Holografía de volumen (fotorrefractivos).

There are some frameworks of the Mincer wage equation: individuals have identical abilities and opportunities, credit markets are perfect, the environment is perfectly certain, but occupations differ in the amount of schooling required. Individuals sacrifice wages while in school but incur no direct costs. Because individuals are ex ante identical, they require a compensating wage differential to work in occupations which require a longer schooling period. And finally, the compensating differential is determined by equating the present value of earnings streams net of costs associated with different levels of investment (Heckman et al., 2006). Furthermore, the Mincer wage equation assumes that (1) an individual with X years of schooling has wages which do not depend on age, for example a 40 year old new graduate will obtain the same as an 18 year old new graduate,

when they are graduated in the same time; (2) present value of lifetime income is the same across individual regardless of schooling if no post-schooling investments are made; and (3) the number of years spent at work are independent of the number of years schooling (Bunzel, 2008).

In the regression, the standard Mincer wage equation is represented by log of wage (W), which only depends on education (years of schooling/X), years of experience (L), and the squared of experience (L2_{), with a linear relationship between education and wages, the}

proof of log linear relationship is shown in Appendix II. In the present research, Mincer wage equation for panel data is used to analyse the change of wage for a given sample individuals (i) over time, the standard Mincer wage equation is as shown below:

ln %_-,+ = ;_/,++ ∑ ;_%,0,+1_-,0,++;_1,+<_-,++ ;_2,+<1_{-,+ + =}

-,+ (3.6),

where:

*> %_-,+: wage of individual i at time t (in log),

1_-,0,+: education level of individual i at time t, > is 1 to 4 (primary to university level) or > =1 if education variable is defined as years of schooling,

<_-,+: years of experience of individual n at time t; or potential labour market experience, =_-,+: a random error term,

;%,0,+: the rate of return to education for > (1…4 level of education) at time t, ;1 and ;2

are parameters of experience, ;_/,+: the intercept, Σ is set (vector) of explanatory variables; n is individual (i=1…I) and t refers to time period.

In an empirical research, actual or potential wage (W) can be used in the estimates. Actual wage refers to wages that individuals actually receive. If actual data are not available, an alternative variable that can be used is potential wage, i.e. the potential income that might be earned if the individual played by the rules and worked for salary as much as other individuals do. There are some wage proxies: net or gross, hourly, weekly, monthly or yearly wages (Pereira and Martins, 2001). Swaffield (2000) defines wage as the gross average hourly wage and is transformed into the real wage by using a nominal wage index (constructed from the New Earnings Survey’s average hourly wage). Meanwhile, Chevalier et al. (2002) calculate an hourly wage rate from the ratio of usual wage including overtime pay to usual hours (from the respondent’s main job including overtime) and deflate all wages to 1993 prices using the Retail Price Index. One advantage of using hourly wage is that it could eliminate unobserved heterogeneity caused by the omitted working hours (Li and Urmanbetova, 2007); moreover, workers sometimes have

more overtime in one month, but not that much time in another month. Transforming yearly wage into hourly wage is hoped to eliminate this problem.

Education attainment (X) could be defined as the highest level of education successfully completed and is either indicated by the highest educational qualification (vocational or academic) achieved, or by the number of years of education or schooling completed or in which case each year is regarded as a kind of level (UNESCO, 2010). Most studies calculated this variable by attaching the average of years to several standardised education levels or the total years of schooling (Asplund and Pereira, 1999). Meanwhile, other studies used a set of dummy variables as individual’s educational and vocational qualifications, allowing non-linear effects of the level of education. This specification also takes into account that, for a given completed educational/vocational degree, fewer rather than more years are considered as a positive signal (Steiner and Wagner, 1996). In terms of labour market experience (L), the standard Mincer wage equation also indicates a linear function between experience and wages, due to homogeneous individuals. Meanwhile, the quadratic function of experience variable could capture the fact that on-the-job training investments decline over time, as stated in the standard lifecycle human capital model, the algebra of this relationship is provided in Appendix III. Most empirical studies used actual and potential experience as labour market experience variables, indeed potential experience can be used if the data were not available. There is a distinction between both variables; actual experience refers to the sum of lifetime hours spent working and training while potential experience refers to the time elapsed since leaving school (Regan and Oaxaca, 2009). Thus, there is a possibility of different data between actual and potential experience.

The equation postulates that experience in the labour market has a positive impact on wages. Furthermore, the effect of the square of experience is negative which implies that there are diminishing returns in experience. If the model assumes a linear relation between wage and experience, the correlation between both variables shows a concave shape. In addition, to reflect labour market experience, some studies also used job tenure which represents the individual’s years of experience in their present job; this variable is usually viewed as a measure of firm-specific training and knowledge, at the same time. The hypotheses are the same as experience variables.

Burdett and Coles (2010) argue that wage changes both with experience and with tenure because of two reasons: (1) individuals accumulate human capital by working, for example: typists become better typists while working as typists and; (2) human capital can be dichotomised into general human capital and firm-specific human capital. A worker who enjoys an increase in general human capital becomes more productive at all jobs (related to experience), and accumulating firm-specific human capital implies a worker is only more productive at that firm (tenure effect). As such, workers who change jobs, or those who are laid off, lose their firm-specific human capital, but keep their general human capital. As experience variable, the quadratic function of experience variable could capture the fact that on-the-job training investments decline over time. In the development, most research modifies the standard Mincer wage equation with control variables, i.e. personal characteristics such as sex (Comola and de Mello, 2009), and marital status (Chevalier, et al., 2002; Comola and de Mello, 2009); job and firm related variables such as present labour market experience or tenure (Purnastuti et al., 2013), firm size and firm age (Pereira and Martin, 2001), industries (Comola and de Mello, 2013), formal and informal sectors (Dasgupta et al., 2015); urban and rural area residential (Dumauli, 2015); and some interaction terms such as gender-material status and gender-dependency ratio (Comola and de Mello, 2009). These modifications are done with the aims to capture other factors that may affect the wage equation.

It is worth noting as well that Mincer (1958) also asserts that the resulting age-wage

profile was steeper for more educated employees than for those less educated. In other

words, log wage is not a strictly separable function of education and age. There is no such thing as a single rate of return to education but rather a different rate of return for each age group. In contrast, Mincer (1958) also points out that in schooling, experience and wage, the experience-wage profiles are relatively parallel for different education groups.

Limitations of the Mincer Wage Equation

The Mincer wage equation has been commonly used to estimate return to education, and also offers a good starting point (Humphreys, 2012). Lemieux (2006) asserts that Mincer wage equation provides a parsimonious specification that fits the data remarkably well in most contexts. However, there are some valid critiques of the model. In terms of

assumptions, mainly the same present value of lifetime incomes cannot be fulfilled, only for simplification purpose.

There are some limitations of the Mincer wage equation, i.e. (1) an endogeneity of education exists due to an ability bias and other omitted variable bias (this will be explained in detail in the next section); (2) measurement error in education variable causes the biased and inconsistent OLS estimates. Bias due to measurement error in the schooling variable is generally known to produce an attenuation bias in the coefficient of schooling; (3) sample selection bias occurs due to non-random selection of the sample used for the estimation process, when the sample is only based on a subpopulation; (4) the relationship between education and wages could be non-linear, this may be because of sheepskin effects, where achieving the final credential (e.g. a high school certificate or university degree) is more important than non-credentialed education. For instance, completing four out of four years of a higher education degree may well result in a large wage premium, but a person who completes only three out of four years of the same degree may receive a much smaller wage premium, as Mincer (1997) argues; (5) there are differences in experience profile in the labour market or heterogeneous experience, for example: high-skilled jobs may include a significant amount of “on the job” training and greater opportunities for professional advancement, while low-skilled jobs could only have little experience (Humphreys, 2012; Firpo et al., 2005)). The present study will focus on two of its limitations, i.e. the endogeneity and sample selection bias, which will be discussed in the next part.

Although there are many limitations of Mincer wage equation, Lemiux (2003) concludes that the equation is still a good approximation in many cases, but it may overstate or understate the effect of experience and schooling on wages for some groups. Lemiux (2003) evaluates the empirical performance of the standard Mincer Wage Equation for the US data, using the Current Population Survey (CPS) for the years 1979-2001. The research finds that the equation does not appear to fit the data of the US in the 1980s and 1990s, but it fits the data from the 1960s and 1970s; because there was an increasingly convex function of years of schooling and experience-wage profiles are no longer parallel for different education groups. However, the Mincer wage equation remains useful and accurate in a stable environment where educational achievement grows smoothly over successive cohorts of employees. In short, the Mincer wage equation remains a

parsimonious and relatively accurate model of the relationship among wage, education and experience, particularly in a stable environment.

Endogeneity Issue in Mincer Equation

Referring to the first assumption of the Mincer wage equation: all individuals are identical apart from the difference in education and training, it seems that the assumption cannot be fulfilled since different people cannot be identical, as they have different social environment, family background etc. Endogeneity problem arises due to unobservable variables such as ability. Ability can determine wage in the labour market and at the same time it can be correlated with education. This problem leads to biased results in the OLS estimations, because the education variable will be correlated with the error term in wage equation. The evidence of this endogeneity problem is explained in Appendix IV. To address the endogeneity issue, instrumental variable method can be used to solve this problem. The first step is estimating the predicted value of schooling variable, i.e. 1? = ;/+ ∑ ;%,0,+@-,0,++ ;1,0,+∑ A-,0,++ =-,+ (3.7),

where: 1? is predicted value of education/schooling variable; @_-,0,+ is vector of all explanatory/control variables; and A_-,0,+ is instrument variables.

After the predicted value of education is obtained, in the second stage, education variable is replaced by the predicted one (from the first stage):

ln %_-,+ = ;_/+ ∑ ;_%,0,+@_-,0,+ + ;_1,+1?_-,++ =_-,+ (3.8).

In terms of instrumental variables, some conventional variables can be used, such as: 1. family background, including the parent’s education, and household wealth

(Blackburn and Neumark, 1993). The idea is more educated families affect their wage by providing education friendly environment or by providing more financial help for their children. However, this could become an unfit instrument if family factors affect the wage directly by securing better and well-paid jobs for the children using their social affiliations and power;

2. IQ or other academic scores (Harmon et al., 2003), those variables are assumed to capture natural ability; students with greater abilities (or some other hidden advantages) are likely to receive more schooling and also receive higher incomes, which could result in a correlation between schooling and wage that does not describe a causal link. If ability is related to both schooling and wage, then the

standard Mincer equation would give an upward biased result, and will also cause a convex relationship between education and (log of) wages (Humphreys, 2012); 3. siblings or twin data, such as Butcher and Case (1994) use of “the presence of any sisters” within a family as an instrumental variable for schooling of female workers on the basis that gender composition of siblings in a family has a significant effect on educational attainment but no effect on inherent ability; 4. availability of educational institutions nearby (Card, 1993), since the availability

of school in a locality can increase the level of schooling in general, because living far from education institutions increases the cost of schooling in different ways such as transportation cost, fatigues and homesickness;

5. bad habits such as smoking since according to the health economics, more educated people have better health and better health habits. Furthermore, Grossman (2008) asserts that completed years of formal schooling is the most important correlation of good health and this is based on some measurements, such as: mortality rates, morbidity rates, self-evaluated health status or psychological well-being.

Alternatively, the analysis can use policy or natural instruments such as: compulsory schooling law or other related education policies (Angrist and Krueger, 1991; Duflo, 2001; Comola and de Mello, 2010; Purnastuti et al., 2015). The idea is that a child who was born earlier or before the policy is implemented, will have a lower level of education as compared to the people born later on.

Even when there are many alternatives of instrumental variables, searching for a valid instrument is hard. Weakly correlated instruments with the endogenous variable causes IV estimates to be biased in the same direction as the OLS and may not be consistent. Using many instrumental variables could also decrease the number of observations that has a serious effect for small sample studies particularly.

To evaluate whether the instruments used are appropriate, the standard quality, validity and relevance criteria of the instruments are considered (Purnastuti et al., 2015). The most important thing is to use a valid instrument if it affects earnings through schooling only. The first test is for the quality of the instruments. This is assessed using an F-test of the joint significance of the respective instrument set in their first-stage equation. Moreover, the R squared from the first-stage equation for the IV models based on the conventional instruments must be at a reasonable level. In addition, test for overidentification

restrictions and Hausman test for relevance criterion can be used. Hausman test can confirm the necessity to use IV/OLS estimations.

Sample Selection Issue

The problem arises due to non-random selection of the sample used for the estimation process, when the sample is only based on a subpopulation. For example: Mincer wage equation estimation is based on individuals whose wage is observed or individuals who choose to actively participate in the labour market as a wage earner. Thus, the differences between characteristics of actives and inactives may cause the sample selection bias. If the decision to or not to participate was a random decision, OLS estimates would be an appropriate estimating procedure; yet it is not a random decision, instead it is driven by some other factors (Bhatti, 2012). Moreover, Comola and de Mello (2010) assert that information on earnings is usually available only for salaried workers, thus OLS estimates are inconsistent if the earnings distribution is truncated.

Gronau (1973) firstly raised this issue. Most empirical studies are only based on the observed wage distribution. Meanwhile, the observed distribution represents only one part of the wage offer distribution, as the other part being rejected by the job seekers as unacceptable. As a result, the traditional estimation procedures may involve certain biases when applied to the secondary labour group such as married women, teenagers, and the aged. The study finds that the US females participating in the labour force were different in characteristics from those who decided not to be included in the labour force. Hence, simple OLS may produce biased estimates for different factors influencing wage in the labour market.

The corrective measures can be used in order to avoid the possibility of sample selection bias; the results may be considered for the whole target population. While ignoring this correction, it means that the result is valid only for the subpopulation of people who decided to work in the labour market. Heckman proposes maximum likelihood (ML) estimator (1976) and then a two-step estimation procedure (1979). The estimation procedure eliminates the possible sample selection bias in two steps. The first step uses ML probit regression, in which the decision to or not to work in the labour market is used as a response variable that depends on different explanatory factors. Then, the Inverse Mills Ratio (IMR) is calculated from the coefficient estimated in the first step. ML probit regression is estimated by separating the sample into two groups:

B"CDEF = 31 GH IJ(K+> GK G>L+*LJM G> /N,JM /+(O G> *NP+Q( RN(OJS

0 +SℎJ(/GKJ V

Then, ACTIVE can be estimated by equation:

B"CDEF_-,+ = W_/ + ∑ ;_%,0@_-,0,++ =_-,+ (3.9),

where:

B"CDEF_-,+ is probit / dummy variable for active and not active,

@_-,0,+ is the number of explanatory variables that affect the likelihood of participation of individuals into waged work.

From the equation above, the Inverse Mills Ratio (IMR) is calculated by:

DX!_-,+ = _%#(3(3%4)_%4) (3.10),

where: (. ) and (. ) are density and distribution function of the standard normal distribution.

And the second step, estimating Mincer wage equation with the IMR as an additional regressor, or

ln %_-,+ = ;_/,++ ∑ ;_%,0,+1_-,0,++ ∑ ;_%,0,+@_-,0,+ + ;_2,+DX!_-,++ =_-,+ (3.11), this will account for the bias due to the non-random nature of the sample of wage earners. A significant coefficient for the IMR points at the presence of the sample selectivity. In short, a first-stage probit equation estimates the selection process, which is estimated as a probit (the dependent variable is binary variable for being selected into the sample or dummy variable is one if the woman is participating in the labour force and is thus being paid and observed for the wage equation). The results from the first equation are used to construct a variable that captures the selection effect in the wage equation. One example of instrument variables is the presence of children for women, since the assumption is