Mareva Sabatier
email: mareva.sabatier@univ-savoie.fr

Myriam Carrère°1
email: myriam.carrere@grenoble.inra.fr

DO FEMALE RESEARCHERS FACE A GLASS CEILING IN FRANCE? A HAZARD MODEL OF PROMOTIONS

Keywords: promotion, glass ceiling, gender gap Promotion, Glass Ceiling, Gender Gap Code JEL: J16, C41 Promotion, Glass Ceiling, Gender Gap Code JEL: J16, C41

Our article aims at testing whether French female researchers face a glass ceiling, an invisible barrier to promotion. Using an original database from the National Institute for Agricultural Research, we estimate duration models of promotions. This methodology allows us to take into account censored observations and unobserved heterogeneity. Our results exhibit a significant gender effect, which does not contradict the glass ceiling hypothesis. Moreover, gender does not have a uniform effect. It interacts with other variables so that there exist factors that accelerate promotion, while others tend to slow it down.

Finally, the empirical literature does not refute the hypothesis that women are less likely to gain access senior position. This seems to illustrate the existence of a glass ceiling for academics, whatever the discipline. But, existing results are based on American or British data, countries which have very similar academic systems.

It could be argued that gender gaps result from a particular organization of academia which is unfair to females. It would be useful to test the glass ceiling hypothesis in another type of organization and the French academic system provides an interesting alternative framework. Indeed, French academia has a number of specific features that make it quite different from the USA or Great Britain (see Ginther (2001) and Euwals and Ward (2000) for a detailed description of each academic system).

First, in contrast to other countries, the academic sector is two-headed and is comprised of universities and national research laboratories. Each institution is independent and has its own working rules. For example, researchers working in one of the national research institutes have no teaching duties, unlike those working in universities.

Second, in the USA or Great Britain, academic careers depend on tenure rules.

After their PhD., young researchers are hired as assistant professors on a fixed term contract. Afterwards, for those who gain access to it, life-long employment (as Full Professor) is proposed. Promotion criteria include scientific achievements, such as the number of publications and their quality. French academia is organised quite differently. The key difference is that the life-time contract begins soon after hiring, whatever the institution (universities or national research 12 months probation and this occurs almost automatically. Civil servant status implies a life-long job and, for a given rank, a fixed wage scale. Two main ranks exist in each research institution: assistant professor (or its equivalent in national laboratories: the researcher rank) and full professor (or the senior researcher rank). For a given status, wages are fixed by a national collective agreement and are the same for all universities or research laboratories. Finally, no difference in terms of wages for a given level will be observed.

In France, the objective of seeking promotion is not to get tenure (since this is automatic). Higher wages and greater responsibilities (such as being a PhD.

advisor or managing a team of researchers) motivate researchers or assistant professors to become senior researchers or full professors. As in other countries, promotion to the senior rank depends on scientific achievements, which are examined by promotion committees.

Another difference is that all disciplines in French academia are organized according to this general framework: general hiring and career rules are common.

As stressed in the stylized facts, if the promotion process is studied, one finds that large gender differences exist. This suggests that, in spite of the different organization of the academic sector, French female researchers are also underrepresented in senior ranks, and this is a sign of a glass ceiling. The aim of this article is to test whether this hypothesis can be refuted or not on by studying promotion paths. As in the previous literature, we will take account of both observed heterogeneity, such as individual attributes and scientific achievements, which can explain promotions gaps and also unobserved heterogeneity, which is often neglected. As career paths in French academia can only be described by rank evolution, the gender effect is evaluated on the hazard of becoming a "Senior Researcher".

We do face one major difficulty though since, in France, no data set is generally available to study academic careers. In section two we explain how we have constructed a panel data set for researchers' careers. This data set allows us to follow a group of biologists, working at the National Institute for Agricultural Research, called INRA, one of the national research institutes in France. Focusing both on life scientists in only one institute will enable us to test the glass ceiling hypothesis with homogenous data (one discipline in one institute) and to provide the first study of this phenomenon for France.

II-The Data

As no dataset exists to describe the career paths of researchers in France, we have constructed one, based on administrative files from the National Institute for Agricultural Research (INRA). Founded in 1946, this As in other national research institutes, gender parity is nearly established in the "Researcher" rank, but, women are under-represented in the senior rank: 5.5% of researchers are female senior researchers. Furthermore, at INRA, the situation for female researchers is worse than in other public research institutes or universities.

In Table 1, it can be seen that the share of senior researchers among women is ten percentage points lower at INRA than in other public institutes.

[INSERT TABLE 1]

At INRA, the traditional career path is to begin at the Researcher rank and later possibly to accede to the Senior rank 2 . We focus on this particular promotion path. Promotion to the "Senior Researcher" rank occurs mainly through an internal competitive process. The promotion process is formal: available positions are published on INRA's website or in newspapers. Applicants have to submit their CV, an outline of their previous research activities (mainly realized during their tenure at INRA) and of their future projects. Promotion committees, composed of researchers from INRA and other institutes or universities, examine applications and make a first selection, on the basis on scientific achievements.

Selected researchers are then interviewed, ranked and eventually promoted. In the dataset, we can observe the whole of an individual's career at INRA and how long individuals stay in the Researcher grade before reaching the Senior 2 A small number of direct entries at the senior rank are observed and this very recently. This type of career cannot be regarded as a promotion at INRA and is not analysed in this study. We observe several cohorts of researchers. A dummy variable, COH1 (being hired at INRA before 1980), is created to capture potential cohorts effects, as in Ransom and Megdal (1993). These effects could reflect changes in the promotion process. Indeed, as in the French academic sector as a whole, recent recruitments and promotions seem to be more competitive than in the early eighties.

We also have information on several individual attributes. For example, we know if researchers have graduated from a Top University (TOP_UNIV). These universities, the "Grandes Ecoles", are considered, in France, as attracting the best students. We also know whether a researcher can act as a PhD. Supervisor (HDR). In France, a particular diploma, the "HDR"3 , is required to be able to supervise PhDs and our data indicates whether a researcher has this diploma. These two variables, TOP_UNIV and HDR, then could act as signal of a higher human capital and play a role in the promotion process.

Our data also contain information on the researchers' mobility. This mobility could result from a postdoctoral fellowship (POSTDOC) or a visiting professorship or sabbatical abroad, after being hired at INRA (MOB). Mobility is often viewed as an opportunity for acquiring new competencies and for networking. Developed networks through the scientific community provide higher opportunities for collaborations and could increase scientific achievements. Mobility could then boost promotions.

In contrast to other data sets used in the literature, our sample contains information on all aspects of the researchers' work. We know each research's publication record and, in order to complement this information, we add a third data set provided by the Science Citation Index (SCI) which gives us, for each publication, its impact factor (according to the journal index quality)4 . Using these two variables, we construct a publishing score (articles published weighted by the journal quality), reflecting publishing productivity (PUB_SCORE). Following Mc Dowell et al. (2001), this mixed indicator is preferred to a simple quantitative measure of publications, which ignores the visibility or reputation of the scientific work. In addition there is information on the degree of implication in scientific projects (as participant, NPROJECT, or coordinator, NPROJ_C) and in The richness of our data set may have a negative counterpart: scientific achievements might be endogenous. For example, the most highly motivated researchers could be the ones who have the most important activities and who are the most likely to be promoted. This type of mechanism probably underlies the career process. But, to be identified, such a process needs valid instruments.

Unfortunately, our dataset is not informative enough to allow us to test both determinants of scientific achievements and those of duration to promotion. Furthermore, our administrative data set does not gather information on personal characteristics, such as marital status and number of children or on research departments' activities. However, previous studies have found these variables to have a significant effect on the promotion process. Neglecting these attributes could generate an omitted variable bias and this point will be discussed in the next section. shows that there are large differences in the average researcher's profile according to gender and rank. First, large differences exist between individuals who have been promoted to the SR rank (column SR) and those still in R rank. 17.4% of senior researchers are women (20 percentage points less than the number of women in the sample). Those promoted have been recruited earlier at INRA, on average, in 1976INRA, on average, in (instead 1985 in the full sample). They also have lower publishing scores, and are more involved in administrative activities. Women tend to have been recruited more recently than men at INRA. Females also have higher publishing score than male and have fewer administrative activities.

[INSERT TABLE 2] III-Modelling the determinants of promotion duration

The descriptive evidence clearly indicates that women are under-represented in "Senior Researcher" position at INRA. Our aim is to test whether this gender differential remains after controlling for observed and unobserved heterogeneity.

Instead of estimating the probability of being promoted, we focus attention on the hazard rate, denoted ( )

t i
. This hazard rate can be written as follows:

( ) ( ) ( ) ( ) t S t f t T p t T dt t T t p t i ) ( / = + < = (1)
where T is the length of time passed in the "Researcher" rank, f(t) is the density distribution and S(t) the survival function. Using the model of Mc Dowell et al. (1999), can be viewed as the probability at time t that an individual's productivity exceeds the department productivity threshold (probability of being promoted), given that this productivity is lower at least until t (probability of being not promoted until t). As both individual productivity and the department's norm are latent variables, denotes the probability of becoming senior researcher, given that no promotion occurs before t.

Estimating this hazard rate involves the use of duration models (Lancaster, 1990).

This methodology allows us to take into account that 67.6% of the individuals are still in the "Researcher" rank at the sample date, that is more than two thirds of observed durations are right-censored. We estimate a parametric model (with an accelerated failure-time form) which allows one to control for both observed and unobserved explanatory factors. Kaplan-Meier estimates have shown that hazard rates are non-monotonic, and therefore a log-normal distribution 5 is applied.

In our parametric specification, the hazard rate, i , is assumed to depend on three arguments: a vector of observable characteristics i X , an individual specific effect, i v and an error term i .

The ( ) ( ) ( )

( ) ( ) i v i i i i dv v f v t S t S i = (2) with: ( ) ( ) [ ] i i i i t v t S ln / = , (3)
1 = k i kv k i v e k k v f i , where 1 = k (4)
From this general specification, three different models are estimated. Model 1 imposes the restriction that the unobserved heterogeneity terms are zero ( =0), while model 2 relaxes this assumption. In model 3 we introduce interaction terms between gender and the other explanatory variables. This should allow us to control for multicollinearity, as proposed by Mc Dowell et al. (2001). For each estimated model, robust t-statistics are calculated (White, 1982). The results are 3. They reflect the ceteris paribus effects of each covariate on the promotion duration. As accelerated failure-time models are estimated, a positive significant sign indicates that a given characteristic increases the duration to promotion, or equivalently decreases the promotion hazard.

First, let us focus on the importance of correcting for the unobserved heterogeneity. Model 2 provides an estimate of the parameter, which is significantly different from zero. This indicates that unobserved factors must be taken into account the model. We prefer therefore the model 2 to model 1, since neglecting the i v terms would introduce bias into the estimated effects, including the gender impact. More precisely, this would lead to a slight overestimate of the gender effect.

[INSERT TABLE 3]

Let us now look in at the effect of gender. As model 2 indicates an "average woman", i.e. a female researcher who would have the same characteristics than a male, has a longer wait until promotion. This result could be evidence of the glass ceiling hypothesis. But, more detailed comments can be made with the estimated hazard rate by gender (figure 1). These estimated hazards are evaluated for female and male average characteristics.

[

INSERT FIGURE 1] F o r P e e r R e v i e

w

If women have on average lower predicted hazard rates, we observe that this general result is not uniform throughout the career. In the first half of the career, women have lower predicted hazard rates. But, women have slightly higher rates from 180 months onwards. This result is obtained after controlling from observed and unobserved factors. It cannot be explained by omitted individual attributes.

A statistic explanation could be proposed. As females are promoted later than males (see below), females who have suitable competencies to be promoted are more numerous after 15 years career than male. We thus observe more females at risk in this period than males. Finally, the female promotion rate is higher.

However, higher female hazard rates at the end of the career do not make up for the lower rates in the first half. Another point strengthens this conclusion. The peak of the female hazard rate occurs later and is lower than the male peak.

Females are less likely promoted and when they are this tends to happen later.

Thus, in spite of differences during the career, the existence of a glass ceiling could not to be rejected. This fits in with what Kahn (1993), Mc Dowell et al. (1999) or Ginther and Hayes (2003) have found for promotions in USA. Despite strong differences between the French academic system and those in the US and UK ones, female researchers at INRA also face greater difficulties of getting promoted than their male counterparts.

Apart from this general result, model 3 provides evidence of interaction between gender and other covariates. This suggests that gender affects both promotion duration directly but also indirectly through the effect on explanatory factors of promotion. For example, being a female Ph.D. advisor (HDR) or having been graduated from a top university (TOP_UNIV) boosts promotion to the "Senior Researcher" rank. The significant impact of these two variables is not surprising.

Both generally act as a signal of higher competencies. More surprising is that these variables do not have a direct effect on promotion duration, that is no effect for men, but only a cross effect with the FEM variable. This could indicate that human capital accumulation through attending top universities and obtaining the "HDR" diploma are better exploited by females or that these signals play a greater role in the female promotion process than in the male one.

In contrast, mobility, captured through postdoctoral fellowships (POSTDOC) and mobility after entry at INRA (MOB), seems to produce a complex effect on female promotion. These two variables decrease the global promotion duration, which could confirm that mobility provides opportunities for networking and then accelerates promotions. But, for females, only mobility after the entry at INRA plays this role of a booster, whereas postdoctoral fellowships slow down their promotion. This finding could be explained in two ways. First, on the basis of sociological research on networking (Granovetter, 1973), it is possible that older networks become depreciated. This depreciation is, as for any capital, a natural process, but could be strengthened if relationships are not sustained. In our sample, females could have neglected their former networks, which have become inefficient. The second explanation is that postdoctoral fellowships held by female could be less in line with their recent research or more dedicated to teaching, as highlighted by Schneider (1998). Skills accumulated during this period would then not be essential for promotions at INRA, where researchers have no teaching duties. However, our data do not allow us to explore more these potential explanations in more detail. A third cross effect concerns gender and administrative activities, such as managing a research team (BOSS) or coordinating scientific projects (NPROJ_C), which slow down the promotion process for females. This finding is a bit surprising as administrative responsibilities are viewed at INRA as one of the promotion criteria. But, in our data, very few females are involved in this type of activity. Besides, these females seem to have more scientific achievements, in terms of publications. In contrast, researchers, mainly male, who have invested in management activities, have fewer publications. It could be that two strategies for promotion coexist: the first based on scientific achievements, publications or participating in projects, the second based on administrative responsibilities. In our data, the fact is that the choice of one of these two strategies seems to depend strongly on gender. Further investigations must be undertaken into the existence of this gender specialization Beyond these interaction effects, our results confirm two of the findings in the previous literature. First, there are cohort effects on promotion duration (COH1).

Promotions for younger cohorts are more difficult, probably because of a more competitive context: more researchers could apply for promotions positions, promotions are increasingly scarce. But, the cross effect between gender and cohort effect produces no significant effect. Unlike in Ramson and Magdal (1993) or Mc Dowell et al. (2001), the glass ceiling does not seem to be affected by a cohort effect. At INRA, no cracks in the glass ceiling appear. This could be explained by the fact that both women and men face the increased competition We also find that publishing scores (PUB_SCORE) increase hazard rates. This confirms that publications are a criterion in promotion success. But, the positive effect of publications is true only for recent cohorts (COH1*PUB_SCORE). This could be explained by the fact that gathering information on publications and on their quality is more precise for recent cohorts (see footnote 4). Our cross effect allows us then to correct for the possibility that for past cohorts, publications may have been measured with error.

IV-Conclusion

In spite of substantial evidence of the existence of a glass ceiling in French academia, no study has so far been undertaken to refute this hypothesis. We thus propose a first analysis of the promotion of French researchers. As there is no dataset available on researchers' careers, we begin by constructing a database which allows us to analyse the full career path and research activities of French researchers. We then focus attention on biologists' promotion duration to the senior rank at the National Institute for Agricultural Research. Using duration models, we conclude that females have a significantly lower hazard rate, in particular in the first half of their career, compared to their male counterparts. This result is obtained after controlling for both observed and unobserved heterogeneity. Furthermore, we find that gender does not have any uniform effect on promotion, but interacts with other covariates. This suggests that there exist accelerator and "slowing-down" factors for female promotion. Finally, our

I-Introduction

Whatever the profession [START_REF] Altonji | Race and Gender in Labor Market[END_REF], for an overview and Albrecht, et al., 2003;Joy, 1998;Spurr & Sueyoshi, 1994, for studies of specific jobs), the literature provides a large amount of evidence for gender-related differences in earnings and promotion. Focusing on promotion, females seem to be underrepresented in senior positions, suggesting that women face a glass ceiling that limits their promotion. This glass ceiling is a result of gender discrimination, which, like other forms of discrimination, is socially unacceptable. However, the glass-ceiling phenomenon may also generate negative incentives for women (because they are less likely to be promoted, they could, quite rationally, invest less in their work), depriving the economy of competencies that could be used more efficiently. These social and economic costs have provided a driving factor for research into the existence and effects of a glass ceiling.

In academia, the question of whether or not a glass ceiling exists is all the more interesting because this sector is attracting increasing numbers of women; therefore, negative incentives may generate higher costs than in other sectors.

Nevertheless, Benjamin (1999) notes that academia does not seem to have escaped the glass-ceiling phenomenon. The ETAN Report (2000) states that, in all OECD countries, the proportion of females decreases further up the rank ladder. On average, there are three times as many women in "assistant" positions (30.5% are women) and twice as many women in "lecturer" positions (20.5% are women) than in "full professor" positions (10.4%).

These statistics seem to be consistent with the presence of a glass ceiling but observed gender differences among academics could be caused by gender that a greater proportion of women are involved in teaching activities, which could explain why women tend to publish less and why they are less likely to be promoted.

In order to establish the existence of a glass ceiling in academia, other factors that affect careers must be taken into account. Econometric analyses are thus required in order to obtain ceteris paribus evaluations of the situation facing women.

However, microeconometric studies are relatively scarce and most of them have focused on wages. Studies carried out using Mincer equations generally find significant wage gaps between men and women, even after controlling for individual characteristics, publication scores and department characteristics, etc.

Using American data from the Survey of Doctorate Recipients (SDR), Ginther and Hayes (1999) calculated the gender gap in Human Sciences to be 9% in favour of men. According to Ward (2001), women in Scottish academia earn 26% less than their male counterparts. Although these studies do not refute the glass-ceiling hypothesis, they show that the phenomenon may not be clear-cut. First, the gender wage gap has decreased since the 1970's (Ransom & Megdal, 1993).

Second, estimated wage gaps are mainly caused by gender differences in observable heterogeneity. For example, by applying an Oaxaca decomposition, Ward (2001) showed that only three percentage points of the estimated 26% difference in wages can be attributed to discrimination. Ginther and Hayes (2003) confirmed this result and demonstrated that gender wage gaps are mostly due to gender rank differentials. This suggests that wages are directly related to rank. More recently, research has focused on the promotion process. Ginther and Hayes (2003) estimated promotion probabilities using univariate probit models. They concluded that women in the Human Sciences are significantly less likely to be promoted to tenured positions, ceteris paribus: the estimated gap is about 8%.

Similarly, Mixon and Trevino (2005) reported discrimination against female economists in the US South. Applying the Oaxaca decomposition to a logit model of promotion, they found that the promotion probability is 12.2 percentage points lower for females and that 7.6 of these 12.2 points cannot be explained by differences in productivity and are therefore due to discrimination.

The glass ceiling can still be seen when the dynamic process of promotion is taken into account. Using a random-effects probit model, Mc Dowell et al. (1999) concluded that the "average woman" is 36% less likely to be promoted to the "assistant professor" rank and 9% less likely to be promoted to the "full professor" rank. Similarly, Kahn (1993) found that the risk ratio for female economists obtaining tenure is about two-thirds of the male ratio. Ginther and Hayes (2003) found similar results in the Humanities, where the estimated gender gap in promotion rates is large: women are 25% less likely to be promoted, ceteris paribus.

The empirical literature does not refute the hypothesis that women are less likely to gain access to senior positions, which suggests that a glass ceiling does exist for academics, whatever discipline they are in. However, existing results are based on data from America or the United Kingdom, countries that have very similar academic systems, and it could be argued that gender gaps result from certain characteristics of these systems that are unfair to females. Therefore, it would be In this respect, the French system provides an interesting alternative, as French academia has a number of specific features that set it apart from the American or British systems (see Ginther (2001) and Euwals & Ward (2000) for detailed descriptions of these two academic systems).

Firstly, in contrast to other countries, the French academic sector has two branches: universities and national research laboratories. Each branch is independent and has its own working rules. For example, researchers working in the national research institutes have no teaching duties, unlike those working in universities.

Secondly, in the USA or the United Kingdom, academic careers are dominated by tenure rules. After completing a Ph.D., a young researcher is hired as an assistant professor on a fixed term contract. Tenured status (as a Full Professor) is not awarded until later in an academic's career and this status is not offered to all academics. Promotion criteria include scientific achievements, such as the number of papers published and their quality. French academia is organised quite differently. A key difference that applies to all French institutions (universities and national research laboratories) and all disciplines is that lifetime contracts are awarded soon after hiring. Recruitment is based on the quality of the research carried out during the Ph.D., but researchers become tenured civil servants after only 12 months' probation and this occurs almost automatically. Civil servant status implies a life-long job and, for a given rank, a fixed wage scale. There are two main and equivalent ranks in French academia: assistant professor and full professor in the university system and researcher and senior researcher in the In France, the objective of seeking promotion is not to get tenure (since this is automatic) but to earn a higher salary and to obtain greater responsibilities (such as being a Ph.D. supervisor or managing a team of researchers). As in other countries, promotion to the senior rank depends on scientific achievements, which are evaluated by promotion committees.

Another difference is that all disciplines in French academia are organized according to this general framework and they all follow the same general hiring and career rules. As stressed in the stylized facts, an examination of the promotion process reveals large differences between the genders. This suggests that, despite the differences between the French and American/British academic sectors, French female researchers are also under-represented in the senior ranks and, therefore, a glass ceiling exists. These 357 researchers were then divided into a number of cohorts. Following the example of Ransom and Megdal (1993), we created a dummy variable, COH1

(hired by INRA before 1980), in order to capture cohort effects, which could, for instance, be produced by changes in the promotion process. In fact, in recent years recruitment and promotion procedures in the French academic sector as a whole seem to have become more competitive than they were in the early eighties.

We also had information about several individual attributes. For example, we know which researchers graduated from the "Grandes Ecoles", France's top universities (TOP_UNIV), which are considered to attract the best students. We also know if a researcher can supervise Ph.D. students, a role for which a specific diploma (HDR2 ) is required. These two variables, TOP_UNIV and HDR are likely to indicate a higher human capital and play a role in the promotion process.

Our data also contain information on a researcher's mobility. This mobility could be due to undertaking a postdoctoral fellowship (POSTDOC), a visiting professorship, or a sabbatical abroad after being hired at INRA (MOB). Mobility is often viewed as an opportunity for acquiring new competencies and for networking. Networks built up within the scientific community provide greater In contrast to other data sets described in the literature, our sample contained information on all aspects of a researcher's work, including each researcher's publication record. These publication records were combined with data from the Science Citation Index, which provides an impact factor (based on the journal quality index) 3 for each publication, in order to construct a publishing score (articles published weighted by journal quality) that reflects publishing productivity (PUB_SCORE). Like McDowell et al. (2001), we preferred this mixed indicator to a simple quantitative measure of publications, which does not take into account the impact or reputation of the scientific work. In addition, we also had information about each researcher's degree of involvement in scientific projects (as a participant, NPROJECT, or a coordinator, NPROJ_C) and in administrative activities. These activities include managing a research team or a department (BOSS), or networking activities, such as belonging to a professional body (NETW) or membership of strategic, recruitment or promotion committees (COMMIT). All these attributes provided us with more detailed information on a researcher's scientific achievements and reputation, which are pillars of the promotion criteria.

However, the richness of our data set may have a negative counterpart: scientific work might be endogenous. For example, the most highly motivated researchers could be the ones who do the most research and contribute most to the literature, 3 The impact factor is complete for all publications from the early 1980's onwards, but it may be more imprecise for earlier publications. This must then be taken into account in the econometric results and comments. We therefore introduced a cross variable between COH1 and PUB_SCORE, in order to treat the potential collinearity. and who are the most likely to be promoted. But, valid instruments are needed to identify these processes. Unfortunately, our dataset is not informative enough to allow us to test both the determinants of scientific achievement and those of length of service before promotion.

In addition, our administrative data set does not provide information on personal characteristics, such as marital status and number of children, or on the activities of each research department. Previous studies have found these variables have a significant effect on the promotion process; therefore, neglecting them could generate an omitted-variable bias. This point will be discussed in the following section.

Table 2 provides descriptive statistics for the whole sample and for sub-samples determined according to gender and/or grade. Among the 327 individuals in the sample, 35.6% were female and 40.9% were senior researchers. However, only 19.2% of women held senior positions. These figures are very similar to the general situation at INRA (i.e. for all disciplines): women are under-represented in the highest ranks.

[INSERT TABLE 2]

For some staff promotion duration (defined in months) is right-censored; however, the median time taken to achieve promotion is 136 months, with the median time for males being 8 months less than the median time for females. In order to take into account censored observations, we estimated simple Kaplan Meier survival rates on yearly intervals.

[ Non-parametric hazard rates highlight the fact that, throughout a person's career, the hazard rate for females is always lower than the hazard rate for males: the cumulative hazard rate is about 77% for males but only 49.2% for females.

However, this difference could be caused by gender differences in other variables that affect promotion (see Table 2). First, large differences exist between individuals who have been promoted to the senior researcher rank and those still at the researcher rank. In general, staff promoted to the senior researcher rank joined INRA at an earlier date: 64.4% were hired before 1980 (only 32% in the full sample). More surprisingly, senior researchers had lower publishing scores (at the hiring date) and were more involved in administrative activities. Second, female senior researchers had specific characteristics. In general, they had been hired more recently than male senior researchers, they had higher publishing scores than the males and they carried out fewer administrative activities.

As the general profiles of senior researchers and of female staff were very different, it was necessary to carry out an econometric analysis of the dataset in order to evaluate the gender gap in promotion rates at INRA.

III -Modelling the determinants of promotion duration

The descriptive evidence clearly indicates that women are under-represented in senior researcher positions at INRA. Our aim was to test whether this gender differential remains after controlling for observed and unobserved heterogeneity.

Instead of estimating the probability of being promoted (as in Mixon & Trevino, 2005), we focused on the hazard rate, denoted ( )

( ) ( ) ( ) ( ) t S t f t T p t T dt t T t p t i ) ( / = + < = (1)
where T is the length of time (in months) spent at the researcher grade, f(t) is the density distribution and S(t) the survival function.

Using the model of Mc Dowell et al. (1999), can be viewed as the probability at time t that an individual's productivity exceeds the department productivity threshold (probability of being promoted), given that this productivity is lower than the threshold at least until t (probability of being not promoted until t). As both individual productivity and the productivity norm for the department are latent variables, denotes the probability of becoming a senior researcher, given that no promotion occurs before t.

Estimations of this hazard rate were performed using duration models (Lancaster, 1990), which allowed us to take into account the fact that 67.6% of the individuals studied were still at the researcher grade at the sampling date; that is to say, more than two thirds of the observed durations were right-censored. We estimated a parametric model (with an accelerated failure-time form) that allowed us to control for both observed and unobserved explanatory factors. Kaplan-Meier estimates have shown that hazard rates are non-monotonic, and therefore a loglogistic distribution4 was applied. The survival function, denoted S(t), can then be written as follows: (3) From this general specification, three different models were estimated. Model 1 estimated the effect of gender on promotion duration for the whole sample, including both the observed and the unobserved heterogeneity. Models 2 and 3 gave results by gender in order to test whether or not the effects of explanatory variables on promotion duration are gender dependent.

( ) ( ) ( ) i v i i i i dv v f v t S t S i = (2) with: ( ) ( ) [ ] i i i i t v t S ln / = , (3)
For each estimated model, robust t-statistics were calculated (White, 1982). The results are presented in Table 4. They reflect the ceteris paribus effects of each covariate on the promotion duration. Time ratios are also given. A time ratio lower (higher) than one indicates that the characteristic decreases (increases) promotion duration. Time ratios provide interesting information because, as well as giving the sign of the effect of a variable, they enable its quantitative effect to be evaluated by indicating how much the promotion duration increases or decreases for a given explanatory variable. For example, if the time ratio of a covariate X is 1.21, the promotion duration for researchers with the X attribute will be 1.21 times higher than the duration for researchers lacking this caracteristic, ceteris paribus.

Model 1 shows the importance of correcting for unobserved heterogeneity, in that it provides an estimate of the parameter, which is significantly different from zero. Thus the model must take into account unobserved factors, as neglecting the i v terms would introduce bias into the estimated effects, including the impact of gender.

[INSERT TABLE 4]

Model 1 also allows us to examine the effect of gender. The model shows that an "average woman", i.e. a female researcher with the same characteristics as a male researcher, has to wait longer for promotion. Promotion durations for females are 1.12 times longer than for their male counterparts. Gender is one of the variables with the highest effect on promotion duration. This result supports the glass-ceiling hypothesis; however, a more detailed picture can be revealed by examining estimated hazard rates by gender (Figure 2). These estimated hazard rates were evaluated for female and male average characteristics.

[ INSERT FIGURE 2] Although women had lower predicted hazard rates, on average, than men, we observed that this overall result does not apply throughout women's careers. In the first half of their careers, women had lower predicted hazard rates but, after 180 months, their hazard rates were slightly higher. This result was obtained after controlling for observed and unobserved factors. It cannot be explained by omitted individual attributes; however, a statistical explanation is possible. As females are promoted later than males (see below), after 15 years employment females with the competencies needed for promotion are more numerous than males. Thus, at this stage in their careers, we observe more females at risk than males. Finally, the promotion rate for females is higher than that for men. However, the higher hazard rates for females in the second half of their careers do not compensate for the lower hazard rates in the first half. This conclusion is strengthened by the fact that the female hazard rate peaks later and at a lower value than the male hazard rate. Females are less likely to be promoted and when they are promoted it tends to be later in their careers. Hence, although there are differences in the career patterns of female and male researchers, a glass ceiling still seems to exist. This is consistent with the findings on promotions in the USA reported by Kahn (1993), Mc Dowell et al. (1999), and Ginther and Hayes (2003).

Although there are major differences between the French academic system and the American and British systems, female researchers at INRA still find it more difficult to gain promotion than their male counterparts. As well as gender, promotion durations also seem to be affected by recruitment date. Our results show that older cohorts were promoted more quickly than more recent cohorts. For example, the promotion duration for personnel recruited before 1980 was 0.89 times that of more recent cohorts. This could be due to a less competitive recruitment environment before 1980, to a greater availability of promotions, and/or to fewer researchers being eligible for promotion. Among scientific achievements, which are the main criteria for promotion, the most influential variable is BOSS. Managing a team reduces promotion durations by a factor of 0.81. Developing and coordinating projects also shorten promotion durations, but the publication score (PUB_SCORE) has no significant effect. Hence, it seems that the promotion criteria do not all have the same effect on promotion duration and that investing in managerial activities is more profitable than carrying out research in terms of achieving promotion. Models 2 and 3 provide evidence of interaction between gender and other variables, suggesting that gender affects promotion duration both directly and Estimates of promotion duration by gender highlight that unobserved heterogeneity only affect the promotion duration of females (see model 3). This could be explained by the fact that our dataset does not included attributes such as marital status, number of children and career interruptions due to motherhood.

Recent studies have shown that these factors do affect women's careers.

Our promotion duration models allowed us to make a number of predictions and simulations.

[INSERT TABLE 4]

The results of model 1 were used to estimate the median promotion durations for males and females. When censored observations, and unobserved and observed covariates were taken into account, we found that females have to wait about 2.75 years longer for promotion than males. However, simulations carried out with female attributes evaluated equally to male attributes (using male ˆ), and inversely, with male attributes evaluated equally to female attributes (using models 2 and 3), gave longer promotion durations than those predicted by model 1. However, the gender gap in these simulated promotion durations was still less than one year in favour of men. In fact, in the hypothetical case of male attributes being evaluated equally to female attributes, the simulated promotion duration for males would be 2.8 years longer than the predicted duration. For females, the simulated promotion duration was only 1 year longer. This result seems to show that promotion duration is not only affected by gender differences in the covariates but also by the way these covariates are evaluated.

IV-Conclusion

Although there is substantial evidence for a glass ceiling in French academia, no previous attempts had been made to prove or disprove its existence. Therefore, the present study is the first to investigate whether the promotion durations of French researchers are dependent on gender. As there was no available dataset on researchers' careers, we began by constructing a database that would allow us to analyse complete career paths and research activities of French researchers.

Focusing on biologists at the National Institute for Agricultural Research, we examined promotion durations for elevation to the senior researcher rank. Our duration models show that females have significantly lower hazard rates, in particular in the first half of their careers, than their male counterparts. This result was obtained after controlling for both observed and unobserved heterogeneity.

We also found that the explanatory factors for promotion durations are very different for the two genders. This seems to suggest a sort of gender Our analysis does not refute the hypothesis that the promotion of women at INRA is limited by a glass ceiling; however, further research is needed to investigate the effects of the differences in the promotion strategies adopted by male and female researchers.

  disciplines. While hiring depends on the quality of research performed during the PhD., researchers become tenured civil servants after only

  institute aims at developing scientific knowledge, particularly in the fields of agriculture, food and the environment. In 2002, INRA had 260 research departments and employed about 1,800 researchers, 37% of whom are female. As in other national laboratories, these researchers are grouped in two ranks. The lowest rank comprises and the higher Senior Researchers (SR), and 35% of the INRA researchers are at the senior rank.

  In section three, we are interested in testing whether gender produces a significant effect on this duration, which is sometimes right-censored. Among researchers at INRA, we have decided to focus on researchers in biology, which is the main discipline at INRA. Our sample contains 583 researchers and in order to describe their career paths, we match two administrative data sets. The first describes the length of time spent in each known rank. The second data set gives us access to the activity report that each researcher supplies for his or her annual evaluation. These data are collected from the time the researcher begins to work at INRA to the time of their promotion to the SR position or to the end of 2002, if they are still in the researcher rank at this time. It must be noted that most of the observed researchers have begun their career at INRA: they do not have prior experience.

  These activities comprise managing a research team or a department (BOSS) or networking activities such as professional affiliations (NETW) or being involved in strategic committees, recruitment or promotions committees (COMMIT). All these attributes then allow us to have more precise information on scientific achievements and their visibility, which are a main pillar of the promotion criteria.

  standard normal distribution, and:

  INRA for promotions and gender does not matter in this particular framework.

  different areas of academia. For example, Schneider (1998) notes

  the glass-ceiling hypothesis in another type of academic system.

  . Salaries for each rank and status are fixed by a national collective agreement and are the same for all universities and research laboratories. Academics at the same level in the hierarchy all receive the same salary.

  journals. In order to apply, applicants must fulfil certain eligibility criteria, including possession of a Ph.D. and at least eight experience years (at INRA or another research institution). Applicants must submit their CV together with outlines of their previous research activities (mostly carried out while at INRA) and of their future projects. Applications are examined by promotion committees composed of researchers from INRA and other institutes or universities, who draw up a short list of the most suitable, eligible candidates. These short-listed candidates are then interviewed, ranked and eventually promoted.This description of the promotion process at INRA highlights the fact that applications for senior posts are mostly endogenous. Researchers' decisions to apply for senior researcher posts are usually based on seniority, the quality of their scientific work and the number of positions available. The probability of applying must therefore be examined. Unfortunately, our administrative dataset about promotion decisions and not about applications.Furthermore, no details are provided about decisions concerning the eligibility of applicants or the number of positions available. In order to minimize bias, the empirical part of our study focused on researchers who have sufficient experience to be promoted. Nevertheless, the potential endogeneity bias could not be fully controlled in our study and our results must therefore be interpreted with caution.Despite this limitation, the dataset allowed us to observe individuals' entire careers at INRA and the length of time people stay at the researcher rank before being promoted to senior researcher. Section three of the present article investigates whether gender has a significant effect on this duration, which is sometimes right-censored.Of the researchers at INRA, we decided to focus on the 583 researchers in biology, INRA's main discipline. In order to describe their career paths, we combined two administrative data sets. The first lists the length of time spent in each rank; the second contains the activity reports each researcher supplies for his or her annual evaluation. These data are collected from the time a researcher begins work at INRA until the date that person is promoted to a senior researcher position, or to the end of 2002, if he or she is still at the researcher grade at this time. From the 583 researchers observed, we selected individuals for further study on the basis of two criteria: they had to have had more than eight years' experience at INRA and they had to have been recruited during a year in which both male and female researchers were recruited. These two criteria allowed us to focus on researchers eligibility criteria for promotion and to compare cohorts containing both male and female subjects. Our final sample contained 357 researchers.

  and can increase scientific achievement; therefore mobility can increase the chances of promotion.

  specification, the hazard rate, i , was assumed to depend on three factors: a vector of observable characteristics i X , an individual specific effect, i v and an error term i .The X vector included gender, mobility characteristics, publishing score, investment in projects and administrative activities. The i v term was added to capture individual unobserved heterogeneity. Using panel models,Mc Dowell et al. (2001) pointed out that neglecting unobserved heterogeneity could cause endogeneity bias and lead to spurious results. Several attributes, such as number of children, marital status and the characteristics of the research department, were missing from the administrative dataset used for our study. As noted earlier, studies have shown that these variables have significant effects; therefore, their omission increases the risk of endogeneity bias. We were able to overcome this difficulty by modelling i v , a term with a gamma distribution (

  distribution function for the standard normal distribution, and:

  effect on the explanatory factors of promotion. A different career path can be identified for each gender. For females, promotion is accelerated by higher scientific production in terms of publication score (PUB_SCORE) or projects (NPROJECT), whereas for males promotion is accelerated by managerial achievements (managing a research team (BOSS) or coordinating projects (NPROJ_C)). This result indicates the coexistence of two strategies for promotion: the first based on scientific achievements, publications or participation in projects, the second based on managerial responsibilities. Our data suggests that the choice of strategy depends strongly on gender. Further work is needed to confirm the existence of such gender-based specialization.

  greater scientific achievements providing the fastest route to promotion for female researchers and greater managerial responsibilities being the best way of ensuring promotion for male researchers.

Figure

  Figure 1: Kaplan-Meier hazard rates

Table 2

 2

	provides descriptive statistics on the overall sample and on sub-samples
	based on gender or/and rank. Among the 583 individuals in the sample, 37.4% are
	female and 32.4% are Senior Researchers. However, only 5.7% of women are in
	senior positions. These figures are very close to the general situation at INRA (i.e.
	for all disciplines): women are under-represented in the highest rank. Table 2 also

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	analysis does not refute the hypothesis that a glass ceiling limits the promotion of
	Table 1: Proportion of researchers in senior rank positions
	women at INRA.	Men	Women
	INRA	51%	15%
	Universities	43%	18%
	Public research institutes	45%	25%
	Source: Livre Blanc, 2002
	F o r F o r F o r
	P P P
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		R e v R e v R e v
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		w w w
			19 21

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript F o r P e e r R e v i 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 23

Table 2 :

 2 Descriptive statistics

	Variables

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

Table 3 :

 3 The determinants of promotion duration

	Model 1	Model 2	Model 3

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK 1 DO FEMALE

RESEARCHERS FACE A GLASS CEILING IN FRANCE? A HAZARD MODEL OF PROMOTIONS

	First draft
	Mareva Sabatier*
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  INRA is worse than at other public research institutes or universities. Table1shows that the proportion of senior researchers among women is ten percentage points lower at INRA than at other public institutes.Most of the scientists recruited by INRA are hired as researchers, with promotion to the senior researcher rank, if justified, being awarded later in their careers 1 .Our research focused on this particular promotion path. Promotion to the senior researcher rank mainly occurs through a formal, internal, competitive process that begins with the publication of available positions on INRA's website or in

	in rank, the gender effect is evaluated according to the probability of becoming a senior researcher. In order to carry out this research, we had to overcome a major obstacle: there is no generally available data set on academic careers in France. In section two, we explain how we constructed a panel data set for researchers' careers. This data set female researchers at [INSERT TABLE 1]
	allowed us to examine the career paths of a group of biologists working at the
	National Institute for Agricultural Research (INRA), one of France's national
	F o r research institutes. By focusing on life scientists at a single institute we were able produce homogenous data that could be used to test the glass-ceiling hypothesis, F o r
	P thereby providing the first study of this phenomenon in France. P
	e e
	e r As there is no official dataset describing the career paths of researchers in France, II-The Data e r
	R e v we constructed one, using information from the administrative files of INRA. INRA was founded in 1946 to develop scientific knowledge in the fields of R e v
	i e agriculture, food and the environment. In terms of publications in these fields, i e
	w INRA ranked is second in the world. In 2002, INRA had 260 research departments w
	The aim of this article is to test whether a study of promotion paths supports this and employed about 1,800 researchers, 37% of whom were female. As in other
	hypothesis. As in the literature, we will take into account both observed national research institutes, INRA's researchers are divided into two ranks:
	heterogeneity, such as individual attributes and scientific achievements, which researchers and senior researchers. In 2002, 35% of INRA's researchers held the
	can explain promotion gaps, and unobserved heterogeneity, which are often senior researcher rank.
	neglected. As career paths in French academia can only be described by changes Also like other national research institutes, there is almost gender parity amongst
	researchers but women are under-represented amongst senior researchers: only
	5.5% of researchers are female senior researchers. Furthermore, the situation for
	7 8

Table 1 :

 1 Proportion of researchers in senior positions

	Men	Women

Table 2 :

 2 Descriptive statistics

	Variables

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

Table 3 :

 3 The determinants of promotion duration Estimated coefficients have been rounded to two decimal places. Robust t-ratios (using heteroscedasticconsistent errors fromWhite's (1982) procedure) are reported. ***: statistically significant at 1% level, **: significant at 5% level, *: significant at 10% level, ns: not significant

		Model 1		Model 2		Model 3
	Explanatory factors	Full sample		Male		Female
	Constant	Time ratios 1.02	t-ratios 2.01**	Time ratios 0.99	t-ratios 1.04 ns	Time ratios 1.01	t-ratios 0.73 ns
	FEM: being female	1.12	2.67***	-	-		-	-
	COH1: hired before 1980	0.89 -3.11*** 0.71 -3.96***	0.95	-3.01***
	TOP_UNIV: graduated from a top university	0.93	-1.87*	0.92	-2.15*	0.98	-1.65	ns
	HDR: having the Ph.D. supervisor diploma	0.90	-2.12**	0.98 -1.21	ns	0.92	-2.28**
	POSTDOC: having held a postdoctoral fellowship	1.01	-1.18	ns	1.02	0.97	ns	0.96	-2.19**
	MOB: mobility since entry at INRA	0.95	-2.09**	0.94	-2.08**	0.98	-1.14	ns
	NPROJECT: number of projects	0.87	-2.12**	0.88	-1.93*	0.95	-1.98**
	NPROJ_C: number of projects coordinated	0.84 -3.73*** 0.76 -3.82***	0.98	-1.54	ns
	PUB_SCORE: publication productivity BOSS: managing team or laboratory NETW: having networking activities COMMIT: participating to strategic committees	0.97 0.81 -6.26*** 0.63 -4.02*** -1.53 ns 0.99 -1.54 ns 0.97 -1.42 ns 0.98 -1.07 ns 0.98 -0.61 ns 0.97 -1.04 ns	0.56 1.01 0.96 1.03	-2.31*** ns 1.06 ns -1.38 0.97 ns
	COH1*PUB_SCORE	1.07	2.15**	0.94	2.61***	1.04	1.13***
	Sigma	0.31 17.04*** 0.23	7.41***	0.18	5.59***
	Theta	1.53	3.88***	1.18	4.33***	1.79	4.06***
	Log-Likelihood	-223.52		-218.91		-201.65
	Observations	327		230			127
	NB:

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Table 4 :

 4 Predicted and simulated median promotion durations

		Predicted from model 1	Simulated from models 3 and 4*
		male	female	male	female
	Median duration	192.18	225.26	225.04	236.23

"HDR" diploma or "Habilitation" consists in writing a document which outlines the contribution to science. As the PhD., this document is defended in front of a jury.

It must be noted that the impact factor is complete for all publications from the early 80's, but it could be more imprecise for earlier publications. This must then be taken into account in the econometric results and comments.

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

In recent years, a small number of scientists have been recruited directly as senior researchers. As this type of career path does not constitute promotion within INRA it was not analysed in this study.

In order to obtain an "HDR" diploma, also known as a "Habilitation", a candidate must prepare a written document outlining his or her contribution to science. As for a Ph.D., this document must then be defended in front of a jury.

Various specifications for distributions of durations (log-normal, weibull, etc) were tested. The results were not affected by the specifications chosen.

Acknowledgements :

The authors are grateful to all the participants in the research project "Female careers in academia" and to

Stephen Bazen for helpful comments on earlier drafts of the paper. Thanks also to the National Institute for Agricultural Research which provided access to the data and financial support. Any errors are our own.

Acknowledgments:

The authors are grateful to all the participants in the research project "Female careers in academia", especially Christine Musselin and Vincent Mangematin. We would also like to thank Stephen Bazen and Bart Cockx, for their helpful comments on earlier drafts of the paper, as well as the National Institute for Agricultural Research, for providing access to the data and financial support. Any errors are our own.

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 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


Simon Sosvilla-Rivero

Pedro N Rodríguez

G15 -International Financial Markets < G1 -General Financial Markets < G -Financial Economics, C32 -Time-Series Models < C3 -Econometric Methods: Multiple/Simultaneous Equation Models < C -Mathematical and Quantitative Methods

Keywords: International stock markets, Causality JEL Classification Numbers: G15, C32 International stock markets, Causality

In this paper we propose a new approach to evaluate the predictable components in stock indices using a boosting-based classification technique, and we use this method to examine causality among the three main stock market indices in the world during periods of large positive and negative price changes. The empirical evidence seems to indicate that the Standard & Poors 500 index contains incremental information that is not present in either the FTSE 100 index or the Nikkei 225 index, and that could be used to enhance the predictability of the large positive and negative returns in the three main stock market indices in the world. This in turn would suggest a causality relationship running from the Standard & Poors 500 index to both the FTSE 100 and the Nikkei 225 indices.

Introduction

Interdependence among national stock markets is an important concern for investors since in recent years the global market has became more integrated as a result of a broad tendency toward liberalisation and deregulation in the money and capital markets of developed as well as developing countries, thereby reducing the opportunities for international diversification. Furthermore, market co-movements can also lead to market contagion as investors incorporate information about price changes in other markets into their trading decisions in an attempt to form a complete information set, carrying the risk that errors in one market may be transmitted elsewhere (see, e. g., [START_REF] King | Transmission of volatility between stock markets[END_REF].

As traders place orders and take positions simultaneously using different indices, one expects that different indices would be closely linked by both hedging activities and cross-market arbitrage (see, e. g., [START_REF] Karoly | Why do markets move together? An investigation of U.S.-Japan stock return comovements[END_REF]. Furthermore, modern technological advancements and computerised trading systems have greatly facilitated the transfer of information from market to market.

One strand of research has examined long-term interdependence in international stock markets using multivariate cointegration techniques [see, [START_REF] Kasa | Common stochastic trends in international stock markets[END_REF], [START_REF] Corhay | Common stochastic trends in European stock markets[END_REF], [START_REF] Blackman | Long-term relationships between international share price[END_REF], [START_REF] Bachman | Common factors in international stock prices: Evidence from a cointegration study[END_REF] and Fernández-Serrano andSosvilla-Rivero (2001, 2003) , e. g., DeFusco et al. (1996) and Aggarwall et al. (1999)] or price and volatility spillovers using variations of the GARCH approach [see, e. g., [START_REF] Hamo | Correlations, price changes and volatility across international stock markets[END_REF], [START_REF] Koutmos | Asymmetric volatility transmission in international stock markets[END_REF], [START_REF] Chiang | Dynamic analysis of stock return volatility in an integrated international capital market[END_REF] and [START_REF] Fratzscher | Financial market integration in Europe: On the effects of EMU on stock markets[END_REF]].

More recently, there has been a growing interest in the market dynamics and the transmission mechanism driving international market linkages [see, e. g., Eun and Shim (1989), [START_REF] Arshanapalli | International stock market linkages: Evidence from pre-and post-October 1987 period[END_REF], [START_REF] Masih | Dynamic linkages and the propagation of stock market fluctuations driving major international stock markets: An analysis of the pre-and post-crash eras[END_REF] and Connolly and Wang (2002)].

Recent advances in machine learning and statistics have contributed to the appearance of robust classification and evaluation techniques. In particular, these techniques allow us to focus on the predictability of specific price changes (codified into populations).

Especially, one would like to discriminate positive from negative returns and/or large positive or negative price changes from the rest of price movements. Doing so allows us to test whether or not lagged returns from a main stock market index provide incremental information concerning the classification of financial movements. Moreover, it permits us to compare and determine which set of explanatory variables provides more information to discriminate index movements.

The purpose of this paper is to investigate the casual relationships between the three major stock markets in the world using daily data covering the period February 1986-June 2004. Our study differs from the previously published papers in several ways. First, The paper is organised as follows. In Section 2, we provide a brief review of the Gradient Boosting Machine classification technique. Section 3 discusses the receiver operating characteristic (ROC) curve and the area under it, both used to evaluate discriminatory accuracy. In Section 4, we report the empirical results. Finally, Section 5 provides some concluding remarks.

The Gradient Boosting Machine classification technique

In the function approximation problem, one has a system consisting of a random response variable y and a set of random explanatory variables x={x 1 , x 2 ,..., x n }. Given a training sample {y i ,x i } N 1 of known (y,x)-values, the goal is to find a function F*(x) that maps x to y, such that over the joint distribution of all (y,x)-values, the expected value of some loss function is minimised.

Regression and classification problems can be viewed as a task in function approximation. In a classification problem, the goal is to discriminate between two (or more) populations, given a set of explanatory variables. In our particular case, the relevant question is if lagged price changes are capable of providing information for discriminating large positive financial movements.

To answer such question empirically, we must test the out-of-sample discriminatory accuracy of the classifier chosen, in order to understand specific movements. Moreover, this out-of-sample performance should be evaluated with a technique that is invariant to a-priori class probabilities and that is independent of the decision threshold (or the cut-off value).

In this paper, we have employed the Gradient Boosting Machine classification technique, which we now proceed to review. Regarding the evaluation of the discriminatory accuracy, in the next section we discuss the receiver operating characteristic (ROC) curve and the area under it. The underlying idea of boosting is to combine simple "rules" (or tree-based models) to form an ensemble (or weighted committee) such that the performance of the single ensemble member is improved (e.g., "boosted"). Boosting was proposed in the machine learning literature by Freund and Schapire (1997) with the creation of AdaBoost, and has since received much attention.

From the statistician's point of view, the breakthrough took place with the paper by [START_REF] Friedman | Additive logistic regression: A statistical view of boosting[END_REF]. They show that AdaBoost is an optimisation method for finding a classifier that minimises a particular exponential loss function, and that this loss function is very similar to the (negative) binomial log-likelihood. For an excellent paper that traces the developments of boosting methodology and its applications to the exponential family and proportional hazards regression models see [START_REF] Ridgeway | The state of boosting[END_REF].

Using the connection between boosting and optimisation, [START_REF] Friedman | Greedy function approximation: A gradient boosting machine[END_REF] proposes the Gradient Boosting Machine (hereafter GBM). Using this technique, function approximation is viewed from the perspective of numerical optimisation in the function space, rather than in the parameter space. The estimation algorithm of the GBM is shown in Chart 1.

[Chart 1, here]

With the purpose of increasing execution speed, approximation accuracy and robustness against over-fitting, we incorporated randomness in the procedure as (or tree-based models) was the Gini index.

The GBM has three tweaking parameters: the total number of iterations M, the learning rate (shrinkage parameter v) and the level of interaction among explanatory variables J. It is widely known that fitting the data too well can lead to over-fitting, which degrades the accuracy power on independent data bases. However, M and v do not operate independently: smaller values of v lead to larger values of the "optimal" M.

Empirically, via simulation, [START_REF] Friedman | Greedy function approximation: A gradient boosting machine[END_REF] finds that low values of v (v < 1%) favour better accuracy on test samples. In this paper, we fixed the shrinkage parameter (v)

to one percent and allowed 500 boosting iterations (M). Clearly, better results can be obtained if we monitor these parameters in a validation set. Nevertheless, this was not done in order to maximise the number of observations in the test sample. Regarding the level of interaction (J), experience indicates, hitherto, that 4 8 J ≤ ≤ works well in the context of boosting, with results being fairly insensitive to particular choices in this range (Hastie, Tibshirani, and Friedman (2001). Consequently, we fixed J equal to five in all our experiments. The implementation was carried out in R: Environment for Statistical

Assessing the discriminatory accuracy

The receiver operating characteristic (ROC) curve is a well-established method for summarising performances of diagnostic tests [see, [START_REF] Hanley | Receiver operating characteristic (ROC) curves[END_REF]; [START_REF] Zhou | Statistical Methods in Diagnostic Medicine[END_REF], among others]. Now, it is widely used for evaluating machine learning algorithms [see, e. g., [START_REF] Weiss | Learning when training data are costly: The effect of class distribution on tree induction[END_REF]; [START_REF] Provost | The case against accuracy estimation for comparing induction algorithms[END_REF]; [START_REF] Bradley | The use of the area under the ROC curve in the evaluation of machine learning algorithms[END_REF]].

A ROC curve is obtained by plotting Sensitivity versus 1 -Specificity for various cut-off values. The points on a ROC curve are either joined by line segments or smooth curves with the use of non-parametric and parametric procedures, respectively.

The area under a ROC curve (AUC) is equal to the probability that a randomly selected observation from population one scores higher than a randomly selected observation from population two (Hanley and McNeil (1982). Formally, the AUC can be expressed as:

1 AUC = ( ) ( ) 2 P y x P y x > + = (1)
where y and x denote the classifier output (class probability) for a randomly selected observation from population one and two, respectively. In this paper, we make use of the Mann-Whitney-U Statistic, a non-parametric approach to obtain the AUC. The Mann-Whitney-U Statistic is given by: The variance of the AUC can be obtained from the following:

1 1 1 AUC = = m n ij i j Z mn = = ⊕ ∑ ∑ (2) where 1 ( ) ( ) 2 ij i j i j Z I y x I y x = > + = and
2 2 1 2 (1 ) ( 1)( ) ( 1)( ) ( ) m Q n Q Var mn ⊕ -⊕ + - -⊕ + - -⊕ ⊕ = (3) and 2 1 2 2 ; 2 1 . Q Q = ⊕ -⊕ = ⊕ + ⊕ Equation 3 is the exponential approximation formula
of Hanley and McNeil (1982).

Another important application of the ROC curve is to compare the overall discriminatory accuracy of classifiers. The term 'overall' is emphasised, since the interest is in the global picture of a test and not in the accuracy performance at a particular cut-off value. See [START_REF] Metz | Statistical comparison of two ROC-curve estimates obtained from partially-paired datasets[END_REF] to understand how different ROC-curve estimates can be compared. We employed the Gradient Boosting Machine classification technique to extract patterns from the explanatory variables in order to classify large positive and negative price changes, and we used the area under the ROC curve to evaluate and compare the 'overall' discriminatory accuracy of the classifiers. In order to identify large positive price changes, for each index we chose the returns that satisfy the following condition:

F

(return (large, positive return)) 80% prob < = . In other words, the large positive returns represent 20 per cent of the probabilistic distribution of the returns (or right-tail of the distribution of the returns) 2 . Concerning the large negative price changes, we chose those observations that represented the left-tail of the distributions of the returns (e.g., (return (large, negative return)) 20% prob < = ). Observations that satisfied the condition were codified with 1's, and those that did not were codified as 0's.

Once the dependent (or response) variable was codified, we analysed three sets of the test set is larger than 1000. Therefore, our testing sample satisfies the train-and-test procedure (see, e.g., [START_REF] Henery | Methods for comparison[END_REF]. Note also that the testing period is long enough to reduce the effects of data snooping.

In the top section of Table 1 ( change cases (returns greater than 0.68%) scores higher than a randomly chosen observation from price changes from returns lower than 0.68% is 61.29 per cent. Notice that when there is no difference between the two populations, the area under the ROC curve will be 0.5 (or coin-toss classifications). The 95 per cent confidence interval for the area can be used to test the hypothesis that the theoretical area is 0.5. Since the confidence interval in this case (0.5758, 0.6482) does not include the 0.5 value, there is evidence that the GBM technique is able to distinguish between the two groups (or populations). Test B reports the results when we use lags of both Standard & Poors 500

and Nikkei 225 indices as explanatory factors, while Test C presents the results when lags of the all three are used. As can be seen, including those lags leads to a small reduction in the discriminatory power of the GBM technique (61.09 and 60.75 per cent, respectively), although the new confidence intervals do not include the 0.5 value either.

Concerning the large negative price changes, predictable components were non-existent, since the GBM, trained under the three different sets of explanatory variables, was not able to beat a coin-toss (or random) classification.

In the lower section of Table 1 (Panel II), we report the z statistic, testing the difference between areas under the ROC curves, as well as the p-value. As can be seen for the large positive price changes, the z statistics obtained when comparing Test A vs. However, when analyzing large negative price changes, none of the explanatory variable sets contained any useful information to discriminate large negative price changes from the rest of price movements. Furthermore, in one of our experiments the ROCKIT software did not converge since the data set was degenerated. In general, degeneracy should be found only in very small datasets and/or in those with many tied values, and in our case it was due to the existence of many tied values.

[Table 1, here]

Regarding the FTSE 100 index, we observe in Panel I of Table 2 that there is a significant improvement in the discriminatory accuracy for the large positive price [Table 2, here]

Finally, Table 3 reports the results for the Nikkei 225 index. As can be seen in the The traditional method for testing causality in economic time series makes use of the well-known Granger definition of causality (Granger, 1969). Given two variables, x and y, x is said to Granger-cause y if the latter can be predicted better by past values of x and y, rather than by past values of y alone. From this definition, the results in Tables 1

Concluding remarks

In information. Indeed, there is a large literature on the fact that investors tend to react more to news from the US market than from other markets [ see, e. g., [START_REF] Eum | International transmission of stock market movements[END_REF], [START_REF] Becker | Economic news and equity market linkages between the US and UK[END_REF], and Masih and Masih (2001)].

Our evidence is also consistent with that presented in [START_REF] Karoly | Why do markets move together? An investigation of U.S.-Japan stock return comovements[END_REF], who conclude that large return shocks propagate more internationally than small return shocks.

Our findings support the conclusion coming from agent-based models for financial market which account for behavioural phenomena such as herding, overreaction and the common use of trading rules, that are likely to spread non fundamental price variations across markets [START_REF] Day | Bulls, bears and the market sheep[END_REF][START_REF] Brock | Simple technical rules and the stochastic properties of stock returns[END_REF][START_REF] Connoly | International equity market co-movements: Economic fundamentals or contagion?[END_REF][START_REF] Daniel | Investor psychology in capital Markets: Evidence and policy implications[END_REF][START_REF] Hirshleifer | Herding and cascading in capital markets: A review and synthesis[END_REF]. In this sense, [START_REF] King | Transmission of volatility between stock markets[END_REF] argue that trading of stocks in one market per se affects stock prices in other markets, even if the source of the trading is purely noise. This is called the "market-contagion hypothesis". [START_REF] Karoly | Why do markets move together? An investigation of U.S.-Japan stock return comovements[END_REF] also find evidence consistent with this interpretation, pointing out that "[c]ontagion effects results when enthusiasm from stocks in one market brings about enthusiasm for stocks in other markets, regardless of the evolution of market fundamentals".

m i i i i i m i F F L y F g F ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( , ( ) ( )
m m i m F F v T π ρ ∧ ∧ - ← + Θ x x x )
End For

  , among others]. The other main area of research has attempted to investigate short-run market

  focus on markets that are located in neighbouring geographic areas, we examine linkages across global markets. Second, instead of employing shortrun market relationships through correlation tests or long-run co-movements, we investigate the relevance of lagged returns for discriminating price changes by using a boosting-based classification technique. Finally, while a growing body of research is devoted to the impact of financial crises on stock market linkages, we examine their relationships both during periods of high, positive and negative returns.By evaluating and comparing the 'overall' discriminatory accuracy of the boostingbased algorithms (The Gradient Boosting Machine) trained under three different sets of explanatory variables, we find that the S&P 500 does provide incremental information to enhance the predictability of the large price changes in the three main stock market indices in the world. Moreover, this predictive structure behaviour is neither present in the FTSE 100 nor in the Nikkei 225.

  (2002). At each iteration, a sub-sample consisting of 50 percent of the total observations ( )50% N N =is drawn at random (without replacement) from the training sample. This sub-sample is then used to fit the tree and compute the model output for the current iteration. The loss function employed in all our experiments with the GBM was the Bernoulli function, and the loss function used to generate the "rules"

  Computing and Graphics with the following add-on package: gbm (developed by G. Ridgeway).

  ( ) I • is an indicator function. The variables m and n are the total number of observations for population one and two, respectively.

  The data set compromises daily time series on closing values for the three major stock market indices: the FTSE 100 index (United Kingdom), the Nikkei 225 index (Japan), and the Standard & Poors 500 index (United States). The sample period examined spans from June 2, 1986 to June 25, 2004. The data set was obtained from Econwin.

  exploratory factors per index: lags in Standard & Poors 500 index, lags in the FTSE 100 index , and lags in the Nikkei 225 index. These explanatory variables were incorporated in the GBM algorithm depending on the trading hours. Note that the Japanese stock first to open among the three considered, followed by the UK stock market, and the US stock market is the last one to open 3 . Therefore, when examining each particular stock market, we will successively incorporate the publicly available information on stock prices taking into account these trading hours. For example, to analyse the Japanese stock market, we first take into account only lags in the Nikkei 225 index, then we introduce lags in the FTSE 100 index, and finally we consider also the lags in the Standard & Poors 500 index. As is well known, keeping a test set additionally to the training set is a general method to estimate the accuracy of a classifier. Therefore, we have split our sample into two sub-samples: the training sample runs from June 2, 1986 to December 31, 2000, while the testing sample covers the period January 3, 2001-June 25, 2004. Usually a fraction of 20-30 per cent of the available data is chosen as the testing set if the size of

  Panel I), we evaluate the discriminatory accuracy of the GBM for the US stock market under different sets of explanatory variables. Test A shows the GBM classifying power when only lags of the Standard & Poors 500 index are used.For the large positive price changes, the discriminatory power is 0.6129, meaning that the probability that a randomly selected observation from the large positive price3 The relevant time with respect to Greenwich Mean Time is +9 for the Nikkei 225, 0 for the FTSE 100, and -6 for the Standard and Poors 500.

  Test B and Test A vs. Test C are positive, suggesting that Test A has a greater area under the ROC curves than those of Tests B and C. Moreover, the p-values suggest that the pair-wise comparisons of all three ROC curves are not significantly different. Therefore, based on this evidence we can conclude that including more explanatory variables does incremental information to improve the discriminatory power of the GBM technique when identifying the large positive price changes in the Standard & Poors 500 index.

  changes (returns greater than 0.74%) when the lags of the Standard & Poors 500 and the Nikkei 225 indices are introduced in the information set. As can be seen, Test C presents the greatest area under the ROC curve. Moreover, when comparing the areas under the ROC curves for the three sets of explanatory variables, we obtain a negative value for the z-statistic, suggesting that Tests B and C have a greater area under the ROC curve than Test A, being also statistically significant at the usual levels. These results, jointly taken with the results when comparing Test B vs. Test C, indicate that the Standard & Poors incremental information to enhance the discriminatory power of large positive returns in the FTSE 100 index. Furthermore, the same pattern emerges in the predictability of large negative price changes, where the Standard & Poors 500 index provide useful information for discriminating the FTSE 100 large negative price changes from the rest of price movements.

  to 3 could be taken as empirical evidence of causality running from the Standard & Poors 500 index to both the FTSE 100 and the Nikkei 225 indices.

  this paper, we extend the previous literature by examining stock market linkages during large positive and negative price changes. The main novelty of the paper lies in its use of the Gradient Boosting Machine classification technique to examine the relevance of lagged returns for discriminating price changes. The empirical evidence presented in this paper seems to indicate that the Standard & Poors 500 index contains incremental information that is not present either in the FTSE 100 index or in the Nikkei 225 index and that could be used to enhance the forecastability of the large positive and negative returns in the three main stock market indices in the world. This in turn would suggest a causality relationship running from the Standard & Poors 500 index to both the FTSE 100 and the Nikkei 225 indices.Therefore, our results indicate that the US index plays a prominent role in price leadership across global markets. This is consistent with the fact that the US market has long been the centre of financial transactions as well as the most influential producer of

  the negative gradient as the working response/output 1 ( )

  a learning rate v, update the estimate of ( )

  table, the information provided by the lags in the Nikkei 225 index is not relevant for discriminating large positive price changes (returns greater than 0.82%). In contrast, both

	F o r
	P
	e
	the Standard & Poors 500 index and the FTSE 100 index contain relevant information in e r
	this context. Nevertheless, the results obtained when comparing Test B vs. Test C suggest that the Standard & Poors 500 index contains incremental information that is not present R e v in the FTSE 100 index and that could be used to increase the discriminatory accuracy of i e the large positive returns in the Nikkei 225 index. Moreover, the predictability of the large negative price changes is greatly enhanced due to the information extracted from w
	the Standard & Poors 500 index lags.
	[Table 3, here]

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

* Pedro N. Rodríguez thanks CONACYT (Mexico) for financial support (Fellowship: 170328).

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