Francis Green

Steven Mcintosh
email: s.mcintosh@lse.ac.uk.

Is there a Genuine Under-utilisation of Skills Amongst the Over-qualified?

Is there a Genuine Under-utilisation of Skills Amongst

the Over-qualified?

Introduction

There is evidence that an increasing proportion of workers are finding themselves in jobs that require qualification levels lower than those they have obtained. According to the Skills Survey data set used in this study [START_REF] Felstead | Work skills In Britain[END_REF], some 37% of workers were 'over-qualified' in this sense in 2001, compared with just 32% in 1997. During this time, less than one in five workers remained 'under-qualified,' that is, doing jobs that would require a new recruit to have a higher qualification level than currently held by the job-holder. The rise in over-qualification followed a period of relative stability dating back to the mid 1980s, though the decade before that saw an earlier rise in over-qualification [START_REF] Green | The utilisation of education and skills: evidence from Britain[END_REF]. If the recent rise heralds an ongoing trend, it becomes more urgent now to understand the significance and implications of this phenomenon.

Who are performing the jobs for which they do not have the appropriate levels of education or skills? Are the over-qualified genuinely under-using their skills, and is there any evidence that the under-qualified are suffering from a skills deficiency?

The paper builds on an expanding literature about 'over-education' that exists in Labour and Education Economics 1 (see for example [START_REF] Alba-Ramirez | Mismatch in the Spanish labor market: overeducation?[END_REF], Battu et al., 1999[START_REF] Cohn | The wage effects of overschooling revisited[END_REF][START_REF] Dolton | The incidence and effects of overeducation in the graduate labour market[END_REF][START_REF] Duncan | The incidence and wage effects of overeducation[END_REF], Green et al., 2002[START_REF] Groot | Overeducation and the returns to enterprise related schooling[END_REF][START_REF] Groot | The incidence of, and returns to overeducation in the UK[END_REF][START_REF] Groot | Allocation and the returns to over-education in the UK[END_REF][START_REF] Hartog | Overeducation and earnings: where are we, where should we go?[END_REF][START_REF] Hartog | On returns to education: wandering along the hills of ORU land[END_REF][START_REF] Hartog | Overeducation and earnings: where are we, where should we go?[END_REF][START_REF] Rumberger | The impact of surplus schooling on productivity and earnings[END_REF][START_REF] Sicherman | Overeducation' in the labor market[END_REF][START_REF] Sloane | Overeducation and the formal education/experience and training trade-Off[END_REF], 1999, Tsang et al., 1991, Verdugo and Verdugo, 1989). This literature has documented the extent of over-education and under-education that F o r P e e r R e v i e w 3 exists in a number of countries, and highlighted the wage impact of working in a job for which one is over-or under-edcuated 2 . Describing the results very broadly, about a quarter to a third of a nation's employees tend to work in jobs for which they are over-qualified, with a somewhat smaller proportion working in jobs for which the required education level exceeds their actual qualifications.

Despite the extent of over-qualification, it would still be of only minor importance if it was a temporary phenomenon for individuals, for example whilst gaining experience before future promotions, or accepting any job whilst continuing to search for a more appropriate opening. The limited amount of evidence available suggests that this is not the case, however. [START_REF] Dolton | The incidence and effects of overeducation in the graduate labour market[END_REF] find that amongst UK graduates who are over-qualified in their first job, two-thirds are still working in a job for which they are over-qualified six years later. [START_REF] Frenette | The overqualified Canadian graduate: the role of the academic program in the incidence, persistence, and economic returns to overqualification[END_REF] observes three-quarters of those initially overqualified in his Canadian sample remaining in this state, although in this case there are only three years between the two survey points. To the extent that these findings can be generalised, being over-qualified therefore seems to have a degree of permanence for many individuals in this state.

Being over-or under-qualified makes a difference. Those who are over-qualified tend to earn less than their similarly qualified peers who work in appropriate jobs, although they do still earn more than those with the required qualification for the job in which they work. Similarly, those working in a job for which they are under-qualified tend to earn more than workers with the same qualification working in an appropriate job, but again this differential does not ensure parity This paper attempts to explain why certain individuals are over-or underqualified for the work that they do, and if so, why this has the effects that it does. The next section considers some possible answers, followed by a description of the data to be used to test these theories, and a discussion of the results.

Three Possible Reasons for Over-Qualification and Under-Qualification

The two ideas most often advanced to explain the phenomenon of overqualification are some sort of assignment or job competition model, and human capital differences. Considering the former idea first, the assignment theory of job allocation is described by [START_REF] Sattinger | Assignment models of the distribution of earnings[END_REF], while the job competition model is most often associated with Thurow (1979). The assumption behind these theories is that there is a skill level attached to a job regardless of the attributes of the person who fills it. Whilst this may sound reasonable, it does not feature in the basic human capital theory, in which an individual's particular level of human capital will provide a certain level of productivity, irrespective of the job in which that individual works. Individuals are then assigned to these jobs, according to their characteristics. Thus, higher skilled individuals are more likely to be matched with job vacancies requiring a higher level of skills. The matching process need not be perfect, however, for a couple of reasons, leading to the possibility of certain individuals being over-qualified for the work that they do, and others being under-qualified. For example, there may simply be F o r P e e r R e v i e w 5 more skilled workers than required in an economy, so that there are insufficient skilled jobs to go round. In this case, some skilled individuals, who lose out in the race for the good jobs, will end up performing jobs for which they are overqualified.

However, strong evidence against the 'too many skilled workers' theory is provided by the wage inequality literature. If wages respond to market forces, then an over-supply of skilled workers would be expected to lower the wage that they receive, relative to that of less-skilled workers. However, the evidence reveals sustained and substantial gross returns to academic qualifications at all levels and to vocational qualifications above level 2 (Machin, 1999[START_REF] Dearden | The returns to academic and vocational qualifications in Britain[END_REF]. The point is reinforced by continual and sustained reports from surveys of the UK business community of skills deficiencies including, especially at times of cyclical upswing, recruitment difficulties (see Campbell et al., 2001). Finally, given that the over-qualification phenomenon is observed in a range of countries, we would be reluctant to conclude that there could be such a widespread glut of skills throughout the industrialised world.

Even if there is no over-supply of skilled workers, it is still possible that the range of jobs on offer will not be matched perfectly to the available individuals, however. This could be the case, for example, if there is mismatch in the labour market. In this case, individuals are not necessarily assigned to the most appropriate job, due to a lack of information or rigidities in the labour market. A lack of information implies that individuals do not find the most appropriate job for their skills, while rigidities may prevent them accepting the most appropriate F o r P e e r R e v i e w 6 job, even if they found it. Such rigidities may be related to family situations, whereby the presence of a partner or, especially, children, may prevent individuals from moving to accept the most appropriate job 3 . Some existing evidence supporting this mismatch explanation derives from the finding that workers with families, especially part-time workers, are more likely to be found amongst the over-qualified [START_REF] Green | The utilisation of education and skills: evidence from Britain[END_REF].

One of the most thorough tests of such ideas can be found in [START_REF] Büchel | The theory of differential overeducation: does it work? Scottish Journla of Political Economy[END_REF]. They find some evidence that married West German women living in rural areas are more likely to be over-qualified for the work they do than other combinations of gender, marital status and region of residence. The implication is that such women are tied to an area with few job opportunities by their families. Note that males in rural areas do not have a high over-qualification rate, because they are more likely to commute to areas of greater population density than women. Thus, once commuting distance is controlled for, married men in rural areas are also more likely to be over-qualified, though not to the same extent as married women. These results are at odds with those of [START_REF] Mcgoldrick | Gender differences in over-education. A test of the theory of differential overqualification[END_REF], who perform a similar analysis using US data and find no impact or marital status or region of residence on the likelihood of being over-qualified. Their analysis does not, however, allow for the possibility of commuting.

Turning to the human capital 'explanation' for over-qualification, the point here is that those apparently over-qualified in actual fact are not. They only appear to be over-qualified because not all aspects of their human capital are observed. It is necessary here to drop the assumption that all individuals with the same qualifications are homogenous, and acknowledge that there will be a range of skills and abilities, not observed by the researcher, in addition to other aspects of human capital such as training, work experience and current job tenure, which may or may not be observed. If this is true, then the apparently over-qualified may simply be those workers from a particular qualification category who have low values of other, unobserved, aspects of human capital. They are therefore actually in a job commensurate with their human capital.

There is some limited evidence that such theories may be relevant. [START_REF] Bauer | Educational mismatch and wages: a panel analysis[END_REF] and [START_REF] Frenette | The overqualified Canadian graduate: the role of the academic program in the incidence, persistence, and economic returns to overqualification[END_REF] both present wage equations estimated using panel data sets, which control for individual fixed effects. When they do this, the wage penalty associated with being over-qualified falls dramatically, suggesting that it was caused by unobserved low earnings capacity. [START_REF] Chevalier | Measuring over-education[END_REF] identifies individuals who are apparently, rather than actually, over-qualified as those workers who appear to be over-qualified in terms of their qualifications, but who claim to be satisfied with the match between their education and their work, and therefore are presumably the less able in that qualification category. He shows that the wage penalty associated with over-qualified status is greater for the genuinely over-qualified than for the apparently over-qualified. [START_REF] Büchel | Overeducation and skill endowments. The role of school achievement and vocational training quality[END_REF] provide evidence that even among individuals with similar levels of formal education in West Germany, there can be large differences in the likelihood of being over-qualified, and these differences are related to school achievement and type of vocational training undertaken. Other evidence suggests that the over-qualified may not necessarily have low values of unobserved human capital characteristics such as ability, but may simply have acquired the 'wrong' type of human capital, where 'wrong' here means skills that are less in demand in the labour market. Thus, in the UK, [START_REF] Dolton | The incidence and effects of overeducation in the graduate labour market[END_REF] find that graduates of social sciences, arts and languages are more likely to be over-qualified than graduates of subjects in high demand and short supply in the labour market, such as engineering and sciences. [START_REF] Frenette | The overqualified Canadian graduate: the role of the academic program in the incidence, persistence, and economic returns to overqualification[END_REF] obtains similar findings in Canada, with graduates in fine arts, humanities, social sciences and agricultural and biological sciences being less likely to find graduate level work, relative to graduates in education, engineering, computer science, law and medicine.

The aim of this paper is to provide further evidence on the causes of overqualification, focussing on the mismatch and heterogeneous ability/unobserved human capital theories outlined above. The observable difference between the two theories is that with mismatch, the over-qualified are genuinely failing to obtain appropriate jobs for their skills and abilities, and so are under-utilising these skills, while in the heterogeneous ability story, individuals are actually in appropriate jobs and are not under-utilising any skills, despite the formal qualifications that they hold. The papers mentioned above that have investigated the causes of over-qualification have not investigated this relationship between over-qualification and over-skilling, with the exception of [START_REF] Chevalier | Measuring over-education[END_REF], who investigates whether the over-qualified are satisfied with the match between their skills and their job, but cannot determine how well matched they actually are because of data limitations, something that the data set used here makes possible.

The closest paper to our own is one by [START_REF] Allen | Educational mismatches versus skill mismatches: effects on wages, job satisfaction, and on-the-job search[END_REF], who

Data

We utilise data drawn from the 2001 Skills Survey, which is a cross-sectional survey of 4470 individuals aged between 20 and 60 in Britain in paid work at the time of interview in spring 2001. The design of the survey was patterned on that of the first Skills Survey, conducted in spring 1997 [START_REF] Ashton | Work skills in Britain[END_REF]. Random sampling methods were used, and the achieved sample was representative of the British population. Full details of the sampling frame and fieldwork methods can be found in [START_REF] Felstead | Work skills In Britain[END_REF]. The questionnaire comprised a detailed investigation of the nature of the individual's job with an emphasis on the activities that the job entails. Additional information was obtained on the organisation in which the individual worked, pay and changes that had occurred in the job in the last 5 years. Some background demographic information on each individual was also collected.

The key questions for our analysis are those that generate the over/underqualified and over/under-skilled variables. For the qualification variables, a list with a large number of qualifications was offered to the respondents, from which they indicated those qualifications that they hold. These were then ranked and assigned a level from 1 to 5, with 0 indicating no qualifications 4 . Earlier in the interview, the same list of qualifications was presented, but here the respondent was asked which would be required by someone now in order to get the job in

i i i i i RQ AQ if OQ RQ AQ if OQ = > = 0 1
where OQ i is a dummy variable taking the value of 1 if the respondent is overqualified and 0 otherwise, AQ i is individual i's highest qualification (on the 0-5 scale described above), and RQ i is the required qualification level for individual i's job, on the same scale.

Similarly, the under-qualified variable is defined as: If the respondent indicated that they were over-skilled according to either of these questions, i.e. they disagreed or strongly disagreed with the first statement, or they answered 'very little' or 'a little' to the second question, then they were classified as being over-skilled, since they were not making full use of their skills and abilities in their jobs 5 .

i i i i i i RQ AQ if UQ RQ AQ if UQ = < =
The under-skilled variable was based upon the following question: "How much do you agree or disagree with the following statement: 'I would perform better in my current job if I possessed additional knowledge and skills'?: Strongly agree Agree Disagree Strongly disagree" A dummy variable taking the value of 1 if the respondent strongly agreed with this statement, and 0 otherwise, was defined 6 .

Turning to other variables used in the analysis, the wages measure is the log of hourly pay. The personal characteristics included are gender, age, marital status, the presence of children and work experience. As well as their highest qualification level, as described above, the highest maths qualification that each respondent has achieved is also known. For graduates only, the subject area of 12 their degree and the type of institution they attended is observed. As for job characteristics, as well as the required education level for the job, as described above, information on full-time/part-time status, permanent/temporary status, whether shift work is involved, establishment size, industry, public/private sector status and occupation is also used. The next section examines some of the relationships amongst these variables.

Results

(i) Reliability Testing of the Main Variables

A first step to be undertaken is to check whether the over-/under-qualified and over-/under-skilled variables are performing the skill utilisation measurements that we want them to. To this end, the extent of each by one-digit industry and occupation was calculated. The results appear entirely reasonable, suggesting that these self-reported variables are picking up what we want them to pick up.

In particular, one might expect to find that the over-qualified and the over-skilled are more likely to work in low-skill industries and occupations, and this is what is observed. The three industries with the highest proportion of over-qualified workers are the wholesale/retail trade, hotel and catering, and transportation industries. The lowest rates of over-qualification and over-skilling are found, as expected, in the industries where most jobs are skilled and require high level qualifications for access, for example the education sector. The industrial pattern is less clear for the under-qualified and under-skilled variables. The distribution of these variables varies less across the various industries than was the case with the over-qualified and over-skilled variables. Nevertheless, the industries with and the hotels and catering industries, while the industries with the lowest incidence of under-skilling are construction, hotels/catering and education.

There is a clearer pattern of results across occupations than across industries 7 .

Particularly on the over-skilled variable, there is a monotonic relationship with the top three occupations (managers, professionals and associate professionals)

having the lowest incidence of over-skilling, the middle three occupations (secretarial, skilled trades and personal services) having intermediate levels of over-skilling, and the lowest three occupations (sales, plant operatives and elementary occupations) having the highest incidence of over-skilling.

Thus, these self-reported variables seem to be behaving reasonably.

(ii) The Incidence of Over/Under-qualified and Over/Under-skilled Status

The 2001 Skills Survey data reveal that 37% of employees are over-qualified for the job that they do. This compares to the figure of 32% in the 1997 Skills Survey, implying a rise in the extent of over-qualification over these four years. This is after a period of relatively stable levels of over-qualification, as described in [START_REF] Green | The utilisation of education and skills: evidence from Britain[END_REF]. The level of under-qualification is about half the rate of over-qualification, a finding that is commonly found in the literature. In terms of the less well-documented skill usage variables, 35% of UK employees are overskilled and so do not make full use of all the skills and abilities in their possession, while 13% are under-skilled. This section begins the investigation into the factors causing over-qualification by examining simple Spearman rank order correlation coefficients between these concepts, and the over-skilling variable. The aim is to establish whether the over-qualified are really in possession of skills that are being under-utilised in their jobs. There is a statistically significant positive correlation between the over-qualified variable and the over-skilled variable, revealing that there is some relationship, although the 0.2 coefficient suggests one of only moderate strength.

Using similar variables from a Dutch data set, Allen and van der Velden (2001) find a similar weak relationship. Among the employees who are over-qualified, less than half (47%) report having skills and abilities that they are not using in their job. This compares with 28% of those who are not over-qualified who report under-utilising their skills. While some of the observed over-qualified workers thus appear to be over-skilled, consistent with the mismatch stories, other apparently over-qualified workers report being in jobs commensurate with their skills, consistent with the 'heterogeneous skill within qualification levels' theory.

Amongst those employees who are over-qualified and over-skilled, which skills in particular are being under-utilised? Using questions in the Skills Survey that ask about the importance of various skills in the respondent's workplace reveals that the over-qualified are more likely to work in jobs where there is a low importance attached to professional, high-level communication (such as making presentations, writing substantive reports, instructing others), planning, numeracy, literacy and problem solving skills. Correlation between these skill- as less important (with the addition of client communication skills). This could suggest, although not prove, that it is these skills in particular that are being under-utilised amongst the over-qualified and over-skilled.

Turning to the under-qualified, there is no relationship at all between underqualified status and under-skilling; the under-qualified are no more likely to lack sufficient skills to perform their jobs than those who are adequately qualified.

Thus the under-qualified are not, on the whole, a group struggling out of their depth in jobs for which they do not possess sufficient skills. The interpretation is therefore that these are employees who have gained skills through other routes after the end of their schooling, primarily through years of working experience.

They are now capable of performing jobs that demand a higher qualification level of current new entrants.

(iv) The Determinants of Over/Under-qualified, Over/Under-skilled Status Thus far, the findings indicate that some, though far from all, of the overqualified can be seen as having under-utilised skills, while the status of being under-qualified has no apparent relationship to being under-skilled. In this section we investigate the multivariate determinants of over/under-qualified and over/under-skilled status, in an effort to distinguish further between the competing explanations 8 . Table 1 shows the estimated marginal effects of various explanatory variables on the probability of being over-qualified, derived from probit equations for the full sample, and also for graduates only, for whom we have additional information about degree subject and institution attended 9 . The results reveal that the characteristics of an individual's job are closely related to over-qualified status.

In particular, part-time jobs, jobs involving shift work, jobs in small workplaces and jobs in the private sector are strongly associated with the likelihood of being over-qualified. The effects of job characteristics appear to dominate those of the individual characteristics, all of which attract statistically insignificant coefficients, with the exception of the age variables, which suggest that primeaged workers are less likely to be over-qualified than both the young and the old.

However, the individual and job characteristics are closely related, so that the effects of the former may be picked up by the latter. Thus, if the job characteristics are omitted from the estimated equations, the effects of the individual characteristics are observed more clearly. In particular, such results

(not shown in 1 are however consistent with the 'heterogeneous ability' explanation of over-qualification. The results show that higher achievements in mathematics lower the probability of being over-qualified, in particular by 15 percentage points if a maths A-level is held 11 . A maths degree does not seem to have any further statistically significant impact on the probability of being overqualified. However, this is due to almost all maths graduates in the sample also holding maths A level, and so maths graduates have in effect already been considered. To the extent that maths ability can be used as an indicator of general ability, or as an indicator of an ordered mind capable of planning and problem solving, this result would suggest that those of lower ability are more likely to be over-qualified.

In the graduate-only sample, subject of degree has an important impact on overqualified status, with the negative coefficients on all of the subject variables suggesting that the omitted category, business and management studies, has the highest over-qualified graduate rate. Several subjects lead to an over-qualified probability that is significantly lower than that produced by this subject, namely, computing, physical sciences, 'other' (many of these are education degrees), arts and English. This subject list is consistent with those found by other researchers, as described above, although the presence of arts and English on this list is a bit surprising. With respect to institution type, the results suggest, consistent with [START_REF] Dolton | The incidence and effects of overeducation in the graduate labour market[END_REF], that graduates of the more established universities are less likely to be over-qualified than those of the universities created since 1992, and in particular than graduates of foreign universities, although none of the institution coefficients achieve statistical significance. Turning to the determinants of being under-qualified, these are not reported in full, as they are essentially a mirror-image of the findings in Table 1, with fulltime jobs, those not involving shiftwork and those in the public sector being more likely to be filled by an under-qualified worker. Older workers and those who are married are more likely to secure a job demanding a higher qualification than they actually hold. These findings are consistent with the view that employees in stable full time work, who are more likely to acquire skills at work, are enabled to take on jobs above their qualification level. Similarly, the ability effect is shown in that those who have achieved an A-level in maths are also more likely to obtain a job at a higher qualification level than they actually hold.

These results thus reinforce the finding from the previous section that underqualified status has no correlation with being under-skilled.

In 1), they are not more likely to be over-skilled or under-utilising the skills that they have learnt, as we might have expected if there were simply too many graduates of these subjects for the available number of jobs. The fact that they are more likely to be over-qualified in terms of formal qualifications, and yet just as likely to be in a job making full use of their skills and abilities as graduates in other disciplines, suggests a number of possibilities. One is that the courses they have followed are not associated with the skills necessary to get a graduate level job. Another is that less able students, who are not suitable for graduate level jobs, choose subjects in these fields because they are perhaps perceived as less difficult than other subjects. The final possibility is that graduates of these subjects are more likely to go into jobs where a degree is less of a formal, explicit requirement, than graduates of other disciplines such as medicine, education, engineering and science, whose jobs upon graduation are more likely to stipulate a degree as a definite requirement. The first two hypotheses say that the reason for the lack of over-skilling amongst the over-qualified business graduates is that they are actually only able to do upper secondary education type jobs. In the third explanation, they have graduate level skills and perform jobs that use these skills, although not demanding a degree of applicants. The fact that the wage results that follow show that business graduates are amongst the highest paid, on average, of all graduates, suggests in fact that the last explanation could be key.

Finally the determinants of under-skilled status are again the mirror image of those in Table 2 for over-skilled status, although few variables attract statistically As described in the Introduction, many papers have estimated the impact of being over-qualified (under-qualified) on earnings, and found it to reduce (increase) earnings, relative to similarly educated peers who obtain a job at the appropriate qualification level. Tables 3 and4 provide similar results, for all employees and graduates only, respectively. In each case the dependent variable is the log of hourly pay.

The results in the first columns of each table are consistent with the previous results in the literature; amongst all employees, the over-qualified earn, on average, 18% 13 less than individuals working in jobs for which they have an appropriate level of education. Amongst graduates this figure is 15%. Similarly, the under-qualified earn more than individuals with the same qualification level who work in a lower level job more in keeping with their formal education, by 18% amongst all employees. So far, these findings are standard 14 .

The key piece of analysis to be undertaken in this part of the paper, however, is

to examine what happens to these wage penalties and premiums, once we control for the extent of over-and under-skilling. If the reason why the over-qualified earn less is that they are not using their skills and abilities to the same extent as someone of the same education level in an appropriate job, then once we control The results, in the second columns of Tables 3 and4 reveal, however, that this is certainly not the case. Although the over-qualified coefficient does fall in each table, by two percentage points and four percentage points respectively for all employees and graduates only, in each case the fall is not statistically significant 15 . Thus, holding constant the extent of skill-underutilisation, overqualified workers still earn less than their appropriately-qualified peers, suggesting that the reason for the wage penalty is not that skills are being underutilised and wasted, at least to any significant extent. There must be another reason why, for example, over-qualified graduates are still earning less than those in graduate level jobs, even when we hold constant the utilisation of skills across this comparison. One possibility consistent with, although not proved by, these results is that the over-qualified graduates are less able or have less appropriate and marketable skills than those who find graduate level employment.

Another possibility is that the over-skilling variable is a poor measure of the actual utilisation of skills, and so it does not explain much of the over-qualified effect on wages. However, over-skilling attracts a strongly significant, negative coefficient, suggesting that it does contain important information. As expected, individuals not fully utilising their skills earn less. The under-skilled coefficient is much smaller in absolute value, and does not achieve statistical significance in either of the presented equations. It is unlikely, however, that an employer would continue to hire an under-skilled individual, suggesting that the variable is probably picking up an acceptance that improvement in work performance is possible, rather than genuine underskilling.

Conclusions

This paper has attempted to explain why some individuals are, or appear to be, over-qualified for the work that they do. One possibility is that individuals within a particular education level are heterogeneous with respect to the full range of human capital. They therefore only appear to be over-qualified because certain aspects of their human capital are unobserved. If all aspects were observed, it would be seen that such workers are in jobs commensurate with their skills, and there is therefore no under-utilisation. Using data from the 2001 Skills Survey, substantive evidence for this 'heterogeneous skill within qualification levels' theory is found. Thus, although the correlation coefficient between over-qualification and over-skilling was positive and statistically significant, it was quite low at only 0.2. Less than half of the over-qualified are over-skilled. In addition, the fact that the wage penalty associated with being over-qualified is not significantly reduced once possible over-skilling is controlled for suggests that the reason why the over-qualified earn less is not because they are underutilising their skills relative to the appropriately-qualified.

One such possible reason is, of course, low level unobserved skills and abilities. An alternative to low-level skills is the holding of higher level skills that are simply not in large demand relative to supply.

Also consistent with the same explanation is the finding that holding a maths qualification, which is often taken as an independent signal of an ability that is valued in the labour market, is associated with a lower likelihood of being overqualified and a greater likelihood of being under-qualified. At a degree level only, it appears that graduates of the more science-based subjects are also less likely to be over-educated.

Finally, evidence here suggested that the over-qualified are more likely to work in jobs that do not attach a large importance to communication, planning and problem solving skills. One interpretation of this finding is that it is these skills and abilities that the over-qualified are lacking, so preventing them from working in jobs that might appear more commensurate with their formal qualification levels. It is perhaps interesting that these are precisely the skills often mentioned as being in short supply by employers in surveys such as the Employers' Skill Survey 16 .

Putting several literatures together, therefore, evidence suggests that currently in the UK there are growing numbers of highly-educated individuals, growing, or at least steady, returns to high level qualifications, yet at the same time, employer reports of skill shortages, as well as the presence of large numbers of seemingly over-qualified people. One possible way to make sense of these various results, consistent with the findings obtained here, is that there is a shortage of the skills Finally, it should be noted that the above description does not cover all incidences of over-qualification, and in some cases there is a genuine underutilisation of skills amongst the over-qualified, which may be caused by mismatch. Evidence for this is the positive relationship between overqualification and the presence of dependent children and associated part-time working. This evidence of some mismatch supports the need for policies to ensure labour market flexibility, especially to reduce constraints implied by shortages of childcare facilities. More research on employment dynamics would be helpful to determine how long people tend to remain over-qualified, and hence gain a better understanding of the extent to which skills mismatch is a permanent problem. individuals therefore seemed to represent a more extreme group, who may be struggling to even perform adequately in their job, and need additional skills or abilities just to reach such a level.

F

7 Obviously, an industry can only be classified as high skill or low skill on average, with each industry actually employing workers from the full range of skills. With occupations, it is more likely that almost all will be of a certain required skill level, for example professional jobs requiring a high level of skills, and elementary occupations requiring a lower level of skills.

8 Separate probit equations are estimated for the likelihood of being over-qualified and underqualified. An alternative estimating strategy would have been to estimate a bivariate probit, thus allowing the error terms in the two equations to be correlated, under the reasonable assumption that the same unobservables will influence the probabilities of being over-qualified and underqualified (with opposite signs presumably). However, this implied that different samples could not be used in the two equations, and so if the full sample was used, then those with no qualifications would be included in the over-qualified equation, and those with the highest level of qualifications would appear in the under-qualified equations. Since neither of these situations (unqualified being over-qualified and highest qualified being under-qualified) can occur, when a bivariate probit was estimated, this led to suspect and sometimes perverse coefficients on any variables correlated with the likelihood of being unqualified or highly qualified. For example, those in part-time work, who are more likely to be unqualified, suddenly seem to have a lower probability of being over-qualified, this of course being due to the fact that they have no qualifications, rather than anything to do with the nature of part-time work. Similar outcomes occurred when over-qualified and under-qualified status were combined, together with adequately qualified, into a single variable, and a multinomial logit used to explain variation in this variable.

9 Individuals with no qualifications are excluded from the analysis in this table as they cannot, by definition, be over-qualified. 10 We also investigated whether the burden of childcare falling principally on women meant that it was women who were taking such jobs for which they are over-qualified, by including separate interaction terms between gender and number of children and between gender and full-time/parttime status. The coefficient on the former interaction term implied that the effect of children on 36 the probability of being in an over-qualified job is 60% higher for women than for men, though this coefficient was not statistically significant. The coefficient on the latter interaction term was highly statistically insignificant, suggesting that both men and women who choose or accept parttime jobs are more likely to be over-qualified. It is true, however, that about 90% of those individuals working in part-time jobs are women.

11 In a further estimation, not shown, we also controlled for the highest qualification held, although this potentially creates an endogeneity problem as this variable is used in the construction of the dependent variable. This estimation did not alter the pattern of results.

12 The children coefficient is again statistically significant when the job characteristics are omitted (not shown), but loses this significance once the job characteristics are included, again suggesting that the driving of some such workers into unstable forms of employment is causing their over-skilling.

13 Calculated as e -1, where is the estimated coefficient in the log-linear equation, in this case -0.166. 14 In addition, the other coefficients are all consistent with wage equation results in the literature.

15 Similar effects are observed by [START_REF] Allen | Educational mismatches versus skill mismatches: effects on wages, job satisfaction, and on-the-job search[END_REF]. 16 See DfES (2002).

Page 37 of 37

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

Submitted Manuscript

  -educated workers employed with the appropriate required qualifications for such a job.

  over-and under-skilled variables as us, found in their Dutch data set. We now turn to a description of our data.

  works. Using the same categories as before, this gives a required education level for the job. A respondent was then classified as overqualified if his/her actual qualification exceeded the required qualification for the job, i.e.

  i

"

  the over-skilled variable, this is based upon the following two questions in the Skills Survey: "How much do you agree or disagree with the following statement: 'In my current job I have enough opportunity to use the knowledge and skills that How much of your past experience, skill and abilities can you make use of in your present job?:

  of under-qualified workers are the wholesale/retail trade,

  the Over-qualified also Over-skilled?

  the over-skilled variable reveals that those who claim to have unused skills and abilities work in jobs where exactly the same skills are viewed

  The results do suggest that women and those working in part-time jobs (which, of course, overlap to a large extent) are less likely to feel under-skilled.(v) The Wage Effects of Over/under-qualified and Over/under-skilled Status

  in the labour market, amongst the well-qualified individuals being produced. This could be a shortage of technical science, engineering and computing skills, or more practical planning, problem-solving and communication skills. This shortage of skills creates a high demand for the graduates who possess such skills, thus raising the average returns to high level qualifications, as observed in the returns literature. Those lacking such skills, however, cannot get access to the high level jobs demanding these skills, and have to be content with lower level jobs, for which they are apparently overqualified, but which are actually quite commensurate with their skills and abilities.

  Table1) suggest that individuals with children are around six percentage points more likely than the childless to work in job for which they are over-qualified. Therefore, consistent with the mismatch theory outlined above, it appears that the presence of children may restrict parents' mobility in the labour market because of attachments to particular schools or institutions. The fact that this effect is picked up by the job characteristics variables in Table1suggests that those who face rigidities in the labour market choose jobs that are less demanding on their time or take the only jobs available, and that these part-time,

	Other results in Table
	F o
	r
	P e
	e
	r
	R e
	v i
	e w
	17

shiftwork, typically private sector, jobs do not match the higher level qualifications that they have 10 .

Table 2

 2

	It is interesting, however, that none of the other coefficients on the subject
	variables in the graduate equation attract statistically significant coefficients,

, skill levels rather than qualifications are considered. The results reveal that those workers whom we argued were more likely to be mismatched, namely non-prime age workers and those with family responsibilities, 12 are again more likely to be over-skilled. Therefore, those who are mismatched in this way into unstable forms of employment (part-time, shiftwork, in the private sector) are under-utilising their skills. Other results suggest that maths skills are less likely to be under-utilised.

with the exception of that on the medicine variable. It would therefore appear that, although graduates of business or management degrees are less likely to be

Table 1 : The Determinants of Over-qualified Status

 1

	o
	r
	P e
	e
	r
	R e
	v i
	e w

Table 2 : The Determinants of Over-skilled Status

 2

		All employees	Graduates
	female	-0.023 (0.018)	0.023 (0.041)
	age	-0.024 (0.006)**	-0.051 (0.016)**
	Age 2 / 100	0.025 (0.008)**	0.062 (0.020)**
	married	-0.054 (0.018)**	-0.089 (0.041)*
	has children	0.018 (0.019)	0.034 (0.043)
	in a permanent job	0.014 (0.032)	0.007 (0.062)
	in a full-time job	-0.182 (0.022)**	-0.159 (0.060)**
	ever do shift work	0.050 (0.019)**	0.066 (0.058)
	25-99 employees	0.005 (0.020)	-0.043 (0.045)
	100/499 employees	0.066 (0.021)**	-0.010 (0.046)
	500/999 employees	0.003 (0.033)	-0.136 (0.048)**
	1000+ employees	-0.020 (0.029)	-0.141 (0.043)**
	Public sector	-0.063 (0.017)**	-0.060 (0.040)
	highest maths = GCSE	-0.076 (0.017)**	-0.158 (0.050)**
	highest math = A level	-0.076 (0.024)**	-0.144 (0.050)**
	highest maths = degree	-0.223 (0.056)**
	Maths degree		-0.192 (0.041)**
	Computing degree		-0.077 (0.086)
	Physical Science degree		0.048 (0.068)
	Biology degree		0.026 (0.082)
	Social Science degree		-0.056 (0.063)
	English degree		-0.091 (0.069)
	Art degree		0.066 (0.094)
	Humanities degree		0.026 (0.076)
	Law degree		0.020 (0.108)
	Medicine degree		-0.140 (0.058)*
	Other degree		-0.044 (0.070)
	Oxbridge university		-0.041 (0.083)
	Old university		-0.026 (0.043)
	other HE institution		-0.061 (0.063)
	foreign university		-0.063 (0.071)
	Observations	3925	643
	Robust standard errors in parentheses. * significant at 5%; ** significant at 1%.
	Estimation by probit. Marginal effects reported.

Table 3 : The Effect of Over/under-qualified and Over/under-skilling on Wages :

 3

		All Employees
		log hourly pay	log hourly pay
	overqualified	-0.164 (0.015)**	-0.144 (0.015)**
	underqualified	0.167 (0.018)**	0.161 (0.018)**
	Low level qualifications	0.144 (0.024)**	0.132 (0.024)**
	GCSE qualifications or eq.	0.215 (0.021)**	0.193 (0.021)**
	A level qualifications or eq.	0.353 (0.022)**	0.327 (0.022)**
	Higher qualification below degree 0.557 (0.026)**	0.528 (0.026)**
	Degree level qualification	0.735 (0.028)**	0.701 (0.028)**
	female	-0.131 (0.014)**	-0.134 (0.014)**
	years of work experience	0.028 (0.002)**	0.027 (0.002)**
	work experience squared/100	-0.050 (0.005)**	-0.048 (0.005)**
	married	0.063 (0.013)**	0.060 (0.013)**
	has children	0.042(0.014)**	0.043 (0.014)**
	in a permanent job	-0.008 (0.028)	-0.005 (0.028)
	in a full-time job	0.134 (0.017)**	0.122 (0.017)**
	ever do shift work	-0.047 (0.014)**	-0.046 (0.014)**
	25-99 employees	0.066 (0.016)**	0.067 (0.016)**
	100/499 employees	0.107 (0.017)**	0.116 (0.017)**
	500/999 employees	0.124 (0.029)**	0.126 (0.029)**
	1000+ employees	0.197 (0.025)**	0.199 (0.025)**
	highest maths = GCSE	0.087 (0.015)**	0.086 (0.015)**
	highest math = A level	0.173 (0.029)**	0.174 (0.029)**
	highest maths = degree	0.378 (0.145)**	0.366 (0.146)*
	overskilled		-0.099 (0.013)**
	underskilled		0.006 (0.020)
	Constant	1.157 (0.043)**	1.229 (0.044)**
	Region dummies	yes	yes
	Observations	3572	3572
	R-squared	0.50	0.51
	Robust standard errors in parentheses. * significant at 5%; ** significant at 1%.

Table 4 : The Effect of Over-qualified and Over/under-skilling on Wages : Graduates

 4 35adequately, while still admitting that there is room for improvement. The 'strongly agreeing'

		log hourly pay	log hourly pay
	overqualified	-0.141 (0.044)**	-0.097 (0.045)*
	female	-0.102 (0.042)*	-0.101 (0.042)*
	years of work experience	0.044 (0.007)**	0.042 (0.007)**
	work experience squared/100 -0.096 (0.021)**	-0.091 (0.020)**
	married	0.121 (0.040)**	0.107 (0.039)**
	has children	0.046 (0.046)	0.045 (0.046)
	in a permanent job	-0.051 (0.073)	-0.046 (0.072)
	in a full-time job	0.125 (0.065)	0.096 (0.065)
	ever do shift work	-0.281 (0.058)**	-0.270 (0.057)**
	25-99 employees	0.145 (0.054)**	0.146 (0.054)**
	100/499 employees	0.117 (0.055)*	0.120 (0.054)*
	500/999 employees	0.090 (0.078)	0.068 (0.076)
	1000+ employees	0.227 (0.069)**	0.207 (0.068)**
	highest maths = GCSE	0.049 (0.059)	0.020 (0.057)
	highest math = A level	0.093 (0.066)	0.066 (0.064)
	Maths degree	0.087 (0.153)	0.040 (0.154)
	Computing degree	0.099 (0.175)	0.087 (0.176)
	Physical Science degree	-0.157 (0.074)*	-0.140 (0.073)
	Biology degree	-0.108 (0.087)	-0.111 (0.087)
	Social Science degree	-0.180 (0.079)*	-0.200 (0.079)*
	English degree	-0.329 (0.080)**	-0.349 (0.079)**
	Art degree	-0.233 (0.108)*	-0.213 (0.107)*
	Humanities degree	-0.276 (0.078)**	-0.276 (0.078)**
	Law degree	-0.258 (0.112)*	-0.255 (0.113)*
	Medicine degree	-0.083 (0.086)	-0.114 (0.084)
	Other degree	-0.257 (0.072)**	-0.270 (0.072)**
	Oxbridge university	0.142 (0.122)	0.148 (0.123)
	Old university	0.101 (0.045)*	0.104 (0.044)*
	other HE institution	0.021 (0.070)	0.009 (0.072)
	foreign university	-0.123 (0.100)	-0.137 (0.100)
	overskilled		-0.187 (0.046)**
	underskilled		0.003 (0.055)
	Constant	1.982 (0.148)**	2.099 (0.149)**
	Observations	591	591
	R-squared	0.37	0.39
	Robust standard errors in parentheses. * significant at 5%; ** significant at 1%.

In our own analysis, we prefer the terms 'over-qualifed' and 'under-qualified', and prefer not to use the terms over-and under-education because of the connotation attached that there is too much or too little education being provided, which, as we describe below, is only one possible reason for the presence of over-qualified or under-qualified workers.

Over-and undereducation are defined as the difference between actual qualifications held, and required qualifications for the job (overeducation if this difference is positive and undereducation if negative). Required qualifications for the job can be measured by self-reported qualifications required to get or to do the job, by expert job study analyses of the occupation being undertaken, or by the average qualification level amongst workers in a particular occupation grouping. See, amongst others,[START_REF] Hartog | On returns to education: wandering along the hills of ORU land[END_REF] or[START_REF] Groot | Overeducation in the labor market: a meta-analysis[END_REF] for a fuller description of these measurement methods, and for a discussion of their various benefits and limitations in econometric analyses.

This may be a rational choice by the individual who, for example, may actively choose parttime employment that does not make full use of their skills, so that their energies can be reserved for their other responsibilities, such as childcare. The term 'rigidities' therefore refers to impediments to the labour market achieving its most efficient allocation, and not to impediments that prevent individuals working in the job that they wish (which will be decided according to work allocations across labour market and household time, rather than simply the efficient allocation from the labour market's point of view).

 4 The five levels are a degree or higher degree (

level 5), higher level academic or vocational qualifications below degree level, (level 4), qualifications taken upon completion of upper secondary education (A-levels) or their equivalent in vocational qualifications (level 3), qualifications taken upon completion of lower secondary, compulsory, education (GCSE/Olevels, at grade C or above) or their equivalent in vocational qualifications, and finally GCSE/Olevel passes below grade C or their vocational equivalent (level 1).5 The answers to these two questions were quite highly correlated, and just using one or the other as our measure of over-skilling did not substantially alter the results.6 It was decided to classify only those strongly agreeing with this statement as under-skilled. This is because almost 2/3rds of respondents either agreed or strongly agreed that they could perform better with additional knowledge and skills. This suggests many respondents are performing

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 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


Patricio Pérez

Vicente Esteve

O33 -Technological Change: Choices and Consequences|Diffusion Processes < , O47 -Measurement of Economic Growth|Aggregate Productivity

Keywords: Researchers, Structural change, Idea stock

published or not. The documents may come   L'archive ouverte pluridisciplinaire

the early 1970s and early 1980s. This being the case, one might expect a certain synchrony between the behaviour of output per worker, on the one hand, and certain indicators of technological progress, on the other. Layton and Banerji (2003, p. 1790-1792) noted that cyclical co-movements of the key coincident indicators characterize business cycles. For [START_REF] Romer | Endogenous Technological Change[END_REF], the advance of technical progress depends on the discovery of new ideas. Researchers whose work is devoted to research and development (R&D) and idea stock activity, all other things being equal, determine total factor productivity (TFP) growth. By linking idea stock with TFP, [START_REF] Jones | R&D Based Models of Economic Growth[END_REF][START_REF] Jones | R&D Based Models of Economic Growth[END_REF] transformed the function of production for ideas into a technical progress function.

According to [START_REF] Keely | Technology in growth[END_REF], R&D is a readily identifiable factor input for knowledge production in many technology-driven industries. A look back over the past decades reveals a decline in R&D growth rates that begins in the mid-1960's, "the timing" being "appropriate for declining productivity growth 5-10 years later" (Griliches 1994, p. 2). This view is strengthened by the fact that the share of gross national product (GNP) devoted to R&D shows simultaneous signs of stagnating. As [START_REF] Verspagen | Technology indicators and economic growth[END_REF] points out, and as table 1 illustrates for the G-5, there appear to be huge differences (in terms of R&D spending) between the OECD countries. The USA and Switzerland started out as the leading countries in this respect, but during the 1970s and 1980s certain major European nations, also accompanied by Japan, caught up.

[Insert Table 1 around here] In this paper, our goal is to provide a characterisation of the takeoffs and slowdowns observed in input and output measures of R&D in the United States, Germany, France and the United Kingdom. A sequential methodology is applied to test for breaks in the number of researchers and in the idea stock, which introduces the possibility of examining the long run behaviour of growth rates. The testing procedure covers the period between 1950 and 2001. The estimates bear out the perception of a slowdown in R&D process, although they bring forward the date of change. The four countries mentioned experience a trend and level break in the researcher series for the mid-1960s, with a slight variation in break year dates. The results as a whole also corroborate the thesis of new ideas slowdown, in the middle of the 1960s (coinciding, moreover, in the United States with the first oil crisis). The United States, at the top, and Germany, at the bottom, represent the extremes in the range. Both statistical procedures allowing for two shifts and multiple structural change methods work out quite similar results.

The rest of the paper is organized as follows. The next section describes the data and discusses measurement issues. In the third section, a time frame is spelt out to detect the presence of some breaks and their impact. The fourth section focuses on the timing of the breakpoints and assesses for the economic implications. Finally, the fifth section offers some concluding remarks.

II. DATA

According to [START_REF] Romer | Endogenous Technological Change[END_REF] model, the cumulative stock of knowledge used to produce output, A, corresponds to the number of ideas invented over the course of the

α α σ - = 1 Yt t t t H K A Y , ( 1
)
where K is physical capital and H Y is the total quantity of human capital employed to produce output. It assumes 0<α<1 and σ>0. In practice, A t is measured as multifactor productivity in equation ( 1). The accounting exercise is conducted in the same spirit as Solow's classic growth accounting model. (For data sources, see Appendix A).

On the other hand, effective research effort made by a country, H A , is the weighted sum of researchers where the weights adjust for human capital:

∑ = At t At L h H θ .
(2)

In this equation, L A is the number of researchers, h is human capital per person and θ ≥ 0. Scientists and technicians are viewed by the OECD as the central element within the research and development system. In accordance with the observations made by [START_REF] Bils | Does Schooling Cause Growth?[END_REF]Klenow (2000, p. 1162) in relation to human capital, national scientists may both speed up the adoption of technology and also be necessary for technology use.

We are well aware of the potential problems caused by possible inadequacies presented by the data used to carry out the analysis. In this respect, idea stock (the residual of the production function) measures all other sources not taken into account by the growth rates of conventional inputs [START_REF] Atella | Do R&D expenditures really matter for TFP?[END_REF]Quintieri 2001, p. 1387). On the other hand, the series for numbers of researchers appears to be more reliable, though certain considerations will have to be borne in mind (Romer 2000, p. 21). To provide a rough empirical measure of H A , we will assume that θ = 0 in equation (2). Nonetheless, "measured R&D is the only data we have, and it probably represents a reasonable benchmark provided these caveats are kept in mind" (Jones 2002, p. 226). Indeed, any 3 other indicator one might choose would certainly be accompanied by its own peculiar disadvantages. For example, scholars like [START_REF] Griliches | Patent Statistics and Economic Indicators: A Survey[END_REF] have laboured long in their endeavours to measure patents, without coming up with any convincing outcome.

III. THE TIME SERIES FRAMEWORK

This section lays briefly out the model and statistical procedure, allowing for two shifts in the deterministic trend at two distinct unknown dates. The reader is referred to [START_REF] Perron | The great crash, the oil price shock, and the unit-root hypothesis[END_REF], 1997), Banarjee et al. (1992), Zivot and Andrews (1992), [START_REF] Lumsdaine | Multiple Trend Breaks and the Unit Root Hypothesis[END_REF], [START_REF] Vogelsang | Additional tests for a unit-root allowing for a break in the trend function at a unknown time[END_REF][START_REF] Ben-David | The Great Wars, the Great Crash, and the Unit Root Hypothesis: Some New Evidence About an Old Stylised Fact[END_REF], 2000) and Atkins and Chan (2004) for further details. It is possible to think of y t as being the sum of a deterministic component TD and a stochastic component Z t ,

t t t Z TD y + = , ( 3
)
where TD is linear in time t,

t TD t β µ + = . ( 4
)
Once the unit root hypothesis has been rejected, the analysis focuses on the timing of the breakpoints and their severity. Our objective is to test for possible multiple structural changes in long-term output (logarithm of the stock of ideas and of researchers). The null hypothesis of no structural change is that µ and β are constant over the span of the data, whereas the alternative allows for one or more simultaneous changes in both the intercept and the slope. Firstly, the null hypothesis of no structural change is tested, within a framework in which the break years are not exogenously predetermined, but where a process that endogenises the search is used. [START_REF] Sen | Are US macroeconomic series difference stationary or trend-break stationary?[END_REF]Sen ( , p. 2026) ) shows that "use of the mixed model will yield more reliable estimates of the break-date". So the test for trending data involves regressions of the following form:

F o r P e e r R e v i e w 4 t k j j t j m i t i i m i t i i t y c DT t DU y ε γ β θ µ + + + + + = ∑ ∑ ∑ = - = = 1 1 1 (5)
The period in which a change takes place in the trend function parameters is identified as T Bi . The break dummy variables take the following values: DU it =1 and DT it = t-T Bi if t>T Bi , 0 otherwise. The equation is estimated sequentially for all possible pairs (T B1 , T B2 ), where T Bi = 2, … T-1, i = 1, 2, and T is the number of observations after adjusting for lag length k. C(L) is a lag polynomial of known order k.

For each choice of T Bi , the value of the lag length k is established following the criterion employed by [START_REF] Campbell | Pitfalls and opportunities: What macroeconomists should know about unit roots[END_REF]. This is a recursive method, where an upper bound k max is set a priori. If the last included lag is significant, choose the upper bound; otherwise, a unit reduces k. If there is no significant lag, set k=0. We set the upper bound on k equal to 8 and the criterion of significance of the last lag statistic is set at 1.6, corresponding to 10% of the asymptotic normal distribution. The SupF t statistic is the maximum (among all the possible trend breaks) of twice the standard Fstatistic to test θ 1 =γ 1 =0. The null hypothesis of no structural change is rejected if it exceeds the critical value.

Once T B1 has been fixed in the manner indicated above, the equation ( 5) is estimated for each potential break year (T B2 ), calculating the statistic SupF t as described.

The procedure now consists of testing the null hypothesis of a one-break, as against a two-break alternative, subject to the constraint that the second break be separated from the first by a gap of at least five years. The possibility of more break points may be investigated, adding additional dummy variables to the equation. In this context, slowdown is to be understood as a statistically significant negative break in the trend function of the growth process. Recession, in contrast, is defined as a severe slowdown, whereby the pre-break growth rate is positive and the post-break rate is negative (Ben- We start by estimating regressions for a flexible model, allowing for multiple breaks, both in the slope of the trend function and in the intercept. If the DU it and DT it tstatistics are significant for a certain T Bi , we register the results of the complete model; otherwise the non-significant variable is eliminated and we proceed to re-estimate models that admit breaks in the slope (θ i =0) or in the intercept (γ i =0). So how does a break in the trend function affect steady-state growth? If y(t) has a stationary trend, it asymptotically approaches to a steady-state growth path. Then, using the coefficients estimated from (5), the balanced growth rates converge for each country in the final period of the sample to the constant values:

        - = ∆ ∑ = ∞ → k j j t c y lím 1 1 β ; ( 6
)
or with:

        -       + = ∆ ∑ ∑ = = ∞ → k j j m i i t c y lím 1 1 1 γ β , (7)
when the coefficients of the dummies registering the trend are included. From equations ( 6) and ( 7) we gather that a change in level (θ i ) has an influence on stocks (of researchers and / or ideas), but not on growth rates. Whereas a trend break (γ i ), when there is stationarity, will have an impact on the steady-state growth path.

IV. TREND BREAKS AND STEADY STATE GROWTH

The main results, obtained by applying equation ( 5), are presented in table 2. In general, the data from the researcher and scientist collectives match up well with our intuition (panel A). Whilst expressing natural reservations, given a sample of this size, the process of estimation provides evidence of trend breaks. Using critical asymptotic

F o r P e e r R e v i e w
6 values, the null hypothesis of no-break is rejected at a level of 5% in the US and France.

The decision is not so clear for Germany and Great Britain, although the value of the statistic (16.15 y 16.18) makes it possible to reject the null at a level of 10%.

[Insert Table 2 around here]

It is interesting to observe the T B break years involved here. In all the countries, they are located around the mid-1960s: France in 1966, the United States in 1967 and Great Britain in 1968. Only Germany "jumps the gun", its change occurring in 1963;

although this is conditioned by the fact that the SupF t statistic proves significant at a level of 10%. In all cases the estimation processes identify reductions in the trend function slope, i.e. there is a slowing-down. In the US, there is additionally a drop in the intercept or, in other words, recession. (Appendix B records the coefficients and tstatistics in their totality). The results suggest a high degree of coincidence in the development of the research infrastructure. At the end of the 1960s a deceleration was produced in the growth rate of this collective, anticipating the end of the "golden age"

of the western economies. The results coincide with those of Ben-David et al. (2003, p. 311), whose findings are that more than half of the countries they analysed experienced one of their breaks in 1955 or later, while some did so in the 1970s. Harvey and Mills (2005, p. 174) also provide strong evidence of the existence of a common business cycle among these countries.

As well as this generalised breakdown in the second half of the 1960s, in Germany, 1989 is the epitome of another breakpoint. The series of researchers is characterised by what seems to be a peak, followed by a swift return to the growth path The results in table 2 (panel B) are in accordance with the thesis of research intensity deceleration, between the mid-1960s and mid-1970s. Notwithstanding, the conclusions are not now as evident as those that were extracted from the researcher series. On the one hand, the null is conclusively rejected in the United States and

Germany at a 5% level of significance, in favour of the alternative of stationarity accompanied by trend break in the 1960s. But, on the other hand, the estimation processes do not permit rejection of the null hypothesis of an absence of breaks in France, and the situation in Great Britain is limited to an upwards change of level. Occurring in 1966, the break in the series of ideas (table B2) took on dimensions in the United States similar to the above mentioned researcher series trend break (γ 1,US = -0.003), while it had a much greater impact in Germany (γ 1,GER = -0.009). Furthermore, there was a level break in the United Kingdom (θ 1,UK = 0.032), in 1962, and another in the US (θ 2,US = -0.034), coinciding with the first oil crisis, in 1973 [START_REF] Jiménez-Rodríguez | Oil price shocks and real GDP growth: empirical evidence for some OECD countries[END_REF].

Assuming that the use of this framework keeps on offering evidence against the unit root null hypothesis, we provide additional information in order to reinforce the validity of these assumptions. Therefore, we present and use (in Appendix C) the [START_REF] Bai | Estimating and Testing Linear Models with Multiple Structural Changes[END_REF], 2003a, 2003b) methodology as worthy complement in order to study the presence of breaks in the trend. A key feature of this procedure is that it allows testing for multiple breaks at unknown dates, so that it successfully estimates each break point by using a specific-to-general strategy in order to determine the number of breaks consistently. In that respect, it is of interest to highlight that the results reported in the main body of the text are not modified in any way by the application of this new set of statistics.

[While we mentioned above that the tests do no reject the hypothesis of a nonintegrated process, this could be elaborated upon further. Now that the reach and nature of the breaks have been seen, the (actual) rate of growth along the path of the steady state is compared with what it would have been (counterfactual), if the original path had not been interrupted by the structural change.

Steady state growth rates were calculated from equations ( 6) and ( 7) using the estimated coefficients for the trend ( [Insert Table 3 around here]

The unequal intensity of the crisis in these two countries is reproduced in relation to the ideas (table 3, panel B). The difference between the growth rates of the final and initial steady-states, which is of -0.8 percentage points in the United States, reaches -4.6 points in Germany (ratios of 0.64 and 0.25, respectively). Perhaps the most striking aspect of the process is that, after the structural change, new ideas grow almost at the Did these countries depart from the original steady-state path? The answer appears to be affirmative, although a wider-reaching perspective would be required to respond to the question. Let us take a look at the researcher series: the ratio between growth rates after the last break and prior to the first scarcely surpasses a share of 0.50 on average. If, maintaining the numerator, the growth rate for the period between the first and second breaks is calculated on the denominator, the ratio is around 0.75-0.80. In other words, it has nowhere near recovered the post-trend break standards of the 1960s.

From a long-term perspective, such a supposition is far from clear.

Still, with the main focus on the trend breaks in R&D process, to what degree are we dealing with definitive changes? The neoclassical model foresees a dynamic of transitory deviations from the balanced growth path. In the degree to which the vigorous growth observed up to the second half of the 1960s reflects a transitional period, it could not possibly be sustained indefinitely. But our results also seem compatible with the fact that technological diffusion becomes increasingly difficult as the lagging countries draw closer to the frontier represented by the leader.

V. CONCLUDING REMARKS

Our study sets out to characterise possible breaks in the R&D process in the United States and Europe, in the second half of the 20 th century. Several caveats need to be emphasised. First, the growth rate of TFP in the OECD countries has declined over the past decades, while the shares of GDP devoted to R&D simultaneously show signs Third, the pre-break rates are higher than their post-break equivalents. In this connection, the United States and Germany appear to represent the end points in the range of incidence. In the former country, the slowdown involves a reduction in research growth rate, from 5.6% until 1967, later dropping to 3.1%. In Germany, the fall is far more dramatic, because it drops from 7.3% before 1963 to a mere 1% after that date. Parallel to these situations, the break in the idea stock growth path in 1966 meant that TFP was reduced by a third in the United States and by three quarters in Germany.

Finally, the synchrony between researchers and ideas growth processes, in the US, reinforces the thesis of mutual interaction between them. Meanwhile correlation seems not to be as close among the European countries as it does in the US. • People in work. The starting point is the total employment in 1960, obtained from OECD Labour Force Statistics. The series for the following years was obtained by applying to that number the rates of variation provided by Eurostat, in European Economy. In contrast, the series for the preceding years, 1950-1960, is the result of deducting the annual variations provided by Maddison (1995b) from the number of people employed in 1960.

• R&D expenditures. OECD, Main Science and Technology Indicators (various years), and [START_REF] Verspagen | Technology indicators and economic growth[END_REF] for dates prior to 1990. The issue of testing for structural changes is also considered under very general conditions on the data and the errors. The Bai and Perron tests are based upon an information criterion in the context of a sequential procedure, and allows one to find the numbers of breaks implied by the data, as well as estimating the timing and the confidence intervals of the breaks, and the parameters of the processes between breaks.

This procedure, on the other hand, is not computationally excessive, allowing for the computation of the estimates using at most least-squares operations of order O(T 2 ) for any number of structural changes m, unlike a standard grid search procedure which would require least squares operation of order O(T m ). [START_REF] Bai | Estimating and Testing Linear Models with Multiple Structural Changes[END_REF]Perron (1998, 2003a) propose three methods to determine the number of breaks: a sequential procedure, SP [START_REF] Bai | Estimating and Testing Linear Models with Multiple Structural Changes[END_REF]; the Schwarz modified criterion, LWZ (Liu, Wu and Zidek, 1997); and the Bayesian information criterion, BIC [START_REF] Yao | Estimating the Number of Change-Points via Schwarz's Criterion[END_REF]. Finally, the authors suggest several statistics in order to identify the break points:

• The sup F T (k) test, i.e., a sup F-type test of the null hypothesis of no structural break (m = 0) versus the alternative of a fixed (arbitrary) number of breaks (m = k).

• Two maximum tests of the null hypothesis of no structural break (m = 0) versus the alternative of a unknown number of breaks given some upper bound M (1 ≤ m ≤ M),

i.e., UD max test, an equal weighted version, and WD max test, with weights that depend on the number of regressors and the significance level of the test.

• The sup F T (l + 1|l) test, i.e., a sequential test of the null hypothesis of l breaks versus the alternative of l + 1 breaks.

The results of using the tests are shown in Table C1. We have applied the Bai and Perron procedures with a constant, a trend and one lag of dependent variable as regressor, allowing up to 3 breaks, and constraining each segment to have at least 10 observations. The sup F T (k) tests are significant for all series. The UD max and WD max are also highly significant. So, at least one break is present. In the case of the researcher and scientist series the sequential procedure (using a 5% significance level) selects two breaks for Germany and France, and one break for the US and Great Britain.

In the case of the idea stock series the sequential procedure (using a 5% significance level) selects two breaks in US, and one break for Germany and Great Britain; no breaks are detected in the series of ideas for France.

[Insert Table C1 around here] Thus, the Bai and Perron procedure depicts trend breaks that fit properly the shifts provided above in the text, both in the researcher and in the idea stock series, except for one. It detects indeed a trend break in German idea stock in 1986 out of keeping with the Perron (1997) and Ben-David and Papell (2000) procedures. However it is worthy of attention to highlight that the later point to a likely level break that year.

Therefore, the new estimates reinforce as a whole the results we get in table 2. The conclusion reached again is that there are structural breaks in the series around the midsixties. Nonetheless, we recognise that the GLS tests present better properties (size and power) than those of OLS tests. a The sup F T (k) tests and the confidence intervals allow for the possibility of serial correlation in the disturbances. The heteroskedasticity and the autocorrelation consistent covariance matrix is constructed following [START_REF] Andrews | Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation[END_REF] and [START_REF] Andrews | An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator[END_REF] using a quadratic kernel with automatic bandwidth selection based on an AR(1) approximation. The residuals are pre-whitened using a VAR(1).

Test USA f GER f FRA f UK f sup F T (1)
l b 1 2 2 1 d T 1 ∧ 1966 1965 1964 1967 d T 2 ∧ ─ 1988 1979 ─ d T 3 ∧ ─ ─ ─ ─ B) Idea stock Test USA g GER f UK f sup F T (1)
b l is the number of breaks obtained from the sequential procedure (SP) at the 5% size for the sequential test sup F T (l + 1|l).

c In the implementation of the procedure, we allowed up to three breaks (M = 3) and we use a trimming ε = 0.20 which corresponds to each segment having at least 10 observations.

d T i = 1,2 are the break dates estimated.

e A * , ** and *** denote significance at the 10%, 5% and 1% levels, respectively.

f We apply the procedure with the dependent variable, y t , a constant and one lag of y t as regressor

[z t = {1, y t -1 }].
g We apply the procedure with the dependent variable, y t , a constant, a trend and one lag of y t as regressor [z t = {1, t, y t -1 }]. The logistic curve is given by the equation:

cT A A be l l - + = 1 max ,
where l A is research intensity (which to a significant extent consists of the share of researchers in the labour population), l Amax is the (known) saturation level and T is the number of observations. The above equation is an S-shaped curve, which may be used to represent the research intensity that ceteris paribus will someday saturate the market. Now, by taking the natural logarithm of both sides and rearranging terms, this leads to:

t t t A A cT b l l ε + - =         - log 1 log max ,
where the disturbance term ε t is assumed to be serially uncorrelated and orthogonal to the explanatory variables. The share of the population that works in research is obtained by setting l A = L A /L. Suppose the stocks K and A growth at constant rates. In this case, substituting for l Y = 1 -l A in equation (10) from [START_REF] Jones | R&D Based Models of Economic Growth[END_REF], output per worker y t = Y t / L t can be decomposed as:

( ) ( ) γ λ γ α α δ * - * *         -         + + = t At A t t A k Kt t L l g h l d g n s y 1 1 , where L K k ≡ and φ λ α σ γ - - ≡ 1 1 . Notice that l A L is just H A .
Here, g x represents the constant growth rate of some variable x and an asterisk denotes a quantity that is growing at a constant rate. To maximise output per worker along a balanced growth path, take the derivative respect to l A : [Insert Table D1 around here]

A A A A l l l B l t y ∂ - ∂ = ∂ ∂ * γ ) 1 ( ) ( ,

  documented a slowing down of productivity growth in Organization for Economic Co-operation and Development (OECD) countries, around

  t.[START_REF] Jones | R&D Based Models of Economic Growth[END_REF] paper, this is the first factor on the right side of the aggregate production function:

  break. As for France, the series climbs a rung in 1980 and embarks on a path with a somewhat steeper slope, but not enough to imply a trend change.

Figure 1

 1 Figure 1 plots the logarithmic representation of the researcher and scientist series, and figure 2 does the same in relation to idea stock. In both cases, the series projected are obtained by extrapolating the first pre-break growth paths. It can be easily noted that the actual paths, marked with a continuous line, are situated significantly below the extrapolations (subsequent to the break), depicted by a broken line.

∧β

  ) and lagged y ( j c ∧ s). The post break growth rates also incorporate the coefficient for the trend dummy variable ( ∧ γ ). One of the main implications of the estimates is that the average rates of growth after the break of the 1960s depress the previous growth rates. Before that period, researchers and scientists hardly ever grew below a level of 5% (table 3, panel A). Afterwards, only the United States and France grow at 3%, while in Germany and the United Kingdom they scarcely rise beyond 1%. As a consequence, the difference between average growth rates of the 56 in the United States to 0.14 in Germany.

  and 1.6%) in both countries. In France and Great Britain, meanwhile, there is no evidence of breaks in the growth path.The four countries exhibit features which evidence that both researchers and ideas moved onto a lower growth path after the break in the 1960s. To what point did the trends continue to descend afterwards? An intuitive approach consists in comparing their growth rates between 1950 and the first break year (T B1 ) with the average between the last rupture (T Bm ) and 2001. The steady-state growth rates were calculated for the baseline period and also for the final one in each country, and reported in table 4. The last row provides an indication of the extent of the deceleration. As a general rule, the average annual growth rates of the final path were around 40% of those registered in the base path. The figures, along with the synchrony of the changes, reinforce the thesis of a strong correlation between processes of research intensity and discovery of new ideas in the United States. It is not sufficiently clear whether this occurs in the case of the European countries.[Insert Table4around here]The consequences of the changes in structure are of significance, bearing in mind the relationship between research, technical progress and growth. In the United States, at the rate of balanced growth prior to the break of 1967, the number of researchers and scientists doubled approximately every 14 years. Afterwards, the time required to do this had risen to over 23 years. What are the effects of the slowdown on the rhythms of advance of new ideas? From[START_REF] Jones | R&D Based Models of Economic Growth[END_REF] and the observation of the difference between the initial and final steady-states, the ceteris paribus TFP would have managed to increase to a rate of 2.16% between 1976 and 2001; that is 58% more than the 1.37% In the case of Germany, the potential increase is far more substantial, because there is a difference of 4.6 percentage points, above the meagre 1.57% achieved.

  Second, the countries experience a trend and level break in the researcher series for the mid-1960s, with a slight variation in break year dates. The results as a whole also corroborate the thesis of new ideas slowdown, in the middle of the 1960s (coinciding, moreover, in the United States with the first oil crisis).

•

  GDP per Hour. The data for GDP at 1990's constant prices were calculated using Eurostat (Statistical appendix to European Economy). The values corresponding to the period 1950-1960 are based on the GDP Movement series provided by Maddison (1995b). Weekly working hours in non-agricultural activities were obtained from the Work Statistics Directories, published by the International Labour Organization (ILO), whilst it was necessary to use various issues of the OECD Labour Force Statistics in order to estimate some of the values for the UK. • Human Capital. The data for average years of educational training for population over 25 years old come from De la Fuente and Doménech (2002) (updated to 2003).• Engineers and Scientists Engaged in R&D activities. The source (National Science Board and OECD) is the same as in[START_REF] Jones | R&D Based Models of Economic Growth[END_REF]. The figures for Germany until 1989 are the sum of the old Federal and Democratic Republics. For the years prior to 1960, it was assumed that the ratio of "research intensity" for the three European countries in relation to the US was the same in 1950 as in 1960. This ratio was interpolated for the intermediate years and then multiplied by employment.

  restricted estimates of γ for the US between 1950 and 1993 range from 0.178 when λ = 1 to 0.076 when λ = 0.25, with an intermediate value of γ = 0.123. With this parameter value, we have 109

Figure 1 .

 1 Figure 1. Slowdown in R&D Series: 1950-2001. Trend break years are above the panels. The scales of the panels are not the same.

  The number of scientists and keep growing forever at a constant rate. So saturation would suggest a non-integrative hypothesis, such as a logistic without trend breaks. We will test for this alternative on United States research intensity, as stated inAppendix D.]

	engineers obviously cannot
	F o
	r
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	r
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	9

Table B1 .

 B1 Trend Break Tests Results: Researchers

				Table B2. Trend Break Tests Results: Idea Stock
				USA USA	GER GER		FRA FRA	UK UK
	Trend Breaks Trend Breaks
	T B1 T B1	1967 1966	1989 1966		1966	1968 1962
	T B2 T B2	1973	1963		1980
	Coefficients
	∧ µ Coefficients	1.321	1.138		0.793	0.662
	1 µ ∧ θ ∧ 1 ∧ θ	(6.80) -0.049 (4.24) F o r 0.553 (4.21) F o F o r r	(5.12) 0.080 (3.43) 0.068 (1.99)		(4.65)	(4.81) 0.048 (3.36) 0.191 (3.00) 0.032
	∧ θ ∧ β ∧ θ ∧ β	2 2	0.014 (4.33) P e e 0.027 (4.10) r -0.034 P e P e (3.48) e e 0.008 0.013 r r		0.055 (3.79) 0.019 (3.80)	0.009 (3.07) (3.08) 0.002
	∧ γ ∧ γ	1 1	-0.006 (2.73) (3.63) -0.003	-0.012 (4.02) R e (3.55) -0.009 R e R e	-0.011 (4.32)	-0.006 (2.88) (2.30)
	∧ γ		2	(2.27)	-0.011 (3.46)	v i v i v i
	∧ c ∧ c ∧ c ∧ c ∧ c ∧ c c ∧ c ∧ c ∧ c ∧ ∧ c c ∧	1 2 3 4 5 6 6 5 4 3 1 2	1.17 a -0.35 c 0.19 -0.35 c -0.24 b 0.32 b 0.64 a	(3.04) 1.02 a -0.39 b -0.27 b 0.16 0.24 -0.22 0.98 a -0.10	0.92 a -0.29 -0.27 b 0.35 c e w e w e w	1.11 a -0.30 b 0.79 a
							16 18

Notes: The asymptotic t-statistics are in parentheses. The letters a , b and c denote statistical significance at the 1, 5 and 10% levels, respectively.

Notes: The asymptotic t-statistics are in parentheses. The letters a , b and c denote statistical significance at the 1, 5 and 10% levels, respectively.

Table D1

 D1 They are a mixture of good news and bad news. Looking at the good news first, we see that the specification appears to be statistically sensitive to the different sample periods. Both coefficients are well determined by conventional standards. Now look at the bad news. The earlier 1950-1967 and the later 1973-2001 periods yield c coefficients of the same (negative) sign, while the estimate for the intermediate 1967-1973 period changes to a positive one. The hypothesis of stability is decisively rejected for the Chow test, theF statistic registering at 233.1, which far exceeds any standard critical value. The tabled critical value (1% significance) is 5.10, so, consistent with our expectations, we reject the hypothesis that the coefficient vectors are the same in the three periods.

		Submitted Manuscript
	Table D1. Time Series Estimates of Research Intensity in US
	Coefficients	1950-2001	1950-1967	1967-1973	1973-2001
	log b	1.16	1.30	0.68		1.22
		(75.60)	(132.08)	(51.66)		(89.69)
	c	-0.006	-0.021	0.015		-0.007
		(11.45)	(23.09)	(23.73)		(19.65)
	F o r 0.72 Standard error R 2 0.055 Sum of squares 0.150 F o F o F o F o F o r r r r r	0.97 0.020 0.006	0.99 0.003 0.000		0.93 0.016 0.007
		P e P e P e P e P e P e
			e e e e e e
			r r r r r r
		reports estimates from upper regressions for USA, setting R e R e R e R e R e R e v i v i v i v i v i v i	A l max	* = A l	.
			e w e w e w e w e w e w
						24 29

Note: Newey-West robust t-statistics are in parentheses.

Page 25 of 35

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

Table 1 .

 1 Total R&D Expenditures as a Fraction of GDP The asymptotic t-statistics of ∆y 1 and ∆y 2 , calculated using the delta method, are in parentheses. No trend breaks are detected in the series of ideas for France and the United Kingdom. The most likely trend breakpoints for idea stock in both countries are 1966 and 1973, respectively. Average annual rates, in percentages. No trend breaks are detected in the series of ideas for France and the United Kingdom.

			Submitted Manuscript
	Year	USA	GER	FRA	JAP	UK
	1963		0.014	0.016	0.015
	1967	0.021 a	0.018	0.021	0.016	0.015 a
	1970	0.027	0.021	0.019	0.018
	1975	0.023	0.022	0.018	0.020	0.013 a
	1981	0.025	0.024	0.019	0.023	0.024
	1986	0.029	0.027	0.022	0.027	0.023
	1990	0.028	0.027	0.024	0.031	0.022
	1995	0.025	0.026	0.023	0.030	0.020
	2001	0.028	0.025	0.022	0.031	0.019
	Average	0.026	0.021	0.019	0.022	0.019

a Business R&D expenditures as a fraction of GDP.

Sources: OECD (various years) Main Science and Technology Indicators;

[START_REF] Verspagen | Technology indicators and economic growth[END_REF]

. Page 30 of 35 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Notes: The arrangement of years represents the order in which the breaks were found. Critical values from Ben-David and Papell (2000). Results may be conditioned by the fact that the critical values used are valid for N=120 sample.

Notes: Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Notes: Page 33 of 35 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

  Page 34 of 35 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Slowdown in Idea Stock: 1950-2001. Trend break years are above the panels.No breaks are detected in the series of ideas for France and the United Kingdom. The scales of the panels are not the same.

										Submitted Manuscript
					GERMANY. Break Year: 1966						UNITED STATES. Break Year: 1966
		4											2.8
													2.6
	Logs of Idea Stock	2 3					Extrapolated	Actual		Logs of Idea Stock	2.0 2.2 2.4					Extrapolated	Actual
		1											1.8
													1.6
		0											1.4
		50	55	60	65	70	75	80	85	90	95	00	50	55	60	65	70	75	80	85	90	95	00
	Figure 2.			Year F o									Year
								r
								P e
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												r
												R e
													v i
													e w
																							34

Page 35 of 35 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

ACKNOWLEDGEMENTS

The authors thank A. Colino for constructing the database and for his constant care in keeping it up to date. They are, likewise, grateful to A. Anchuelo, R. Myro, J. Pons, J. M. Sarabia and the referees for helpful comments and suggestions. *V. Esteve acknowledges financial support from the Department of Business, Universities and Science of the Valencian Government, through the projects GRUPOS03/51 and GV05/030, as well as from the Department of Education and Science of Castilla-La Mancha's Government, through the project PBI-05-008. †Corresponding author: Patricio Pérez, Departamento de Economía, Universidad de Cantabria, Avda. Los Castros, s/n, 39005, Santander, Spain. Fax: +34-942 20 16 03. email: perezp@unican.es

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

APPENDIX C: TESTING FOR MULTIPLE STRUCTURAL BREAKS

Earlier work by, e.g., [START_REF] Chow | Tests for Inequality Between Sets of Coefficients in Two Linear Regressions[END_REF] or [START_REF] Brown | Techniques for Testing the Constancy of Regression Relationships over Time[END_REF], focused on testing for structural change at a single known break data. More recently, however, the econometric literature has developed methods that allow estimating and testing for structural change at unknown break dates; see Andrews (1993) and [START_REF] Andrews | Optimal Tests when a Nuisance Parameter is Present Only Under the Alternative[END_REF] for the case of a single structural change, and [START_REF] Andrews | Optimal Changepoint Tests for Normal Lineal Regression[END_REF], Liu, Wu and Zidek (1997) and [START_REF] Bai | Estimating and Testing Linear Models with Multiple Structural Changes[END_REF], 2003a, 2003b) for the case of multiple structural changes.

A key feature of the Bai and Perron procedure is that it allows testing for multiple breaks at "unknown" dates, so that each break point is successively estimated by using a specific-to-general strategy in order to determine consistently the number of breaks. As an additional advantage, the Bai and Perron procedure allows investigating whether some or all the parameters of the estimated relationship have changed.

More specifically, [START_REF] Bai | Estimating and Testing Linear Models with Multiple Structural Changes[END_REF]Perron (1998, 2003a) consider a linear model with m multiple structural changes (i.e., m + 1 regimes), such as:

where y t is the observed dependent variable at time t, Z t (q x 1) is a matrix of regressors, δ j (j = 1, …, m+1) is the corresponding vector of coefficients and u t is the error term at time t. The indices

Z , i.e., the break points, are explicitly treated as unknown.