College Major and the Gender Earnings Gap: A Multi-country Examination of Postgraduate Labour Market Outcomes

Abstract

This paper explores the effects of degree choice on the distribution of occupational benefits in terms of income, and their contribution to the gender earnings gap, among young European higher education graduates. The results reveal that the field of study, which is the result of a personal choice, appears to influence the distribution of work-related benefits among graduates even after controlling for unobservable heterogeneity and observable individual/job specific characteristics. Analysis of the gender earnings gap shows that the earning disparities among female/male graduates in Education, Humanities and Mathematics are smaller.

Appendix

Variables Used in the Multinomial Model for the Choice of Field of Study

Table 10 Descriptive statistics for the choice of field of study analysis

Methodology for Analysing the Effects of Degree Field on Earnings

Analysis of the effects of study field choice on earnings first needs to address the process behind the choice of field in terms of heterogeneity among graduates (Carneiro et al. 2003). That is, to isolate the income effects of the choice itself, we should compare earnings for graduates from different fields, with similar personal characteristics, doing similar jobs. Otherwise, the estimated coefficients should be interpreted as mere correlations between field of graduation and income, rather than the causal effects of field choice on income (Angrist et al. 1996) because students choose their field of study according to their background, tastes, inclinations, preferences and prospects. Accordingly, graduates from a given field are likely to share some personal characteristics, which may themselves influence their earnings beyond the effect generated by the educational choice itself (Heckman 1978, 2001; Heckman and Navarro 2004).

Therefore, the rationale for having two specifications of the earnings model is that it allows comparison between the coefficients of the study field, considered as an exogenous determinant of income (statistical correlation) and an endogenous determinant (causal effect). Under the first specification, we analyse the earnings for graduates from different fields doing comparable jobs (exogenous choice); under the second, we analyse the earnings of graduates from different fields, with similar personal characteristics and doing comparable jobs (endogenous choice).

The so-called direct specification of the model can be represented as

$$ I = \Upphi \left( {F,\,X} \right) + u $$

(1)

where I is income/earnings, F is actual field of graduation, X are the other observable determinants of income, and u is a disturbance term. Here, the field of study is included as an exogenous determinant of I. The estimated coefficient for F captures only the statistical correlation between field of graduation and income because the process behind the choice of field is not addressed.

However, we argue that the choice of field should be considered as an endogenous process that can be represented as

$$ F = \vartheta \left( Z \right) + v $$

(2)

where F again is the field of study, Z are individual-specific characteristics (observed heterogeneity) guiding the choice, and v is a disturbance term representing unobserved heterogeneity among graduates.

Substituting Eq. 2 into 1 yields $\user2{I}=\varvec{\Upphi}[\varvec{\vartheta}\left(\user2{Z}\right)+\user2{v,\,X}]+\user2{u}.$ So, when the choice of field is endogenous, the coefficient of F estimated from Eq. 1 reflects the real influence of the term $\varvec \vartheta \left( {\user2{Z}} \right) + {\user2{v}}.$ Obviously, this also includes the influence of unobserved heterogeneity among graduates from different fields, v, which in turn is correlated with u. This is the case for a regressor correlated with the disturbance term of the model, so the coefficient estimate would represent correlation, but not causal effect.

This problem can be fixed by estimating Eq. 2 first, thus obtaining a prediction for field of study in terms of the individual-specific observable characteristics, and discarding unobserved heterogeneity. This is equivalent to assigning to each graduate the field of study that would suit him/her best according to his/her own personal observable characteristics ${\user2{F^*}} = \varvec \vartheta {\user2{^* }}\left( {\user2{Z}} \right) = {\user2{F - v^*}},$ where (*) indicates an estimate.

By including the predicted field ${\user2{F^*}} = \varvec \vartheta {\user2{^* }}\left( {\user2{Z}} \right)$ as a regressor in Eq. 1 instead of the observed F, the so-called instrumental variable (IV) specification emerges

$$ I = \Upphi (\vartheta ^* \left( Z \right),\,X) + u $$

(3)

Under this specification $\varvec \vartheta {\user2{^* }}\left( {\user2{Z}} \right) ={\user2{F^*}}$ is not correlated with the disturbance term u. Consequently, the coefficient estimate from Eq. 3 captures the causal effect of field choice once the effects of heterogeneity among graduates from different fields have been removed through the two-step estimation procedure.

Variables Used in the Earning Equation

Table 11 Descriptive statistics for the earnings analysis

Methodology for Analysing Gender Earnings Gap

A number of econometric techniques have been developed to parse out the earnings differentials among groups of people (Blinder 1973; Oaxaca 1973; Cotton 1988; Neumark 1988; Oaxaca and Ransom 1994). The Oaxaca (1973) model, modified by Oaxaca and Ransom (1994), is the most widely used and is employed here. The standard procedure is to fit the following two equations, or earnings functions, for the employed members of each population group:

$$ LnY_{m} = b_{m} X_{m} + \upsilon _{m} $$

(4)

$$ LnY_{f} = b_{f} X_{f} + \upsilon _{f} $$

(5)

where subscripts m and f represent male and female workers, respectively; Y symbolises labour market earnings; X represents the measured productivity-determining characteristics of workers such as education, age and other control variables; b , the regression coefficient, reflects the labour market returns to a unit change in characteristics such as age and education; and u , the error term, reflects measurement error, including the effect of factors unmeasured or unobserved by the researcher. Taking the arithmetic average of Eqs. 4 and 5, the stochastic error term drops away, so that

$$ Ln\overline Y _{m} = \mathop b\limits^{ \wedge } {_m}\overline X{ _{m}} $$

(6)

$$ Ln\overline Y _{f} = \mathop b\limits^{ \wedge } {_{f}}\overline X {_{f}} $$

(7)

where hats (^) denote estimated values and bars (—) represent mean values, which simply says that mean earnings are predicted by mean characteristics.

If female workers received the same returns as male workers for their endowments of earnings-determining characteristics, then their average earnings would be

$$ Ln\overline Y _{f}^{*} = \mathop b\limits^{ \wedge } {_{m}}\overline X {_{f}} $$

(8)

which would therefore be the average earnings of female workers that would prevail if there were no wage discrimination.

Subtracting Eq. 8 from Eq. 6 gives the difference between the average male earnings and the hypothetical average female earnings that would prevail if female workers’ human capital in the labour market was rewarded in precisely the same way as male workers’ human capital. The difference between actual and hypothetical earnings reflects the differences between the two population groups’ human capital, so that

$$ Ln\overline {Y_{m} } - Ln\overline Y _{f}^{*} = \mathop{b}\limits^{ \wedge }{ _{m}} \overline X {_{m}} - \mathop b\limits^{\wedge } {_{m}} \overline {X_{f} } = \mathop b\limits^{ \wedge }{_{m}} (\overline {X_{m} } - \overline {X_{f} } ) $$

(9)

Subtracting Eq. 7 from Eq. 8 yields the difference between the actual and the hypothetical non-discriminatory earnings of female workers. This difference reflects the differential returns that the market awards to different population groups with the same human capital characteristics:

$$ Ln\overline Y _{f}^{*} - Ln\overline {Y_{f} } = \mathop{b}\limits^{ \wedge }{ _{m}} \overline X {_{f}} - \mathop b\limits^{\wedge } {_{f}} \overline {X_{f} } = \overline {X_{f} } (\mathop{b_{m} }\limits^{ \wedge } - \mathop {b_{f} }\limits^{ \wedge } )$$

(10)

Adding Eqs. 9 and 10 yields

$$ Ln\overline {Y_{m} } - Ln\overline {Y_{f} } = \mathop{b}\limits^{ \wedge } {_{m}} (\overline X {_{m}} - \overline {X_{f}} ) + \overline {X_{f} } (\mathop {b_{m} }\limits^{ \wedge } -\mathop {b_{f} }\limits^{ \wedge } ) $$

(11)

The overall earnings gap can thus be decomposed into two components: one attributed to differences in endowments of income-generating characteristics (X_m − X_f) evaluated using the male worker pay structure (b_m); and the other attributed to differences in the returns (b_m − b_f) male and female workers receive for the same endowment of income-generating characteristics (X). This latter component is indicative of the extent of wage discrimination (Schultz 1991). This method, although illuminating––since it enables estimation of the extent of labour market discrimination––does not, however, identify the reasons for the discrimination.

Note that in the above decomposition model, the male coefficient vector is chosen as the reference structure against which the contribution of the differences in characteristics is evaluated. The female earnings structure could have been chosen as the reference structure and would have yielded an analogous decomposition

$$ Ln\overline {Y_{m} } - Ln\overline {Y_{f} } = \mathop{b}\limits^{ \wedge } {_{f}} (\overline X {_{m}} - \overline {X_{f}} ) + \overline {X_{m} } (\mathop {b_{m} }\limits^{ \wedge } -\mathop {b_{f} }\limits^{ \wedge } ) $$

(12)

The literature emphasises that there is no unambiguously best way to decide between the two alternative reference structures, which is really an index number problem.

Following Oaxaca and Ransom (1994), letting b* denote the estimated non-discriminatory earnings structure, the average earnings gap in logs can be rewritten as

$$ Ln\overline {Y_{m} } - Ln\overline {Y_{f} } = \mathop{b}\limits{{}}^*(\overline X {_{m}} - \overline {X_{f} } ) +\overline {X{_{m}} } (\mathop {b{_{m}} }\limits^{ \wedge } -\mathop {b^*}\limits^{{}} ) + \overline {X{_{f}} } (\mathop{b^*_{{}} }\limits^{{}} - \mathop {b{_{f}} }\limits^{ \wedge } )$$

(13)

where $b^* = \Upomega \mathop b\limits^{ \wedge }{_{m}} + ({\rm I} -\Upomega )\mathop b\limits^{ \wedge }{{ _{f}}}$ is a weighted vector of the estimated vector of coefficients. The definition of the basic non-discriminatory earnings structure corresponds then to the choice of weighting matrix Ω. Several alternatives have been suggested in the literature. According to Oaxaca (1973), either the male earnings structure (Ω = I) or the female earnings structure (Ω = 0) could be used.

Cotton (1988) proposes the use of (Ω =  λ _m I) where (λ _m ) as the fraction of males in the sample. Neumark (1988) proposes an estimation of the non-discriminatory earnings structure on the basis of the pooled sample of males and females which implies that

$$ \Upomega = \left( {X^\prime X} \right)^{{ - 1}} \left( {X^\prime _{m} X_{m} } \right). $$

Although there are problems inherent in the methodology that may result in misleading results, here we use the more traditional parametric decomposition (see Dolton and Makepeace 1985; Oaxaca and Ransom 1994, 1999; Barsky et al. 2002 for more detail).