have been used to find the nearest neighbours which are in the X matrix.

III. Empirical Results for NYSE and Madrid Stock Exchange Indexes

To illustrate the use of this technique we analyse the time-varying variances and correlations between the daily returns on two equity stock market indexes, the New York Stock Exchange (NYSE) and the Madrid Stock Exchange Index (MSEI). As our task is to describe the relations in the past between these two indexes throughout the sample period, therefore the insample prediction of variances and correlations are appropriated.

Nevertheless, in other cases the out-of sample prediction could be carried out. The data consist of daily close-to-close returns for indexes of the two equity markets from January 2, 1991 to December 30, 2002, which provide a total of 2916 observations. A graph of the data is provided in figure 1.

[Figure 1]

[Table 1]

In table 1 we present a statistical summary based on the first differences of the logarithms of the stock market indexes (multiplied by 100). The daily average return for both series is less than 1 per cent. The standard deviation of the returns varies from 0.94 per cent per day for the NYSE, to 1.27 for the MSEI. In both cases, the returns are skewed to the left and the unconditional distribution of returns has kurtosis coefficients in excess of 3, implying fatter tails than the normal distribution. According to the Jarque-Bera test, we strongly reject the null hypothesis of normality in both cases. Finally, we report the sample correlation coefficient with a value of 0.4056.

Following [START_REF] Casdagli | Nonlinear Modeling and Forecasting[END_REF], the number of neighbours k=28 and the embedding dimension d=6 have been estimated by minimizing the sample prediction error.

[Table 2]

In table 2 we report statistics for the estimated time-varying covariance and correlation matrices. An important use of the time-varying observations. The prediction intervals are obtained by

) ( * 2 ˆ1 , 1 , + + ± t NYSE t NYSE e SE x . (20)
where SE(•) represents the time-varying standard error.

[Figure 2]

For the full sample, the first differences in logarithms of the NYSE lie outside the prediction intervals at 6.8 %. For the differences in logarithms of the MSEI at 6.5%, it implies that LASUR estimation of the time-varying variance is able to collect correctly the risk associated with the predictions since similar results are expected for any measure of dispersion if the distribution of the data is bell-shaped, and anyway these percentages are clearly smaller than those corresponding to Chebyshev's inequality.

The upper part of Figure 3 shows the centred moving averages for 101 observations to eliminate irregular fluctuations from the time-varying variances of both indexes. The behaviour of these two series seems similar, but MSEI variances are around the double of those corresponding to NYSE. (0.00) (0.00)

t N t C D R = = (22)
1 2 , ˆ0.89 0.005 0.13 (0.00) (0.00)

t M t C D R = = (23)
where ˆt C is the fitted time-varying correlation between NYSE and MSEI. , N t D , and , N t D are the time-varying standard deviations of NYSE and MSEI, respectively. P-values are given in brackets. Other functional forms have been considered but the reciprocal gets a good fitting. As Figure 4 shows, for both markets when volatility increases, correlations increase approaching asymptotically to the limit of 0.89. Figure 4 illustrates the relation represented in equations ( 22) and ( 23).

[Figure 4]

In Figure 1 As table 2 shows, although the series sometimes experience negative correlations, such events are rare. They occur less than 10 per cent of the time, suggesting the conditional correlations across the indexes, like their unconditional sample counterparts, are typically nonnegative. This is a typical empirical finding (e.g. [START_REF] Koch | Evolution in dynamic linkages across daily national stock indexes[END_REF][START_REF] Koch | Evolution in dynamic linkages across daily national stock indexes[END_REF][START_REF] Engle | Autoregressive conditional heterocesdasticity with estimates of the variance of United Kingdom inflation[END_REF][START_REF] Engle | Common volatility in international equity markets[END_REF]. However, the range of the estimated correlations is considerable.

This fact has been found in other research as in [START_REF] King | Volatility and links between national stock markets[END_REF] or [START_REF] Darbar | Co-Movements in international equity markets[END_REF]. In figure 5, we present the centred moving averages for 101 observations from the time-varying correlations. This figure shows that the time-varying correlations appear to increase with time.

[Figure 5] In this paper we present a technique for obtaining the time-varying covariance matrix for several time series for nearest neighbour predictors.

To illustrate the use of this technique, we analyse the time-varying variances and correlations between the daily returns on two equity stock market

  most significant in transmitting crises between countries

  Third, it provides a tool for finding spurious observations by studying the influence of isolated points. Fourth, it constitutes a flexible method of substituting for missing values or interpolating between adjacent X-values.

  is well-known in the literature of deterministic chaos, where the Takens (1981) theorem guarantees, under broad conditions, that a hidden deterministic dynamic may be mimicked in the d-dimensional space by the set of d-histories. With independence of the theory of deterministic chaos, nonparametric regression and local polynomial modelling methods propose similar procedures for modeling

  t is a vector of local parameters of size d+1 associated with the segments of d consecutive observations d t x . This vector can be estimated by OLS:

  evaluation of the accuracy of the NN forecast. In standard time series methodology, which uses constant variance ARMA processes, the variance of the forecast error does not depend on the current information set. If the series being forecasted by NN displays time-varying variances, the current information set can indicate the accuracy by which the series can be forecasted by NN. To ensure that the computed value of time-varying variance is reasonable, in figure2we present the first differences in logarithms of the NYSE and its prediction intervals for the last 50

  by the market trend. Taking the standard deviation as a measure of volatility we have estimated the next two reciprocal

  we have signalled two periods with different trends. The first one from 11/22/1994 to 08/25/2000 represents a bull market, and the second one from 08/25/2000 to the end of the sample represents a bear market. We have run the next regression to test whether there is any relation between trend market and correlations are given in brackets. The coefficient of the bear market is significantly different from zero but the trend market explains correlations poorly.

  figure 5.

Figure 2 .Figure 3 .Figure 5 .

 235 Figure 2. First differences in logarithms of the NYSE and the prediction

e w 6 II. Multivariant Nearest Neighbour Predictions with SUR Estimation

	Let { } T t t x 1 = be a time series of scalar observations. We introduce the method
	of local polynomial regression, where the underlying regression curve is
	locally and linearly approximated around a vector of d consecutive
	observations by a linear function, with the objective of getting an in-sample
	prediction of	1 + x . The out-of sample prediction is easily gotten just by t
	taking the sub-sample up to the current t-moment and disregarding the rest
	of the sample. The first step of this methodology consists of embedding the series o r
	P in a d-dimensional space, called the phase space of the time series.
	e Segments of d consecutive elements e r x x x x d t t t d t ) ,......, , ( ) 1 ( 1 =	t	=	d	,	d	+	,...., 1	T	(1)
	of the series, frequently called d-histories, are considered vectors in the R v e space d , and recorded in the matrix d Z .
											i
					d x	d x	1	...		1 x
					d x	1 +	d x		...		2 x
		Z	d	=	. t x	. t x	1	... ...	( 1 ) . t d x	(2)
					.	.		...		.
					T x	1	T x	2	...	T d x
	The parameter d is referred to as the embedding dimension, and each row-
	vector of the matrix

d Z in (2) is called the d-history. For the out-of-sample prediction of 1 + t x the last row of d Z is the 1 d t

x vector.

  )

	is the best linear unbiased estimator for . that will be unbiased on finite samples when the same d-dimensional vectors ,( ) ˆd LASUR has lower variance
	than ,( ) ˆd OLS in (6) because it takes into account the contemporaneous are used in each series. Once ,( ) ˆd LASUR is calculated it can be used to form a
	correlation between the disturbances in different equations. The covariance new estimator for ij using (17) that can be used again to obtain new values
	matrix of ,( ˆd LASUR is consistently estimated by ) of ,( ) ˆd LASUR and so on, in an iterative procedure until a convergence criteria
	is achieved. Besides, if the disturbances, 1, d t 2, d	t , follow a multivariate
	F o r ( , ( ˆ' d LASUR ) ( ) Cov X = normal distribution this estimator is also a maximum likelihood estimator. 1 1 I X (14) ) and the one step ahead prediction vector, which is denoted by 1 ˆt X + , is F There are two conditions under which ,( ) ˆd OLS is identical to ,( ) ˆd LASUR . The o r first is when all contemporaneous correlations are zero. In this case, is a
	obtained as: diagonal matrix and (	P P
									e e
	where					X	t	1 +	e r R e v 1, 1 ' ,( ) 2, 1 ˆt d LASUR t t x P + = = e r x + R e v	(15)
	t P	'	=	1, 0 0 1 x	t	1, 1 0 t x	.... . .			1, ( 1) 0 t d x	2, 0 0 1 x	t	i e w 2, 1 2, ( 1) 0 . 0 .... . t t d i e x x w	. (16)
				To obtain ˆin (13) we first estimate each equation by OLS and
	obtain the residual vector i ˆ. Consistent estimates of are given by
									ij	=	( ) ( ) ' , , d d ˆˆ, i t j t for i j k d	=	1,2	(17)
													12 13

Table 1 .

 1 Summary statistics for daily returns (multiplied by 100)

	NYSE	MSEI

Page 30 of 31 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	F o r
	P
	e
	e r
	R e v
	i e
	w
	2

Table 2 .

 2 Summary statistics for the estimates daily time-varying variances,

	covariances and correlations
		10th Per.	30th Per.	Median	70th Per.	90th Per.
	Variance	0.04*10 -3	0.07*10 -3	0.08*10 -3	0.11*10 -3	0.16*10 -3
	(NYSE)
	Variance	0.09*10 -3	0.12*10 -3	0.15*10 -3	0.20*10 -3	0.30*10 -3
	(MSEI)
	Covariance	0.002*10 -3 0.030*10 -3 0.052*10 -3 0.082*10 -3 0.143*10 -3
	Correlation	0.0137	0.3201	0.4919	0.6264	0.7839

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

Acknowledgment

This research is supported by the Spanish Ministry of Science and Education through project SEJ2006-07701.

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

The sample correlation between these two series is 0.38 indicating a positive relation. In order to investigate causal relations between these series we estimate the next bivariate regressions to apply Granger's causality test

where ,

N t

V and , M t V are the time-varying variances of the first differences in the logarithms of the NYSE and MSEI, respectively. The Wald statistics for the null joint hypothesis: 1 5 ... 0 = = = is rejected for each equation. This means that the process is a feedback system where

[Figure 3] Finally, in Figure 3 we have signalled the period from September to November 1998. In this time interval the largest slump took place in the sample period which corresponds to the Russian financial crisis. Our estimations during the index fall reflect an important increase in the variances in both markets, which diminishes until reaching a trough. Previous studies, some of which have been mentioned in the introduction, suggest that international correlation is much higher in periods of volatile markets and that market trends affect international correlations.

In our case, the correlation seems to be influenced by the volatility of both