The theoretical models in section 2 showed that investment in JRT increases the productivity of the employee and thereby the wage supposedly increases. The traditional human capital theory also shows that the division between firm specific and general training can influence the wage return to JRT for employees who separate from one firm to another. Finally, the extended human capital theory illustrated that the wage return to JRT declines and maybe even disappears in an economy with compressed wage structures. Job separations also decline with respect to JRT due to the existence of a separation cost.
The empirical model is supposed to capture the predictions from the human capital theories. However, as the literature review clearly showed the selection problem due to individual specific effects with respect to JRT and job separations are important to account for in the empirical setup, because it is the key to reducing the bias of the JRT estimates.
First consider a simple Mincer wage equation in the following way:
(1) log(wit+1)=α0 +α1D96+βJRTit+ Xit+1γ +εit+1
Where log of wages for employee i at time t+1 (i.e. 1996) is a function of receiving
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Obviously employees and firms only invest or receive JRT if they expect the employee’s productivity to increase, which also means that wages increase. As previously mentioned, an individual specific aptitude that is not contained in any of the X’s could exist. Thus the estimated effect of JRT might then capture the individual specific aptitude instead of the JRT effect (i.e. the simple Mincer equation would estimate a positive JRT effect). The estimated βbecomes biased because it captures the effect of JRT. For example the high paid wage earner already has a high wage due to an individual specific effect.
As mentioned earlier a way to take care of selection that is independent of time is looking at wage growth (i.e. before and after receiving JRT). Thus, the problem in previous studies of finding an instrument is overcome. So a bias caused by an individual specific fixed effect is easily overcome by estimating the effect of JRT by using a first difference log wage equation, as follows:
(2) )log(wit+1)−log(wit−1)=α1+β(JRTit)+(Xit+1−Xit−1)γ +(εit+1−εit−1
In other words, in this analysis the log wage increase from 1994 to 1996 is a function of a time trend factor α1, the JRT received between 1994 and 1996 (i.e. JRT received in 1995) and the difference in observed characteristics between 1994 and 1996 and an independent error term. Note that JRT is equal to zero in 1994.
One could argue that the selection into JRT is time dependent. Therefore it is necessary to take the selection of training into account (in the first difference estimation as well). By not taking selection into account in the wage growth equation,
β would again be biased just like in the simple Mincer equation.
As described in section 3, previous studies have tried to take training selection and individual fixed effects into account simultaneously, but for two reasons it is not done here. First, it is not obvious that the selection into JRT is time dependent if one thinks about the individual specific effect as an unobserved aptitude for implementing the JRT. Second, even if it is time dependent it is difficult to find a good instrument. Assuming that a random functional form of observable characteristics can identify the likelihood of receiving JRT it is not reliable as argued in section 3. On the other hand using an instrument such as Xu(2005) (described in section 3) is feasible if
the instrument fulfils two assumptions; correlation with the endogenous variable and the orthogonality of the error term. Moreover, Kruger and Rouse’s (1998) use of an exogenous change in the JRT program as an instrument is feasible. However, neither a good instrument nor an exogenous change is possible in this analysis of the Danish JRT in 1995.
In a job separation situation as earlier mentioned two things have to be taken into account. First, as previously indicated it is plausible that there is a combined effect of JRT and job separations. Therefore an interaction-term of JRT and job separation is included in the model. Second, a potential endogeneity problem exists when looking at separations and wage return.
The endogeneity problem can be overcome if the separation can be instrumented. Good instruments are characterized by satisfying two requirements. First, the instrument must be correlated with the endogenous variable and because more instruments are used it is important to see if the instruments are jointly valid. Second, the instruments must be orthogonal to the error term. In other words the instrument is not supposed to influence the outcome variable (wage return) other than through the endogenous variable (job separation). As explained in section 5 the JRTDS includes employees past records on job separations. Thus the individual risk of separating from a current job can be instrumented by the individual’s history of job changes. Clearly it is necessary to instrument both the job separation variable and the interaction term between job separations and JRT. Then the wage growth regression accounting for individual fixed effects and the separation selection is estimated in the following way:
(3) ( ) ( )
Where the incidence of separation is estimated in the following way:
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In equation (3) the change in socio-economic factors are included, (Xit+1−Xit−1). Compared to the simple Mincer wage equation the variables included in equation (3) are changes in the socio-economic variables, and not the level. Thus the changes affect the wage growth and not the level. Variables such as; experience, tenure, occupation group, working industries and working sector have often been included in previous studies.
Here it does not make sense because first of all the sample is full-time employees working in 1994, 1995 and 1996. Therefore experience changes for all employees in the sample for two years. Second, tenure is strongly correlated with job separations, because all the employees that separate will have no tenure or negative tenure. Third, a change of occupational group could change the wage growth, but it does not really help explaining the causality of JRT and wage growth. Fourth, changing jobs from one industry or sector to another industry or sector could affect the wage growth because the different industries and sectors have different wage growth rates. However, in the sample hardly any of the employees who separate from their jobs change industry or sector. Therefore it is not relevant to include these variables. Instead, only the change in the local unemployment rate is included in the equation (3). The local unemployment rate affects the employee’s job opportunities and the employers hiring opportunities as well as the wage growth in the local areas.
To sum up, this paper estimates the return to JRT by taking individual fixed effects into account and by instrumenting the employee’s likelihood of job separations in order to solve the potential endogeneity problem.