Human Capital Depreciation and Education Level: Some Evidence for Switzerland∗ Sylvain Weber† October 23, 2008
Abstract In this paper, we construct an earnings equation where human capital depreciation is identified as a parameter. It can be estimated by nonlinear least squares. Using nine waves (1998-2006) of the Swiss Labor Force Survey, we provide an empirical estimation and obtain an average yearly depreciation rate of 0.8% for males and 1.8% for females. Our model can also be adapted to let depreciation vary across education groups, and depreciation is then found to decrease with the level of schooling. Such a result deviates from the findings of the literature about human capital depreciation, but is consistent with theoretical considerations and with empirical studies about wage growth. Taking advantage of the Swiss dual education system, we define education levels by their types, which goes on step behind the usual classification by duration. For an equal schooling duration, we find that human capital depreciation is lower for workers who achieved academic (general) studies than for those who followed vocational (specific) studies. JEL Classification: J24, J31, M53. Keywords: Human capital, Depreciation, Obsolescence, Experienceearnings profiles, Nonlinear least squares, Switzerland.
∗ This paper was presented at the Lemanic Young Researchers in Economics Seminar, Geneva, Switzerland, April 2008, and at the Annual Conference of the European Association of Labour Economists (EALE), Amsterdam, Netherlands, September 2008. I wish to thank Ulrich Blum, Martin Carnoy, Jean-Marc Falter, Yves Fl¨ uckiger, Jennifer Hunt, ´ Philippe M´ehaut, Jos´e Ramirez, and Eric Verdier for highly valuable comments that led to improvements of the paper. Every remaining error is mine. Financial support from the Swiss Leading House “Economics of Education” (University of Geneva) is gratefully acknowledged. † University of Geneva, Department of Economics, 40 Bd du Pont-d’Arve, 1211 Gen`eve 4, Switzerland. E-mail:
[email protected]. Phone: +41 22 379 86 96. Webpage: http://www.unige.ch/ses/ecopo/staff/webers/weber.html
1
Introduction
Human resources are playing a central role in industrialized economies, which are more and more based on knowledge. As a consequence, human capital depreciation – roughly defined as the decrease of a worker’s market value – necessarily becomes a subject of fundamental interest too. Studying human capital depreciation is important from a political and social point of view, since it should help answer crucial questions such as: How long should people educate? What kinds of training should be promoted? When and how should workers re-train after schooling? At what age should people retire? Despite its relevance, human capital obsolescence has received little empirical consideration.1 The reason stems probably from the fact that it is not estimable in the frame of the seminal model of Mincer (1974), on which almost every earnings’ analysis is based. Some authors like Neuman & Weiss (1995) have nevertheless extended the Mincerian equation to build a model allowing the estimation of a depreciation rate. Their methodology is however very indirect, the estimation of depreciation resulting from the combination of several parameters plus a set of additional assumptions.2 In this paper, we follow a new trend of the literature, illustrated by articles like Groot (1998), Arrazola & de Hevia (2004), Arrazola, de Hevia, Risueno & Sanz (2005) and Wu (2007). Particularly, we build on Arrazola & de Hevia (2004) to construct a model allowing for a proper identification of the human capital depreciation rate, in the sense that it appears directly as a parameter in an earnings equation. The model takes into account the fact that observed earnings are lower than potential earnings, because a fraction of the earnings capacity is devoted to the production of new human capital during the working life. The key assumptions ensuring the tractability of the model are (1) the linearly decreasing shape imposed to the fraction of time invested in training during the working life, and (2) the direct link between the fraction of time invested in training and the quantity of new human capital produced. Even with these simplifying assumptions, the model remains nonlinear in the parameters, so that it has to be estimated by nonlinear least squares (NLS). We provide an empirical estimation of the model, using nine waves (19982006) of the Swiss labor Force Survey (SLFS). This survey is administered annually and contains very detailed information about the labor status, wages, training, socioeconomic characteristics, and the composition of the respon1
A quite recent and exhaustive review of the economic literature dealing with the causes of skills obsolescence is provided by De Grip & Van Loo (2002). 2 In the model of Neuman & Weiss (1995), technical obsolescence – the loss of skills attributable to the worker itself – is assumed to be identical for every worker, but economic obsolescence – the lowering of the value of a worker due to changes in his environment – may differ across high- and low-tech sectors. It may then be possible to disentangle the two types of depreciation. In order to retrieve estimates for the average total depreciation rate, one however needs to make additional assumptions concerning the values for the rate of return on educational post-school investments, the peak of earnings in terms of years of experience and the length of working life.
2
dents’ household. Switzerland is an interesting case for the study of human capital depreciation, thanks to its well-established dual education system. At the end of compulsory school (6 years of primary school followed by 3 years of secondary school), students can either begin vocational studies, or attend a higher level of secondary school preparing them for university studies. In the vocational track, great importance is placed on practical training and it prepares students for responsible positions in specific occupational fields. Apprenticeships indeed consist of on-the-job training in a firm and theoretical studies at a vocational school. On the other side, universities give a much more general training to students. Following the theory developed by Becker (1964), human capital acquired through vocational training can be considered as more specific than the one obtained in universities, which is more general. It is thus possible to test if the two types of training proposed in the dual education protects workers against depreciation in a similar manner. If not, education policy recommendations could be expressed on this ground. Moreover, Switzerland being a small and open economy with weak union power and employment protection legislation, we do not have to worry about the determination of wages. This country can be considered as a price-taker in the international labor market, being subject to competition from other countries. Even if Switzerland is not formally integrated in the European Union, the mobility of workers is ensured, particularly since the enforcement of the Free Movement of Persons Agreement (FMPA) on June 1, 2002. The workforce in Switzerland is in fact composed by no less than 25% of foreigners.3 To the best of our knowledge, the only measure available for human capital depreciation in Switzerland is provided by Ramirez (2002), who applies the indirect methodology proposed by Neuman & Weiss (1995). Our research thus provides novel and probably more reliable estimates for this country. Empirical studies concerning human capital depreciation providing estimates for females are very few, certainly because women’s labor market behavior is more difficult to modelize than men’s behavior. Even if we agree that estimations for females are somewhat hazardous, we do estimate our model for this group of workers too. Comparing the results of the different genders is in fact very enriching. Our results show firstly that the average depreciation rate is stronger for females than for males. In an alternative regression where depreciation is allowed to vary with the level of education, depreciation is found to be lower for more educated workers. Such a clearly negative relationship between depreciation and education has not been observed empirically before. Theoretical considerations nevertheless give support to this result: it can be implied by a greater flexibility of the more educated workers and/or because these individuals are more prone to take on-the-job training. A comparison of the results concerning the two distinct tracks of the dual education system allows to push the interpretation one step further. 3
See the Employment Statistics (ES) of the Swiss Federal Statistical Office (SFSO).
3
Workers having followed academic studies (who possess more general than specific skills) only suffer a low depreciation rate of their human capital. On the contrary, workers having followed vocational studies (who possess more specific than general skills) suffer a higher human capital depreciation rate. General training thus seems to better protect against depreciation than specific training. The remainder of the paper is organized as follows. Section 2 constructs an earnings equation where human capital depreciation appears as a parameter. Section 3 describes the SLFS data that are used for the empirical estimation of the model. Section 4 discusses different sets of estimates obtained through nonlinear least squares and conclusions are offered in section 5.
2
The Model
Human capital theory (Becker, 1964; Ben-Porath, 1967) assumes that individuals invest in themselves to increase their future earnings. The earlier they make educational investments, the longer they will be able to collect benefits from those. It is therefore more profitable to acquire skills early in one’s life. As Mincer (1974, p. 13) states: “Rational allocation requires that most of the investment be undertaken at younger ages. Thus schooling, a largely full-time activity, precedes job-training, a largely part-time activity, and the latter diminishes with age, terminating years before retirement.” Schooling is indeed achieved at the beginning of life, since the returns of education can thus be collected during the whole career. Individuals then specialize in the production of human capital, in the sense that all the abilities are devoted to formal education. Training taking place later in the life cycle – while individuals are working – is called continuing education or adult education. Human capital theory tells us that the fraction of time devoted to such training should rationally be high at the beginning of the career and decline until zero when approaching retirement since no benefit could be retrieved from investments made just before leaving the labor market. Accordingly, experience-earnings profiles predicted by the human capital theory are increasing and concave. Potential earnings are always greater than actual earnings, the difference being due to the fraction of time allocated to training and therefore subtracted from the production of earnings. As this fraction diminishes over time, the two curves converge. Since investment is almost nil when approaching retirement, experience-earnings profiles must be flat at the end of one’s career. Empirical observations since Mincer (1974) however show that earnings peak somewhere before retirement, as illustrated by Figure 1.4 To reconcile theory with facts, one needs to introduce human capital depreciation. 4
One can moreover show that potential earnings (Et ) peak before observed earnings (Yt ). Letting st be the fraction of time devoted to training in period t, we have the following relationship: Yt = (1 − st ) · Et
4
Figure 1: Experience-earnings profiles with human capital depreciation
Let st be the fraction of time devoted to the production of new human capital by an individual of age t. The human capital theory implies that st declines over the life cycle, but does not provide a specific shape for this function. We assume that st declines linearly over the career until it becomes zero at retirement. Hence, the complete path of st over the life cycle writes:5 if t < 6 0 st = 1 (1) if 6 ≤ t < S ? α Xt ? ? α − T −S ? · (t − S ) = α · 1 − L if S ≤ t ≤ T where α is a parameter, T is retirement age, S ? is the age at which schooling ends and working life begins, L = T − S ? is the total working life duration, and Xt = t − S ? is experience (time spent on the labor market).6 Schooling duration is given by S = S ? − 6. Compared with the assumptions of the human capital theory, note that our formulation moreover imposes investments in human capital to be positive until the last period before retirement (T − 1). A schematic representation is provided by Figures 2 and 3. The parameter α is the fraction of time invested in training immediately upon leaving school. Because of our assumption that the fraction of time By differentiation, one gets: ∂Yt ∂st ∂Et =− · Et + · (1 − st ) ∂t ∂t ∂t This equation proves that Yt is still increasing (∂Yt /∂t > 0) when Et is maximal (∂Et /∂t = 0), because st is a decreasing function of time (∂st /∂t < 0). 5 We assume that schooling begins at 6. This assumption is used in the literature since Mincer (1974), and it moreover corresponds to the official age at which children begin schooling in Switzerland. 6 A subscript t is attached to the variable X to explicit that it does vary with time. The variables without subscript are time-invariant.
5
Figure 2: The different periods of the life cycle
Figure 3: Fraction of time invested in the production of human capital
invested in training during the working life declines linearly until zero at retirement, α determines alone the complete history of investment in continuing training during the career. Empirically, we do not have information about the age at which individuals do actually retire, so that we use official retirement ages,7 even if some stop earlier or later. This does however not constitute a severe restriction, since actual retirement ages are remarkably close to official ones in Switzerland (see OECD, 2003). Similarly, schooling duration is in fact the theoretical minimal time needed to acquire some sort of training. If a student has to repeat a year during his cursus, it will not be included in his schooling duration S. As a result, the working life duration L is in fact a potential duration, since career interruptions, delayed entries and early retirements are not taken into account. According to what is usually done in the literature, we assume that po7
In Switzerland, official retirement age was constant at 65 for men during the whole observation period (1998-2006). For women however, it was 62 until 2000, 63 between 2001 and 2004, and 64 since 2005 (see the 10th revision of the Old-Age and Survivors Insurance, OASI).
6
tential earnings Et are exponentially linked to the stock of human capital:8 Et = W · exp(βK Kt + βZ Zt )
(2)
where W is the return per period on a unit of capacity to produce earnings (sum of the human capital and the level of ability), Kt the human capital stock at time t, Zt is a set of observable characteristics supposed to have an impact on earnings (marital status, nationality, occupation, etc.), and βK , βZ are the parameters of interest. In what follows, we note ∆Kt the quantity of new human capital produced during period t, and δ the human capital depreciation rate, which is assumed to be constant across time and individuals. The stock of human capital in period t can be expressed as the sum of the stock that was already available in the previous period minus the loss incurred because of depreciation plus the quantity produced during the tth period: Kt = Kt−1 − δ · Kt−1 + ∆Kt = (1 − δ) · Kt−1 + ∆Kt
(3)
By recursion, one finds an expression for Kt as a function of the stock of human capital acquired at the end of formal education KS : t−1 X
t
Kt = (1 − δ) · KS +
(1 − δ)j · ∆Kt−j
(4)
j=S ?
Taking the logarithms of (2) and substituting Kt by its expression in (4) gives: ) ( t−1 X (1 − δ)j · ∆Kt−j + βZ Zt (5) ln Et = ln W + βK · (1 − δ)t · KS + j=S ?
Potential earnings Et are however not observable, and only actual earnings Yt are. Since a fraction st of time is allocated to the production of new human capital, there is only a proportion (1 − st ) left to the production of earnings. The observed earnings and their logarithms are therefore given by: Yt = (1 − st ) · Et ln Yt = ln(1 − st ) + ln Et
(6)
Combining (5) and (6), one gets: ( ln Yt = ln W + βK ·
(1 − δ)t · KS +
t−1 X
) (1 − δ)j · ∆Kt−j
+
j=S ?
βZ Zt + ln(1 − st ) (7) 8
In order to keep the notation as light as possible, we omit the individual subscript i and the error term until the final equation (10).
7
The final step we need to take in order to render the model estimable is to find a value for KS and ∆Kt . These two variables being unobservable, we have to relate each of them with some observables. Obviously, the stock of human capital at the end of schooling is related to the education received, and we assume a direct link between this stock and the length of schooling: KS = S
(8)
The production of new human capital ∆Kt clearly depends on the fraction of time that is allocated for this activity, and we postulate the simplest possible function: if t < 6 0 (9) ∆Kt = st = 1 if 6 ≤ t < S ? Xt ? if S ≤ t ≤ T α· 1− L This functional form is probably over-simplistic, but it allows the mathematical tractability of the model. A more realistic function would include some measure of the stock of human capital already acquired Kt (like (2) in BenPorath 1967), but retrieving a closed-form solution for the earnings equation is then be impossible, since Kt then reenters the sum of the right-hand side of (7). One may notice that (3), (8) and (9) together imply that depreciation is equal to zero during schooling. To show this, use (3) to express KS as a sum of the quantities of human capital produced during schooling (K0 = 0), and solve it using (9): ?
(3)
KS =
S X
?
(9)
(1 − δ)j · ∆KS ? −j =
j=0
S X
(1 − δ)j
j=6
Thus, (8) holds if and only if δ = 0 for 6 ≤ t < S ? . This assumption is not as restrictive as it might first appear. What it implies is in fact that individuals do not loose any skill while in school. Since the material taught in particular year relies on what was taught during previous years, students should normally have knowledge of everything they have learnt since the beginning of their schooling. Some students clearly forget useful concepts, but they have then to revise (alone or with the help of a tutor) beside the hours spent in school. The complete path of the stock of human capital stock over the life cycle is shown in Figure 4. Substituting (8) and (9) into (7), simplifying, adding an individual subscript i and an error term finally yields the estimated equation: (
1 − (1 − δ)Xit · δ ) ( ) 1 − δ α · Xit α 1+ − + ln 1 − α − · Xit + βZ · Zit + uit (10) δ · Li δ · Li Li
ln Yit = ln W + βK ·
(1 − δ)Xit · Si + α ·
8
Figure 4: Evolution of the human capital stock
Given their definition, the admissible values for the parameters are as follows: • The intercept of (10) represents the (logarithm of) earnings of an individual without any stock of human capital and every covariate in Zit equal to zero: ln W > 0. • The effect of the human capital stock on earnings must be positive: βK > 0. • The human capital depreciation rate has to be between zero and one: 0 < δ < 1. • The proportion of time invested in continuing training immediately upon leaving school must necessarily be between zero and one: 0 < α < 1.
3
The SLFS Data
We use data from the Swiss Labor Force Survey (SLFS),9 realized by the Swiss Federal Statistical Office (SFSO). This survey was conducted for the first time in 1991 and annually onwards. Its main purpose is to provide information about the structure of the labor force and employment behavior patterns. It contains very detailed information about the labor status, wages, training, socioeconomic characteristics, and the composition of the respondents’ household. Conducted over the phone, the SLFS is based on a sampling of households selected at random from the telephone book. Individuals who take part in the survey are contacted up to five years in a row, so that the SLFS constitutes a panel (though unbalanced). Even if we have at hand the complete SLFS from 1991 to 2006, we do not use the dataset in its entirety. Several changes were applied to the survey 9
The German acronym is SAKE for “Schweizerische Arbeitskr¨afteerhebung”, and the French one is ESPA for “Enquˆete Suisse sur la Population Active”.
9
during its early waves, which prevents an exact correspondence with the subsequent waves. Major revisions took place between 1996 and 1998,10 and we therefore decide to discard every data until 1997 included. We are left with an observation period of nine years, from 1998 to 2006. The SLFS contains about 160 000 observations per year until 2001. It was enlarged in 2002 to roughly 330 000 individuals, in order to provide accurate statistics at the canton-level.11 Since 2003, an additional sampling of 150 000 foreign households are selected from the Central Aliens Register. The numbers of males and females that were interviewed each year in the frame of the SLFS are contained in column I of Table A.1 in Appendix. Every person pertaining to the permanent resident population aged 15 and older is susceptible to be interviewed, disregarding his labor status. The original dataset thus contains salaried workers, self-employed workers, apprentices, unemployed, as well as non-active persons. A first filter is thus applied to retain active workers only (column II). This removes almost one half of the female sample and one third of the males, proving that much more women are non-active than men in Switzerland. We then remove the self-employed workers, and retain only salaried workers, employed full-time, aged between 16 and 65, and who claim to earn 300 000 Swiss francs or more (column III). Once again, much more females than males are removed, mostly because a larger proportion of the former are employed part-time. We finally discard the individuals for whom any necessary information is missing, as well as the observations identified as outliers by the method of Hadi (1992, 1994) (column IV). The number of valid observations corresponds to a little more than 40% of the original SLFS sample for the males but to less that 20% for the females. Tables A.2 and A.3 in Appendix contain the descriptive statistics of the final sample for 2006. We quickly comment the most interesting characteristics as well as the evolution of some variables that varied significantly across the waves of the SLFS. The average net annual earnings of the selected sample are around 720 500 Swiss francs.12 As usual, the distribution of earnings is right-skewed with a mode around 600 000 and a median around 650 000. Figure 5 displays the distribution of wages in 2006 for all the salaried workers employed full-time and aged between 16 and 65, i.e., the final sample without constraining the earnings to be greater than 250 000 Swiss francs. It allows to motivate the 10
In particular, the variables about education and earnings were reshaped. The encoding of the education variable does not allow to place all the individuals interviewed before 1998 in a specific group of the recoded variable with certainty. Since education is an essential variable for our research, we do not want to introduce any approximation in its construction. In addition, no distinction was made between the earnings of the main job and potential additional jobs until 1997. Since 1998, different questions are asked about the earnings from the main job and the earnings from a secondary job. For the empirical estimations, we only consider main jobs and discard the secondary ones. 11 Switzerland is composed of 26 cantons. 12 In December 2005, 1 CHF was worth 0.8 USD or 0.65 EUR. Earnings are deflated by the CPI (100 = December 2005).
10
Figure 5: Earnings distribution in 2006
Notes: • The bars are scaled so that the sum of their heights equals 1. • The plain line is an appropriately scaled kernel density estimate of the density. • The graph is based on the final sample for 2006 (120 791 obs), without restricting the earnings to be greater than 250 000 CHF (225 obs), i.e., on 130 016 observations. We do not plot earnings over 2000 000 CHF (55 obs) in order to render the graph readable.
choice of this threshold: there seems to be a kink in the distribution at this point. Moreover, we suspect that a non-negligible portion of the observations with net annual earnings of less than 250 000 Swiss francs are response and coding errors. The gender gap seems to be quite large, with 160 000 Swiss francs separating the mean annual earnings of males and females. Table A.2 moreover shows that earnings are very different across schooling types and are positively correlated with the education duration. The average earnings of individuals with the longest education are more than twice those of workers who have not finished compulsory school. The far mostly widespread training is apprenticeship with 35% of the 2006 valid sample. This proportion seems to be decreasing regularly since 1998, when it was over 50%. The second largest group is composed of workers holding a university degree. Their proportion has been growing from 10% to 17% during the observation period. Another interesting figure to point out is the proportion of workers without any degree, which is 16%. We however mention that this proportion is very unequal for Swiss citizens and foreigners: it is around 6% for the Swiss against 25% for the foreigners. The (hypothetical) education duration, i.e., the minimal time required to obtain a diploma, is constructed from the highest education level reached. For example, if an individual progresses in a “standard” manner, he will obtain an apprenticeship certificate after 12 years: 9 years of compulsory school followed by 3 years of apprenticeship. Similarly, to receive a university 11
degree, one needs to spent at least 17 years: 9 years of compulsory school, 4 years of post-compulsory school to get a high school degree (maturit´e ), and at least 4 years in the university to get a degree.13 This approach does not take into account failed years that the student has to repeat more than once. What we measure is thus a “useful” schooling duration, implicitly assuming that failed years do not add anything to the stock of human capital. According to this methodology, the mean education duration is almost 13 years in our sample.14 Figure 6 displays the empirical experience-earnings profiles for several groups of education duration, by gender. Since the experience-earnings profiles for females are based on much fewer observations than those for males, they do not look as well established. However, both for males and females, the prominent characteristics are as predicted by the human capital theory: more schooling leads to higher wages and earnings are increasing during the early career, then leveling and decrease slightly when approaching retirement, even though the trajectories become quite erratic. Another interesting feature is that earnings profiles are almost flat for low skilled workers, whereas they are very steep for high skilled workers. Such an observation would suggest that depreciation is lower for more educated workers and/or that experience is more rewarding for high skilled than for low skilled workers. An interesting question of the SLFS concerns continuing training: “Did you receive work-related training during the past twelve months?”. Table A.2 shows that highly educated workers use more continuing training. Only 9% of the less educated workers did receive training during the twelve months preceding their interview in 2006. This proportion grows with schooling duration and reaches almost 50% for the most educated workers. The proportion of females in the final sample seems low (42%), but it is mainly due to our selection criteria. As we inferred from Table A.1, many women are non-active or employed part-time in Switzerland, and they are excluded from the sample because we consider full-time workers only. Important differences can be observed about the marital status of genders. Approximately half the women of our sample are single but only 27% of the men are. In the same vein, 17% of the females are separated whereas only 8% of the males are in such a situation. On the other hand, two thirds of the males are married while a low 36% of the females are. These figures illustrate the behavior of females on the Swiss labor market: when married, many of them reduce their working time or even leave the market to take care of their family. This observation is reinforced by the statistics about the number of dependents. Half the men of the sample have at least one dependent, but only 27% of the women are in such a situation.
13 Until 2006, the licence was the lowest university degree issued in Switzerland. The academic system has now been revised and Swiss universities deliver bachelors that are achieved in 3 years. 14 We arbitrarily assign an education duration of 7 years to individuals who did not finish compulsory school.
12
Figure 6: Empirical experience-earnings profiles A. Males
B. Females
Note: The profiles are based on the pooled final samples, i.e., on a total of 620 181 observations for the males and 260 131 for the females (every individual might appear several times).
13
The proportion of Swiss nationals is about one half in 2006, but it is to note that this proportion was much higher (almost 85%) until 2002. The reason for such an abrupt decrease is that a new part of the SLFS is exclusively dedicated to foreigners since 2003, and 150 000 additional individuals are interviewed in this context. 72% of the foreigners (36% of the whole sample) hold a settlement permit (C), and the remaining 28% (14% of the sample) possess a residence permit (B).15 The distribution was a little different before 2003, with 85-90% of permits C and 10-15% of permits B. Concerning the origin of the foreign workforce, a large majority comes from European countries. Almost 70% come out of EU15 countries and more than 20% from the other European countries. Workers coming from a different continent are very scarce.16 Less than 20% of the individuals of our sample are working in firms with 10 employees or less, and over 40% in firms with 100 co-workers or more. We should however mention that the distribution of the original SLFS sample was more oriented towards small enterprises. When discarding self-employed workers of our sample, we naturally kept more individuals working in large firms than in small ones.
15
Other types of work permit are available in Switzerland (cross-border commuter, shortterm residence, trainee, . . . ), but only foreigners holding B or C permits are allowed to stay and work in Switzerland for more than one year. The SLFS being concerned with individuals authorized to stay at least 12 months in the country, foreigners with permits other than B or C type are automatically excluded from the survey. Nevertheless, we assert that this restriction is not severe, since B and C permits are the most widely used and the other permits constitute only a marginal fringe of the workforce (see Weber, 2006, p. 156). 16 Even if Switzerland is not inside the European Union, it negotiated bilateral agreements with every member individually so that the Swiss laws are not the same for every foreigner. The status of the individuals coming from countries of the European Union at 15 (prior to May 1, 2004) is ruled by the Free Movement of Persons Agreement (FMPA) since June 1, 2002. The effects of the FMPA were extended to the 10 new members of the European Union on April 1, 2006 (two years after their joining). The status of the other foreigners is still regulated by the Federal Law on Foreign Nationals’ Residence and Settlement and the Regulation on the Limitation of the Number of Foreigners. Bulgaria and Romania joined the European Union on January 1, 2007, so that they were not in the Union at the end of our observation period. According to these considerations, we gather nationalities by continent except for Europe, where we separate individuals of the EU15 from the rest of Europe. Getting more into details would leave very few observations in some categories and estimates would become less reliable.
14
4
Empirical Results
As usual in studies about earnings, we estimate separate equations for men and women. Even if we only keep full-time workers, the behavior of both groups is too different to be accounted for by a simple dummy variable or even some interaction terms. We use net annual earnings as our dependent variable. It seems indeed more relevant to study net earnings than gross ones, because individuals should rationally react to the former. Tables 1 and 2 present the estimation results, which were obtained by nonlinear least squares with robust standard errors adjusted for the fact that several observations of the same individual are not independent. Different specifications were tried. Model I is the exact estimation of equation (10), with the depreciation rate being the same for each individual. Model II takes into account the possibility that depreciation varies with the type of education.17 We noticed in the previous section that high educated workers take more on-the-job training than low educated ones. In order to account for differences in the rate of post-school investments in human capital across education groups, we let the parameter α vary across education types in model III.18 Finally, model IV allows both δ and α to vary across education groups. According to model I, the human capital depreciation rate in Switzerland is 0.8% for males and 1.8% for females. As Table 3 shows, these results are in line with most previous studies. We also note from Table 3 that very few estimations have been realized for female workers, so that it is not easy to make confident comparisons for this group. In particular, Arrazola & de Hevia (2004) obtain depreciation rates between 1.2 and 1.5% for men and between 0.3 and 1.2% for women, with non-significant estimates for women. We nevertheless believe that a greater human capital depreciation for female workers should be observed. Since career interruptions are not observed in our data, there could be an explanation. Women are indeed more prone to career interruptions, which should lead to both discontinuities in the production of new human capital and a more rapid obsolescence of their existing human capital. 17
Practically, the parameter δ is replaced by a linear combination of dummy variables indicating the different types of education, with apprenticeship (the most widespread education) taken as the base category: δ + δNone · educNone + δCompulsory school · educCompulsory school + δDomestic school · educDomestic school + δGeneral training school · educGeneral training school + δProfessional school · educProfessional school + δHigh school · educHigh school + δUpper prof. school · educUpper prof. school + δTechnical school · educTechnical school + δApplied university · educApplied university + δUniversity · educUniversity . δk are parameters to be estimated and educk are dummies indicating the education types. The estimate of δ in model II gives the depreciation rate for apprentices, the omitted category. To obtain the depreciation rate for an individual with education type k, one has to add the corresponding δk to δ. 18 The αk are constructed in the same manner as the δk in model II (see footnote 17).
15
Table 1: Empirical estimates, Males dependent variable = ln(net annual earnings) Variable
I 10.043*** (0.018) 0.076*** (0.001) 0.010*** (0.001) —
ln W βk δ δNone δCompulsory school
—
δDomestic school
—
δGeneral training school
—
δProfessional school
—
δHigh school
—
δUpper prof.
school
—
δTechnical school
—
δApplied university
—
δUniversity
—
α αNone
0.262*** (0.010) —
II 10.549*** (0.059) 0.057*** (0.002) 0.033*** (0.005) 0.004* (0.002) 0.003** (0.001) −0.007*** (0.002) −0.010*** (0.002) −0.002** (0.001) −0.010*** (0.001) −0.007*** (0.001) −0.010*** (0.001) −0.014*** (0.002) −0.016*** (0.002) 0.447*** (0.027) —
αCompulsory school
—
—
αDomestic school
—
—
αGeneral training school
—
—
αProfessional school
—
—
16
III 10.060*** (0.017) 0.085*** (0.001) 0.018*** (0.001) — — — — — — — — — — 0.329*** (0.011) 0.048*** (0.010) 0.005 (0.006) 0.095*** (0.026) 0.114*** (0.031) 0.029*** (0.011)
IV 10.525*** (0.035) 0.079*** (0.002) 0.050*** (0.004) −0.002 (0.003) 0.001 (0.001) −0.007*** (0.002) −0.010*** (0.002) −0.002*** (0.001) −0.009*** (0.001) −0.007*** (0.001) −0.009*** (0.001) −0.014*** (0.001) −0.015*** (0.001) 0.577*** (0.021) −0.215*** (0.034) −0.119*** (0.008) −0.006 (0.033) 0.026 (0.025) 0.063*** (0.008)
αHigh school
—
—
—
—
αTechnical school
—
—
αApplied university
—
—
αUniversity
—
—
Married
0.057*** (0.004) 0.044*** (0.006) 0.019*** (0.002) 0.015*** (0.005) −0.026*** (0.005) 0.055*** (0.003) 0.001 (0.002)
0.055*** (0.004) 0.041*** (0.006) 0.017*** (0.002) 0.023*** (0.005) −0.028*** (0.005) 0.053*** (0.002) 0.004** (0.002)
αUpper prof.
school
Separated # dependents Language City ≥ 1000 000 inhabitants Continuing training Tenure/10 # Obs # Ind Adj. R2 Log Likelihood AIC BIC
620 181 290 837 0.555 670.847 -1179.695 -447.633
620 181 290 837 0.575 2094.983 -4007.966 -3185.526
0.136*** (0.010) 0.060*** (0.009) 0.089*** (0.012) 0.137*** (0.009) 0.196*** (0.008) 0.062*** (0.004) 0.044*** (0.006) 0.012*** (0.002) 0.012** (0.005) −0.022*** (0.005) 0.050*** (0.002) 0.008*** (0.002) 620 181 290 837 0.570 1740.753 -3299.506 -2477.066
0.074*** (0.007) 0.041*** (0.008) 0.028** (0.011) 0.036*** (0.009) 0.108*** (0.007) 0.058*** (0.004) 0.041*** (0.006) 0.012*** (0.002) 0.019*** (0.005) −0.025*** (0.005) 0.052*** (0.002) 0.010*** (0.002) 620 181 290 837 0.581 2532.551 -4863.102 -3950.284
Notes: • Robust standard errors adjusted for individual clusters in parentheses. • Model I: depreciation (δ) is constant. Model II: δ varies across education groups. Model III: fraction of time devoted to training (α) varies across education groups. Model IV: δ and α vary across education groups. • Other controls not reported: 2 dummies for the foreigners’ permit, 7 dummies for the origin (continents), 4 dummies for the number of unemployment spells in the last 10 years, 4 dummies for the firm size, 5 dummies for the number of subordinates, 8 time dummies (1999-2006), 25 canton dummies, 15 sector dummies. The complete results tables are available upon request. • AIC = −2 · ln L + 2 · k, BIC = −2 · ln L + ln(N ) · k, where ln L is the log likelihood, k is the number of degrees of freedom, and N is the number of observations. • The log likelihood values are positive. For continuous outcomes, the log likelihood is the log of a density, and since density functions can be greater than 1, a positive value for the log likelihood is possible.
17
Table 2: Empirical estimates, Females dependent variable = ln(net annual earnings) Variable
I 9.856*** (0.031) 0.082*** (0.002) 0.018*** (0.001) —
ln W βk δ δNone δCompulsory school
—
δDomestic school
—
δGeneral training school
—
δProfessional school
—
δHigh school
—
δUpper prof.
school
—
δTechnical school
—
δApplied university
—
δUniversity
—
α αNone
0.365*** (0.014) —
II 10.260*** (0.089) 0.068*** (0.002) 0.036*** (0.007) 0.006 (0.004) 0.006** (0.002) 0.006*** (0.002) −0.007*** (0.002) −0.001 (0.001) −0.009*** (0.002) −0.007*** (0.002) −0.007*** (0.002) −0.009*** (0.002) −0.011*** (0.002) 0.494*** (0.040) —
αCompulsory school
—
—
αDomestic school
—
—
αGeneral training school
—
—
αProfessional school
—
—
18
III 9.888*** (0.031) 0.095*** (0.002) 0.030*** (0.001) — — — — — — — — — — 0.484*** (0.013) −0.048*** (0.018) −0.092*** (0.009) −0.081*** (0.019) 0.053** (0.021) 0.046*** (0.009)
IV 10.263*** (0.045) 0.100*** (0.004) 0.062*** (0.005) 0.003 (0.003) 0.005*** (0.002) 0.006*** (0.002) −0.007*** (0.002) −0.002** (0.001) −0.009*** (0.001) −0.008*** (0.001) −0.008*** (0.001) −0.010*** (0.001) −0.012*** (0.001) 0.675*** (0.024) −0.184*** (0.027) −0.130*** (0.010) −0.039** (0.016) 0.023 (0.015) 0.045*** (0.006)
αHigh school
—
—
—
—
αTechnical school
—
—
αApplied university
—
—
αUniversity
—
—
Married
−0.043*** (0.006) −0.054*** (0.007) −0.023*** (0.003) 0.065*** (0.009) −0.007 (0.007) 0.060*** (0.004) 0.021*** (0.004)
−0.044*** (0.006) −0.055*** (0.007) −0.024*** (0.003) 0.061*** (0.008) −0.011 (0.007) 0.056*** (0.004) 0.020*** (0.003)
αUpper prof.
school
Separated # dependents Language City ≥ 1000 000 inhabitants Continuing training Tenure/10 # Obs # Ind Adj. R2 Log Likelihood AIC BIC
260 131 140 067 0.518 544.415 -926.831 -264.990
260 131 140 067 0.535 1005.011 -1828.023 -1084.473
0.065*** (0.009) 0.031** (0.013) 0.049** (0.020) 0.082*** (0.014) 0.149*** (0.009) −0.037*** (0.006) −0.037*** (0.007) −0.030*** (0.003) 0.051*** (0.008) −0.003 (0.007) 0.056*** (0.004) 0.027*** (0.004) 260 131 140 067 0.535 1004.594 -1827.189 -1083.639
0.032*** (0.006) 0.019* (0.010) 0.025* (0.015) 0.055*** (0.010) 0.108*** (0.006) −0.040*** (0.006) −0.038*** (0.007) −0.031*** (0.003) 0.056*** (0.008) −0.007 (0.007) 0.056*** (0.004) 0.028*** (0.004) 260 131 140 067 0.545 1312.728 -2423.456 -1598.197
Notes: • Robust standard errors adjusted for individual clusters in parentheses. • Model I: depreciation (δ) is constant. Model II: δ varies across education groups. Model III: fraction of time devoted to training (α) varies across education groups. Model IV: δ and α vary across education groups. • Other controls not reported: 2 dummies for the foreigners’ permit, 7 dummies for the origin (continents), 4 dummies for the number of unemployment spells in the last 10 years, 4 dummies for the firm size, 5 dummies for the number of subordinates, 8 time dummies (1999-2006), 25 canton dummies, 15 sector dummies. The complete results tables are available upon request. • AIC = −2 · ln L + 2 · k, BIC = −2 · ln L + ln(N ) · k, where ln L is the log likelihood, k is the number of degrees of freedom, and N is the number of observations. • The log likelihood values are positive. For continuous outcomes, the log likelihood is the log of a density, and since density functions can be greater than 1, a positive value for the log likelihood is possible.
19
Table 3: Human capital depreciation rates in the literature Authors
Males
Johnson (1970) 4.6 - 13.3% Mincer & Polachek (1974) — Johnson & Hebein (1974) 1.0 - 3.4% Heckman (1976) 0.7 - 4.7% Haley (1976) 0.5 - 4.3% Groot (1998) 13.6 - 21.0% Arrazola & de Hevia (2004) 1.2 - 1.5% Arrazola et al. (2005) 1.2% Wu (2007) 11.6 - 18.1%
Females — 0.2 - 4.3 % — — — 9.0 - 17.2% 0.3 - 1.2% — 12.4 - 13.2%
The intercept of the estimation (ln W ) can be interpreted as the (logarithm of) net annual earnings for an individual without any human capital and with every covariate being zero. For males (females), model I gives an estimate for the annual earnings of about 23’000 CHF (19’000 CHF), corresponding to 18’400 USD (15’300 USD). This is what an individual would earn if he (she) were paid 11 CHF (9 CHF) per hour. Such an hourly wage is easily reached in Switzerland, even without any education, so that such estimates are plausible. We remark that model I indicates a gender wage gap of “only” 4’000 CHF, which is much smaller than what we observed with simple descriptive statistics (section 3). The effect of human capital stock (βk ) appears stronger for females. This seems to imply that the labor market rewards better the education of women. Finally, the share of time devoted to training (α) is about one fourth for males, but it is more than one third for females. Both of these observations could arise because employers are willing to better integrate females: they possibly give them more incentives to train and offer them more free time. Several authors notice that the level of education may influence depreciation, but no empirical consensus has been reached concerning the sign of this influence. On the one hand, Neuman & Weiss (1995) argue that “elementary school graduate’s human capital does not suffer much from obsolescence since the material taught in elementary schools has not changed much over time”. As a consequence the higher the level of education the more quickly the capital should become obsolete. Mincer & Polachek (1974) also find higher depreciation rates for more educated workers in their study of females’ earnings. On the other hand, Arrazola et al. (2005) do not find any difference and Groot (1998) observes contradictory results when applying his model to British and Dutch datasets. Several articles provide reasons to think that education reduces human capital obsolescence. For example, Weisbrod (1962) notes that “persons having more education are likely to be in a position to adjust more easily than those with less education”. In other words, education gives a greater flexibility and adaptability, in the sense that it is associated with better labor 20
market offers. If there is a change in his environment, a better educated worker will be faster to rebound. Cipriani (1967) mentions that “diplomas and degrees perform an “admission-ticket” function; they often provide the means of entry to certain types of on-the-job training”. It would thus be easier for more educated workers to re-train and thus to acquire new human capital and to slow the depreciation of their existing human capital. It also implies that more educated workers are more likely to take part in continuing training. Mincer (1974, p. 16) makes a similar argument: “the size of single-period investments [in human capital] is likely to be an index of lifetime investments. Longer schooling is likely to be followed by greater post-school investment, and generally, the serial correlation of instalments of investment is likely to be positive.” In an empirical study based on the SLFS data, Gerfin (2004) indeed finds that “training participation is more likely for highly educated workers” and that “training participation is highly correlated over time”. In the same vein, Gould, Moav & Weinberg (2001) develop a model where “higher ability individuals choose to invest in general education and workers with lower ability choose to invest in technology-specific skills. [. . . ] Consequently, less educated workers, who are relatively more invested in technology-specific skills, will suffer higher rates of human capital depreciation due to technological improvements.” Model II allows depreciation to differ across education groups, and the results indicate that depreciation globally decreases with the level of education. The less educated workers suffer a depreciation as high as 3.7% (4.2% for females), while the depreciation rate for the most educated is only 1.7% (2.5% for females). These results provide evidence for the latter view, in which depreciation is reduced by education. Taking a closer look at the different depreciation coefficients of model II, one may notice that the decrease in depreciation is not continuous with schooling length. For example, depreciation is found to be stronger for the individuals holding a degree from a technical of professional school (14 years of schooling) than for the high school graduates (13 years). It thus seems that depreciation depends more on the type of skills embodied in workers, general or specific, than on the length of their training. High school graduates have acquired fairly general skills and are thus prepared to operate in a wide range of occupations. The depreciation rate they suffer is low, since they are able to adapt quickly to environment changes. Contrarily, graduates from technical and professional schools possess much more specific skills. Such workers are “locked” in a specific occupation, so that if a change happens in their environment (technological progress for example), they will suffer a large depreciation of their human capital, either because new skills are needed to operate in their present occupation, or because they have to change job. On the basis of the estimates of model II, we construct the experienceearnings profiles for the average individual of each education group. As can be observed on Figure 7, the experience-earnings profiles globally shift up with the level of education. They are however not parallel, and some trajectories even cross. The steepness of the profiles is inversely related to 21
the depreciation rate, so that individuals with general skills enjoy a steeper profile during their career. Apprenticeships, professional schools, and upper professional schools provide workers with specific skills and we observe that their experience-earnings profiles are indeed flatter than what other education types experience. On the other hand high schools, applied universities, and universities supply their students with more general skills, so that they follow steeper experience-earnings profiles. We also notice that the curve for the high school graduates crosses the one for the professional school graduates, even though the latter have spent one more year for their education. An alternative explanation for such experience-earnings profiles could also rely on different effects of experience on the earnings growth across skills. Workers who possess more general skills (high school, university) still have to learn specific tasks when they enter the labor market. Their wage is thus low at the moment they enter the labor market, but it grows quickly as they learn to perform their job more specifically. Since general skills are more easily transfered across different technologies, these workers will adapt more quickly if new technologies appear. Contrarily, workers entering the labor market with more specific skills (apprenticeship, professional schools) know the tasks they have to perform from the beginning of their career, and they will be relatively slow to learn operating with new technologies. Therefore, experience does not bring much to their productivity and their earnings profile is much flatter. Our results are consistent with those obtained by Brunello & Comi (2004), who find evidence that higher-educated workers have steeper experience-earnings profiles than workers with lower education. They interpret this as evidence in support of the complementarity between technical progress, education and training. In the same spirit, Connolly & Gottschalk (2006) find that both within-job wage growth and between-job wage growth are higher for more educated workers. Model III allows the fraction of time devoted to training along the career to vary with the education level. As we remarked above, more educated workers are more likely to make post-school investments in human capital. This fact is known since Mincer (1974), and has received many empirical evidence. As a consequence, we should observe a higher α for the more educated workers. The results of model III indeed show that α grows with the level of schooling. The estimates are very high for the three academic types of training (High school, Applied university and University), for both men and women. Individuals having spent more time in school during their youth are also the ones who invest more during their working life. Model IV brings together models II and III, by letting both δ and α varying across education groups. The comments made about models II and III remain globally unchanged: education, especially those providing general skills, reduces the depreciation of human capital, and the proportion of time devoted to training is higher for the already high educated workers. We nevertheless have to concede that the estimates for α’s are quite different from those of model III. On the other hand, the estimates for δ’s are very stable across models II and IV. 22
Figure 7: Experience-earnings profiles for some selected education groups, based on the estimates of model II A. Males
B. Females
Note: The education types are abbreviated as follows: Comp = Compulsory school, App = Apprenticeship, Prof = Professional school, HS = High school, UpProf = Upper professional school, ApUni = Applied university, Uni = University.
23
Figure 8: Experience-earnings profiles for some selected education groups, based on the estimates of model IV A. Males
B. Females
Note: The education types are abbreviated as follows: Comp = Compulsory school, App = Apprenticeship, Prof = Professional school, HS = High school, UpProf = Upper professional school, ApUni = Applied university, Uni = University.
24
Figure 8 plots the experience-earnings profiles predicted by model IV. Compared to model II, the divergence between the slopes of trajectories for different education groups is enhanced. The experience-earnings profiles of model IV are driven by the effect of depreciation (δ) and the effect of investment in human capital during the career (α), while depreciation was acting alone in model II. Since the fraction of time devoted to training is found to increase with the level of education, it reinforces the effect of the depreciation rate, which decreases with the level of education. The wage growth of the more educated workers is therefore stronger than what we observed with model II, and the wage growth of the less educated is lower. The fact that university degree holders earn less than workers holding an applied university degree at the beginning of their career is very interesting, since it corroborates what is actually observed (SFSO, 2008). Indeed, applied university students usually have a work experience during their studies, so that they have an advantage when they enter the labor market at the end of their studies. This initial earnings difference in favor of the applied university students is quickly offset because of the larger wage growth enjoyed by university students. The predictive power of the estimations is good, with an adjusted R2 ranging from 52-55% for women to 56-58% for men. To show that the additional parameters introduced in models II, III and IV improve the fit of the estimations, we report log likelihood values. We also performed Wald tests on the parameters across education groups (δk and αk ), and the equality of these parameters is rejected at any conventional levels. Hence, the replacement of the parameters α and δ by their linear combinations are highly justified. The Akaike information criterion (AIC) and the Bayesian information criterion (BIC) can be used to compare the different models. Even if the best fitting model is the one with the largest log likelihood, AIC and BIC are more reliable measures for the choice of the preferred model, since they combine fit and complexity. A model with a smaller value of the information criterions is considered to be better. Here, the three statistics (ln L, AIC and BIC) coincide and the preferred specification is clearly our model IV. It is also remarkable that the estimates of every covariate are very stable across the different models. We now quickly comment the effect of these additional controls and link our observations to the related literature, even if some of them are not reported in Tables 1 and 2 in order to save space.19 We find that being married (compared to single) and having children increase earnings of male workers but diminishes those of females. Such results can be explained because employers expect married men with children to be more reliable than single ones. On the contrary, being married and having children often goes along with a relative geographical immobility for women. It can also be put forward that many women interrupt their career when they get married or have children so that they may suffer wage losses when returning to the labor market. It is interesting to compare our results with those of other studies concerned with various aspects of the Swiss labor market. Ferro 19
The complete results tables are available upon request.
25
Luzzi & Fl¨ uckiger (1998) find that marriage lessens the likelihood to access upper hierarchical positions for females but increases it for males. Fl¨ uckiger & Ramirez (2001) analyze wages and obtain results completely in line with ours. Finally, Weber (2006) observes that married women need more time to find a new job when unemployed whereas the reverse is true about married men. It thus appears clearly that marriage and children constitute a plus for male workers but a considerable drawback for females on the Swiss labor market. Chiswick & Miller (1995) have shown that language fluency is an important determinant of earnings. Even though there is no information about the language skills of the individuals neither about their mother tongue in the SLFS, we use the language used during the interview as a proxy.20 From this information, we construct a dummy variable taking the value one if the language chosen by the individual during the survey corresponds to the official language of the canton where he lives. We believe this constitutes a good proxy for integration in the socio-economic environment. This variable has a positive and significant impact on the earnings of females, and it indicates a wage premium of almost 6%. Having been unemployed in the past causes large wage losses. Our results show that the wage penalty increases with the number of unemployment spells suffered by an individual. Male workers who were at least four times unemployed in the last ten years incur a wage penalty of more than 12%. Jacobson, LaLonde & Sullivan (1993) provide thorough explanations about why unemployed workers experience earnings losses in their future job and how their earnings recover. While studying the effect of different types of career interruption on subsequent wages, Albrecht, Edin, Sundstr¨om & Vroman (1999) show that unemployment spells are the most harmful. This brings evidence for the signalling theory: employers seem to make use of unemployment as a signal of low motivation and productivity. Albrecht et al. (1999) moreover observe that the wage penalty after an unemployment spell is stronger for males than for females, a result that we obtain as well. Firm size has a clearly positive impact on earnings: employees of firms with at least 100 co-workers earn about 8% more than employees of small firms with up to 10 workers. Even if this firm size wage effect has been widely studied, a definitive explanation has still not been reached (see Oi & Idson, 1999 for a thorough survey and e.g., Lallemand, Plasman & Rycx, 2007 for a recent analysis). We moreover control for the number of subordinates, which is certainly a good proxy for the level of responsibility born by a worker. As expected, our results show that the more one has subordinates, the more he earns. 20
Until 2002, the possible choices to answer the SLFS were the three Swiss national languages: German, French and Italian. But since the introduction in 2003 of a special part exclusively dedicated to foreigners, respondents can additionally choose English, Albanian, Serbo-Croatian, Portuguese or Turk.
26
5
Conclusions
In this paper, we use nonlinear least squares to estimate an earnings equation where the depreciation rate of human capital is identified as a parameter. Our dataset is composed of nine waves of the Swiss Labor Force Survey (SLFS), from 1998 to 2006. This survey is well fitted for such an analysis, since many personal characteristics are available and respondents are interviewed five years in a row. We measure depreciation rates both for males and females, and it appears as being twice stronger for females. The figures we obtain in the basic model where depreciation is the same for every worker, 0.8% and 1.8%, are in line with most previous studies about human capital depreciation. A stronger depreciation rate for females has however not often been observed. It may be explained because of a lower commitment of women to their career. A worker who interrupts her career will indeed suffer both discontinuities in the production of new human capital and a more rapid obsolescence of her existing human capital. We moreover estimate a model in which depreciation is allowed to vary with the education level, and we obtain a lower depreciation rate for more educated workers. This result contradicts the hypothesis of the model of Neuman & Weiss (1995), who assume that “the higher the level of education the more quickly the [human] capital becomes obsolete”. To our knowledge, a negative relationship between depreciation and education has not been measured before. It can be explained by a greater labor market flexibility of the more educated workers, in the sense that they have access to more job opportunities, and because these individuals are more prone to take on-thejob training. The interest of our analysis is enhanced because of the dual education system established in Switzerland. The vocational track (apprenticeship) provides individuals with more specific skills than the traditional track (university studies), through which students acquire more general skills. Using this information, we find the depreciation rate to be more related to the type of skills possessed by a worker, general or specific, than with the schooling duration. Traditional studies (general skills) protect workers better against depreciation than do vocational studies (specific skills), probably because the former allow a worker to react faster to a change in his environment. As a consequence, experience appears to be more rewarding for workers who possess more general skills, and their experience-earnings profiles is steeper.
27
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30
Appendix Table A.1: Selection of the valid observations Year
I # obs in SLFSa
II III # active workers in SLFS # obs in sub-sampleb
IV # obs in final samplec
MALES 1998 1999 2000 2001 2002 2003 2004 2005 2006
70 379 70 959 70 943 80 432 180 413 270 094 250 053 230 774 220 164
50 400 50 835 50 762 60 040 120 820 180 847 170 066 150 936 140 789
30 800 40 073 30 939 40 121 80 658 130 284 120 163 110 405 100 582
30 281 30 577 30 424 30 632 70 415 110 504 100 563 90 686 90 099
Total
1480 211
1020 495
720 025
620 181
FEMALES 1998 1999 2000 2001 2002 2003 2004 2005 2006
80 945 90 775 90 800 100 313 220 901 300 608 290 193 280 054 260 142
40 756 50 187 50 210 50 520 120 119 160 195 140 948 140 167 130 149
10 720 10 805 10 738 10 805 30 841 50 467 50 132 40 875 40 462
10 460 10 574 10 516 10 572 30 192 40 675 40 371 40 079 30 692
Total
1750 731
910 251
300 845
260 131
a
17 individuals were recorded with a gender varying across waves. The gender of the 51 observations concerning these individuals was recoded to missing and they do not appear in the count of the original SLFS sample. b Salaried workers, employed at 100%, aged between 16 and 65, and with net annual earnings of at least 250 000 Swiss francs. c Observations without missing values in any of the covariates used in estimations and not considered as outliers by the method of Hadi (1992, 1994). Source: Swiss Labor Force Survey, 1998-2006.
31
Table A.2: Descriptive statistics for 2006, by gender and type of schooling Type of education (duration)
Net annual income (December 2005 CHF)
Experience (years)
Training in the past 12 months
Number of individuals (%)
MALES Comp. school not finished (7 y.) Compulsory school (9 y.) Domestic school (11 y.) General training school (12 y.) Apprenticeship (12 y.) High school degree (13 y.) Professional school (14 y.) Upper prof. school (14 y.) Technical school (14 y.) Applied university (15 y.) University (17 y. or more) Total
520 615.8 550 054.6 730 669.2 700 868.6 660 672.4 710 359.7 780 031.4 850 456.1 860 261.6 960 758.0 1080 971.6
(100 589.6) (130 054.9) (300 363.3) (270 460.0) (190 743.1) (270 197.6) (350 431.6) (250 172.2) (260 270.8) (320 380.2) (390 708.0)
32.5 27.0 24.4 22.0 23.2 21.5 21.4 22.8 22.8 21.1 18.8
(11.5) (11.1) (12.4) (12.7) (11.3) (10.4) (10.3) (9.8) (9.7) (10.0) (9.1)
0.08 0.12 0.16 0.32 0.31 0.28 0.31 0.45 0.37 0.44 0.45
142 10 396 43 50 30 258 469 536 654 341 667 0 1 543
(1.56) (15.34) (0.47) (0.55) (35.81) (5.15) (5.89) (7.19) (3.75) (7.33) (16.96)
770 100.2
(320 195.0)
22.8
(10.9)
0.32
90 099
(100.00)
FEMALES Comp. school not finished (7 y.) Compulsory school (9 y.) Domestic school (11 y.) General training school (12 y.) Apprenticeship (12 y.) High school degree (13 y.) Professional school (14 y.) Upper prof. school (14 y.) Technical school (14 y.) Applied university (15 y.) University (17 y. or more)
410 548.1 420 777.7 550 919.6 580 276.8 550 337.7 600 853.6 640 066.2 700 961.1 680 343.8 740 481.7 840 290.0
(70 742.1) (90 488.6) (170 712.9) (190 172.4) (160 014.2) (170 542.8) (210 729.5) (200 294.5) (180 552.1) (230 842.0) (300 469.7)
27.7 26.3 26.6 19.4 19.8 22.0 20.2 18.8 18.9 17.9 15.6
(10.0) (11.0) (11.8) (10.3) (12.1) (11.2) (11.6) (9.8) (10.4) (10.5) (9.6)
0.10 0.13 0.30 0.46 0.37 0.37 0.42 0.52 0.54 0.53 0.51
59 595 84 74 10 216 292 318 199 82 167 606
(1.60) (16.12) (2.28) (2.00) (32.94) (7.91) (8.61) (5.39) (2.22) (4.52) (16.41)
Total
610 102.5
(230 704.1)
20.5
(11.6)
0.37
30 692
(100.00)
32
Table A.3: Descriptive statistics for 2006, by gender Variable Net annual earnings (December 2005 CHF) Education: compulsory school not finished (7 y.) Education: compulsory school (9 y.) Education: domestic school (11 y.) Education: general training school (12 y.) Education: apprenticeship (12 y.) Education: high school degree (13 y.) Education: professional school (14 y.) Education: upper professional school (14 y.) Education: technical school (14 y.) Education: applied university (15 y.) Education: university (17 y. or more) Education duration (years) Continuing training in the past 12 months Experience (years) Total potential labor market time (years) Tenure (years) Age (years) Marital status: single Marital status: married Marital status: separated (divorced or widowed) # dependents Dependents (yes/no) Language: interview = home canton City ≥ 1000 000 inhabitants Permit: settlement (C) Permit: residence (B) Origin: Swiss Origin: EU15 Origin: EU25 (−EU15) Origin: Europe (−EU25) Origin: Africa Origin: North America
33
Whole sample
Males
Females
720 483 (300 855) 0.016 0.156 0.010 0.010 0.350 0.059 0.067 0.067 0.033 0.065 0.168 12.865 (2.559) 0.335 22.119 (11.170) 45.846 (2.587) 9.541 (9.394) 40.984 (10.834) 0.330 0.564 0.106 0.788 (1.055) 0.428 0.819 0.157 0.357 0.140 0.503 0.331 0.005 0.116 0.010 0.009
770 100 (320 195) 0.016 0.153 0.005 0.005 0.358 0.052 0.059 0.072 0.037 0.073 0.170 12.905 (2.561) 0.320 22.781 (10.911) 46.095 (2.561) 10.112 (9.706) 41.686 (10.594) 0.273 0.648 0.079 0.932 (1.104) 0.495 0.810 0.145 0.375 0.134 0.491 0.347 0.003 0.118 0.010 0.007
610 103 (230 704) 0.016 0.161 0.023 0.020 0.329 0.079 0.086 0.054 0.022 0.045 0.164 12.767 (2.550) 0.373 20.486 (11.626) 45.233 (2.550) 8.135 (8.413) 39.253 (11.219) 0.469 0.356 0.174 0.432 (0.820) 0.264 0.841 0.187 0.312 0.154 0.533 0.293 0.011 0.113 0.009 0.012
Origin: South America Origin: Asia Origin: Australia Unemployment in the last 10 Unemployment in the last 10 Unemployment in the last 10 Unemployment in the last 10 Unemployment in the last 10 # subordinates: none # subordinates: 1-10 # subordinates: 11-19 # subordinates: 20-49 # subordinates: 50-99 # subordinates: 100 or more Firm size: 1-10 Firm size: 11-19 Firm size: 20-49 Firm size: 50-99 Firm size: 100 or more
years: years: years: years: years:
never once twice 3 times > 3 times
0.009 0.015 0.002 0.755 0.185 0.044 0.010 0.007 0.582 0.304 0.042 0.042 0.013 0.016 0.172 0.094 0.178 0.135 0.422 120 791
# obs Source: Swiss Labor Force Survey, 2006. Note: Standard deviations in parentheses.
34
0.006 0.016 0.002 0.761 0.180 0.042 0.010 0.007 0.538 0.334 0.048 0.048 0.014 0.019 0.167 0.095 0.184 0.137 0.417 90 099
0.014 0.013 0.001 0.739 0.199 0.048 0.008 0.006 0.689 0.232 0.029 0.028 0.012 0.010 0.184 0.093 0.161 0.129 0.432 30 692
