Modificación del índice de refracción

Empirical studies find various results on the change of education mismatch depending on the methods and data used. Whereas some studies find that the trend increases (Nazara and Safuan (2005), Mehta et al. (2011), McGuinness et al. (2017)); some others find it decreasing (Yin, 2016); and even remaining stable (McGuinness, 2006). In particular, Nazara and Safuan (2005) find that the trend of undereducation in Indonesia decreases. McGuinness (2006) tries to plot in the graphs based on subjective and objective measures to determine whether the overeducation phenomenon may be becoming more important over time. Based on subjective measures, there are no indications that the incidence of overeducation has been rising over time; in fact, fitting a linear time trend to the observations is suggestive of a slight decrease instead. Nevertheless, given the problematic nature of the data, it would not be wise to attach too heavy a weight to the very slight negative slope of the best-fit line. Slightly differently, objective measures have a positive, sloped trend line. Thus, the study argues that it is probably reasonable to conclude, on the basis of the graphical and tabular evidence, that the incidence of overeducation has remained relatively stable during 1971 – 2000 periods.

Furthermore, McGuinness et al. (2017) analyse the patterns in overeducation between countries using a specifically designed panel dataset constructed from the quarterly

Labour Force Surveys of 28 EU countries over a twelve to fifteen-year period. Mcguinness et al. use the Barro regressions38 _{(Barro, 1997) to analyse the relationship}

between the initial level and the growth rate of overeducation. The study concludes that overeducation is consistently rising across all European countries; in fact, there is a positive trend in fewer than half the countries in the sample which shows overeducation remaining either constant or falling in most cases. Moreover, overeducation is higher among females in the vast majority of these countries. In the more aggregated level, the average trend in overeducation across all 28 countries appears to be relatively stable over the period of 2003 - 2013; though substantial differences do exist depending on the geographical country block. Overeducation rates tend to be the highest and most volatile over time in peripheral European countries, while overeducation in central European countries tends to be lower and appears to follow a somewhat cyclical pattern. Overeducation is consistently the lowest and stable over time in eastern European countries. There is also an on-going convergence in overeducation, where countries with the lowest initial values of overeducation tend to experience the highest growth rates over time. Finally, in terms of the factors driving cross-country differentials, factors relating to both the composition and level of labour demand, labour supply and the structure of educational provision all appear important.

In Asian and other developing countries, Mehta et al. (2011) study overeducation in unskilled jobs in several developing countries (India, Mexico, The Philippines and Thailand) between 1990s and 2000s. Overeducation is determined by RM method and by comparing the mean and the mode. The study find that overeducation increased slightly in the 1990s while undereducation decreased slightly under the mean criterion. The opposite result is found under the mode criterion, where overeducation declined sharply and undereducation rose substantially. Nonetheless, the result shows that a job’s mean and modal years of schooling are poor proxies for required education. Moreover, it also indicates that only 25 per cent of the overeducated workers under the unskilled jobs test are classified as overeducated by the mean method. In other words, 75 per cent of workers who they identify as earning low returns relative to their education are not classified as overeducated by the mean method, because their education backgrounds are not atypical.

38 _{The Barro model is used to examine the relationship between the growth rate of overeducation and the} initial level of overeducation using as regression model, as formulated by:

Meanwhile, Yin (2016) adds that the marginal effects of overeducation in China for seven waves are negative, possibly indicating that the years after 1989 are less likely to experience overeducation compared to the year 1989. This decrease could be because the average educational level of the labour force is increasing, and the increasing degree of economic openness and the accelerated growth of the private sector may provide more opportunities from which the workers can choose.

Handle (2017) analyses education and skills mismatch in developing countries, using The World Bank's Skills Measurement Program. 12 countries which were observed are: Ghana, Kenya, China – Yunnan, Lao, Sri Lanka, Vietnam, Bolivia, Colombia, Armenia, Georgia, Macedonia, and Ukraine. The data were collected between March 2012 and August 2017. The sample was random but was in working age of between 15 – 64 years old. Handle then highlights several issues in developing countries which affected the mismatch: a very high rate of informality, self-employment, and micro-firms (around 55- 80 per cent of the total firms). Very low employment rates among the working age population (around 33 – 55 per cent of the total population) creates other issues such as selection issues and unemployment or inactivity. In turn, these issues reflect a very weak job market and low job generation as well as gender dynamic. Handle also argues that the mismatch likely occurs due to some drivers, such as: (1) labour market friction (imperfect information); (2) transitory business cycle, for example increasing unemployment and job seekers choosing any jobs available without considering their education level and background; (3) life cycle stage, particularly the youth; (4) work/family preferences, for instance women with young children; and (5) social exclusion, such as minority ethnicities or immigrants. Besides, education mismatch prevalence could also reflect problems with education (such as quality) and with the job market (such as low employment rate and low investment) in the country. This finding is consistent with the Harris-Todaro model, as explained in Section 4.2.3.

In Indonesia, Nazara and Safuan (2005) study the overeducation in the formal sector in the Indonesian labour market, using Sakernas data from 1996, 1999 and 2002. Overeducation and undereducation are defined as the deviation from the mean of years of schooling. Furthermore, occupation is divided into 9 groups: professional, management, administrative, sales, labour service establishment, agriculture, production workers and labour, transportation operator, and moving equipment and unskilled workers. The study reveals that there is an indication that overeducation exists in

Indonesia. Moreover, the study estimates that undereducated, matched and overeducated workers in 1999 were 16.8 per cent, 56.5 per cent, and 26.7 per cent from the sample, respectively. The share of undereducation then decreased to 9.13 per cent in 2002; in contrast, the share of overeducation increased to 34.7 per cent. The study argues that overeducated workers exist probably due to limited choices resulting in a very competitive labour market for highly educated people whilst the job-search cost is relatively high. Alternatively, another possible explanation is that this result only reflects the distribution of ability. Wajdi et al. (2017) also study the urbanisation in Indonesia. Even though it is not directly related to overeducation, their findings may support the argument that migration to DKI Jakarta (the capital city) and other metropolitan areas is most likely undertaken for better education or job prospects, since most jobs for highly educated people are more available in the metropolitan areas.

Similarly, Allen (2016) measures the mismatch using the International Standard Classification of Occupations (ISCO) and the International Standard Classification of Education (ISCED). This measure of mismatch divides major occupational groups (1- digit ISCO levels) into four sub-groups and assigns a level of education to each occupational group in accordance with the ISCED. Workers in a particular group who have the assigned level of education are considered well-matched. Those who have a higher (lower) level of education are considered overeducated (undereducated). The study finds that 51.5 per cent of workers are undereducated, 40.0 per cent are matched and 8.5 per cent are over-educated for their occupations, as shown in Figure 4.1.

In particular, occupation mismatch (overeducation) in Indonesia tends to be associated with the low education levels of production workers and agriculture labourers, as well as a large number of clerks who are overeducated for their jobs. Meanwhile, undereducated is also an issue in higher level occupations, such as legislators, senior officials, and managers (Figure 4.1). Furthermore, the large proportion of undereducated workers could be a reason for the slow labour productivity growth and slow transition to high value activities throughout the economy, as well as for the prevalent skill and/or education shortages to occur in Indonesia.

Moreover, education becomes the most important factor for career progression; production workers with post-secondary education are likely to have upward career mobility into more technical or managerial occupations over a 12-month period. Meanwhile, once workers with tertiary education move into professional and technical

occupations, they are likely to still be working in such occupations 12 months later. Thus, workers with university qualifications tend to have a higher incidence of long-term overeducation, which could be explained by jobs rationed by queuing39_{. Allen (2016) also}

further asserts that limited education attainment may tend to act as a barrier to career progression, for instance, workers with junior high school or lower qualifications are likely to shift between working as production workers and as agriculture labours throughout the year. However, these workers find it more difficult to climb the career ladder.

Figure 4.1: Education Mismatch in Indonesia, August 2015 Source: Allen (2016).

Note: Blue is undereducated, orange is matched, and grey is overeducated workers.

39 _{Jobs rationed refer to a system of shared beliefs about who should have access to the job market. Given} the limited supply of jobs, a system of norms has developed about how work should be distributed. Thus, certain individuals are encouraged to consider themselves unsuitable candidates for employment under

ILO (2017) also calculates the undereducation and overeducation levels in Indonesia by using RM method (comparing the mean of occupation group and its standard deviation). The data used are SAKERNAS from 2006, 2009 and 2016. ILO finds that there was an increasing trend of undereducation from around 10 per cent in 2000 to around 17 per cent in 2016. Meanwhile, overeducation trend decreased from around 27 per cent in 2006 to 19 per cent in 2009; though it then became relatively stagnant at around 19.2 per cent in 2016. ILO also reveals some interesting trends during these periods: male workers tend to have lower education level than female workers; higher undereducation rate occurs in urban areas; older generation experiences being undereducated which could also indicate improvement of education achievement; and around 25 per cent of people aged 15-34 years old tend to experience overeducation.

4.3 Method and Data

4.3.1 Method

Marginal effects (ME)

Besides the MNL estimation, the present study also provides a marginal effect calculation for each dependent variable. It is worth noting that those coefficients of the MNL are different from the marginal effect. Multinomial logit coefficients can only be interpreted in terms of relative probabilities (this will be discussed in the next part) whereas the marginal effect calculation is needed to reach conclusions about the actual probabilities. Furthermore, marginal effects can be an informative means for summarising how changes in a response are related to changes in a covariate. As Cameron and Trivedi (2010) point out, a marginal effect, or partial effect, most often measures the effect on the conditional mean of y of a change in one of the regressors, for example; xj. In addition, the marginal

effect calculation is based on the first order derivatives; for interaction (age squared and tenure squared) between two variables, the second order derivative is then required.

The multinomial logit (MNL) model

Most studies on overeducation use binomial logistic regression (logit) model to analyse the determinants of overeducation. Some other studies use multinomial logit model to extend their analysis and to investigate the determinants of both overeducation and

undereducation. MNL is a simple extension of the binomial logistic regression model, allowing for more than two categories of the dependent or outcome variables. It is used to predict categorical placement in or the probability of category membership on a dependent variable based on multiple independent variables. The independent variables can either be dichotomous (binary) or continuous (interval or ratio in scale). MNL uses maximum likelihood estimation to evaluate the probability of categorical membership, similar to binary logistic regression. MNL is also often considered an attractive analysis because it does not assume normality, linearity, or homoscedasticity (Starkweather and Moske, 2011). MNL specification is tractable and simple to estimate. And the most important thing is the independent errors of MNL force an assumption called the independence of irrelevant alternatives (IIA) assumption. As Dow and Endersby (2004) asserted the idea of IIA is that if a chooser is comparing two alternatives according to a preference relationship, the ordinal ranking of these alternatives should not be affected by the addition or subtraction of other alternatives from the choice set. Thus, the IIA property is a minimal condition for logical consistency. The probabilistic analogue imposed by MNL, strengthens this by requiring that the odds ratio of choosing any two alternatives be independent of the addition or subtraction of other alternatives from the choice set. Specifically, the ratio of choice probabilities for any two alternatives does not depend on the characteristics of any of the other alternatives. This is consistent with the context of education mismatch; a worker can be either matched or mismatched (undereducated/overeducated) without any influence from the other alternatives. It is worth noting that the IIA is a logical property of decision-making, not a statistical property such as consistency and unbiasedness.

Moreover, most of the studies which analyse education mismatch adopt MNL, for instance Chevalier (2007), Battu and Sloane (2002), Kiker et al. (1997), Flisi et al. (2014) and Diem (2015). Thus, the multinomial logit (MNL) model in the present analysis is as follows:

!_!,# = #_$,#+Σ#_%,&,#P_!,&,# + Σ#_',&,#HH_!,&,# + Σ#_(,&,#F_!,&,# + Σ#_),&,#A_!,&,# + *_!,# (4.1),

where:

!!,# is Match category (the dependent variable), consisting of 1 to 3, where: 1 is

overeducated, 2 is matched and 3 is undereducated. + represents set or vector of explanatory variables; ,_!,&,# is personal characteristics (1 … / number of personal characteristic variables); 00_!,&,# is household characteristics (1… / variables); 2_!,&,# is

work-related and firm size variable (1… / no of variables); 3_!,&,# is residence or area dummy variables (1…n number of residence dummies). i is individual (1…I); and t is at time t (2000 or 2014). It is also worth noting that the coefficients in equation 4.1 are not the same in terms of notation as in 4.2. The model is a probabilistic model, so the coefficients in 4.1 are interpreted as relative probabilities.

The baseline category of this analysis is the matched category; thus, the interpretation of the variables would be the likelihood of being in either one of the remaining two mismatch categories (overeducated and undereducated), compared to being matched. The variables are considered to be statistically significant at 1 per cent, 5 per cent or 10 per cent significance level.

The multinomial probit (MNP) model

Another alternative method is the multinomial probit (MNP) models, as used by Berlingieri and Zierahn (2014). The main different between MNL and MNP is assumptions about the probability functions. Technically, MNL and MNP are very similar; they differ only in the distribution of the error terms and each model has its own advantages and disadvantages. The advantages of MNL are that the specification is tractable, simple and faster in estimating the models. However, MNL imposes the restrictive assumption that choices are independent across alternatives.

These disadvantages of the MNL’s can be solved by using MNP. The primary advantage of MNP relative to MNL centres on the IIA property. MNP has errors which are not necessarily independent, and these errors are distributed by a multivariate normal distribution. MNP does not assume IIA. On the other hand, MNP imparts a number of potentially serious problems. These are sufficiently difficult to detect that, in the absence of investing exceptional effort in model diagnostics, researchers are justified in using the MNL specification. The most important problem is that even formally identified MNP specifications are often weakly identified in application. This is serious because weak identification is difficult to diagnose and may lead to plausible, yet arbitrary or misleading inferences. The MNP presents a difficult maximum likelihood optimization problem that sometimes fails to converge at a global optimum or produces parameter estimates that are sufficiently imprecise as to make statistical inferences suspect. Except for cases of

profound misspecification, the logit likelihood will optimize at its global maximum and is not prone to optimization errors (Dow and Endersby, 2004).

Considering those advantages and disadvantages, the present study prefers the MNL as the main model of the present study since MNL is appropriate in this context, IIA property can be fulfilled. Some studies even find that logit estimation (MNL) performs as well or even better than MNP, such as Dow and Endersby (2004). Yet, this study will also perform MNP as a sensitivity analysis and the results of both models will be compared.

4.3.2 Measures

Mismatch Determination

The present study analyses the education mismatch in Indonesia in 2000 and 2014 using the multinomial (MNL) model. The model is adopted from Battu and Sloane (2002) to estimate two sets of coefficients: β1 which represents the overeducation coefficient and

β3 which represents the undereducation coefficient. The probability pnm of individual n

being overeducated (m=1) or undereducated (m=3) is conditional on a vector of characteristics Ki (vector of explanatory variable of mismatch determinants). And the

probability of individual n being in the over or undereducated group m (relative to the probability of being in the default group 2 (matched) is given by:

*!"

*!# = exp [8!

+_(#

,− #')] for m = 1,3 (4.2)

with normalisation of β2 to equal 0. To permit identification of the model, the probabilities

are: =_!' =_[%.∑ %_{012 [4} !$5"]] "%&,( for m=2 (4.3) =!, = 012 [4! $₅ "] [%.∑"%&,(012 [4_!$5"]] for m=1,3 (4.4).

Educational match (!) is defined based on the difference between the workers’ highest educational attainment and the mean of education attainment in the same occupation (as the proxy of job requirement). Thus, the mismatch formula is as follows:

! = #$%&'()*+ '((')+-.+( − (-*$. *1 .$%&'()*+ 2)(ℎ)+ *&&%4'()*+ ± )(6 6('+$'7$ $.8)'()*+) (4.5).

The formula is adapted from Hartog (1997). M has three categories: 1 is overeducated, 2 is matched, and 3 is undereducated. Individuals are defined as being correctly matched (category 2) to their occupation if their own years of education or education levels are