«IZA DP No. 3067 How General Is Human Capital? A Task-Based Approach Christina Gathmann Uta Schönberg September 2007 Forschungsinstitut zur Zukunft ...»
Least squares estimates for the return to general, occupation- and task-speci…c human capital are likely to be biased even for exogenously displaced workers, as workers select into the post-displacement occupation. Next, we outline a control function estimator to get consistent estimates of the wage regression.
5.2 Control Function Estimates To estimate the mean returns to labor market skills in the wage equation, we need to model the conditional mean of the error term in (3) (Heckman and Vytlacil, 1998). Arrange the regressors into Dustmann and Meghir (2005) provide evidence that the assumption of plant closure as an exogenous job loss is reasonable in the German context.
If the returns to the three types of human capital accumulation were homogenous across occupations, the exclusion restriction (4) would be su¢ cient to get consistent estimates. Exclusion restriction (5) accounts for the selection into occupations based on the occupation-speci…c returns to human capital.
to a new occupation as well as whether to move to a similar or distant occupation), but not his wage o¤er (conditional on all regressors). Our main instruments for experience are age and age squared. To instrument for occupation tenure, we follow Altonji and Shakotko (1987) and Parent (2000) and use the
within occupations, occupation and task tenure evolve the same. Consequently, the deviation from its occupation-speci…c mean is exactly the same for occupation and task tenure. We therefore require an additional instrument for task tenure. We use local labor market conditions, in particular the size of occupation and the average distance to other occupations in the same local labor market, as well as both variables interacted with age as additional instruments.11 We expect workers to be less likely to switch occupations in a region with more employment opportunities in the same occupation. We also
opportunities in similar occupations. Since all our speci…cations include occupation, region and time dummies, the variation we exploit is changes in the occupational structure over time within the same region. If local labor markets are integrated in the national labor market, factor prices are equalized, and local labor market conditions can be excluded from wages (see Adda et al., 2006 for a similar argument).
To implement the estimator, we estimate in a …rst step the reduced forms for experience, occupational tenure and task tenure and predict the residuals. The second step estimates the log wage equation in (3) including the estimated residuals as well as their interaction with the endogenous regressors. The interactions between the reduced-form residuals and the regressors are the control functions that account for the selection into occupations based on occupation-speci…c returns. To correct for generated regressor bias, we bootstrap standard errors with 100 replications using the individual as the sampling unit. For the high-skilled, we use the semiparametric estimator proposed by Blundell and Powell (2004) to account for censoring in addition to endogenous regressors. We describe this estimator in detail in Appendix B.
Table 9, columns (1) and (2) report results for a sample of …rm switchers. The …rst stage of our control function estimator is reported in Table A.2 (low- and medium-skilled) and A.3 (high-skilled), while Table A.4 shows the coe¢ cients on the residuals and their interaction with the main regressors.
Both the residuals and the residuals interacted with the regressors enter the wage equation signi…cantly, indicating that selection into occupations based on the task match and occupation-speci…c returns is important.
For all education groups, the control function estimate and the OLS estimate for the displaced sample (Table 8, columns (5) and (6)) yield similar returns to experience for a worker with 10 years of (actual) labor market experience. The return to task tenure however increases considerably when the control function estimator is used, while the return to occupation tenure decreases. In the case of the low- and high-skilled, the return to occupation tenure becomes signi…cantly negative.
In columns (3) and (4), we report control function estimates for our sample of workers who are exogenously displaced from their …rm due to plant closure. Note that we are now identi…ed from workers who lose their job due to plant closure more than once–since for workers who experienced only one plant closure our instrument for occupation tenure, i.e. the deviation from its occupation-speci…c mean, is zero. It is therefore not surprising that estimates are considerably more noisy. For the low-skilled, restricting the sample to exogenously displaced workers has little impact on the point estimates, but only the return to experience is statistically signi…cant. For the medium-skilled, the return to experience remains largely unchanged, but the return to task tenure increases and the return to occupation tenure decreases. For the high-skilled, only the return to experience is statistically signi…cant.
5.3 Economic Interpretation What do our estimates imply about the contribution of task-speci…c human capital accumulation to individual wage growth over the life-cycle? After ten years in the labor market, a typical medium-skilled worker in our sample has accumulated 9.1 years of actual experience, 6.5 years of occupation tenure, and
7.9 years of task tenure. According to the OLS estimates for the displaced sample (Table 8, column (6)), this worker can expect his wages to grow by 9.5 percent (0.012 7.9) due to task-speci…c human capital,
17.4 percent (0.028 9.1-0.001 9.12 ) due to general human capital and 8.5 percent (0.013 7.9) due to occupation- speci…c human capital. Control function estimates for the sample of …rm switchers (Table 9, column (2)) imply similar a wage growth due to general human capital (18 percent), but a higher wage growth due to task-speci…c human capital (21.3 percent). Wage growth due to occupation-speci…c human capital accumulation is slightly negative (-0.65 percent).
Task-speci…c human capital plays an even more important role for the high-skilled. According to the tobit estimates for the displaced sample, a typical high-skilled worker12 can expect his wage to grow because of general, task-speci…c, and occupation-speci…c human capital accumulation by 36.2 percent, of which 40 percent are due to task tenure, 14 percent due to occupation tenure, and 47 percent are due to experience. When we base the calculation on the control function estimates for the sample of …rm After 10 years in the labor market, a high-skilled worker has accumulated 6.81 years of actual experience, 4.95 years of occupation tenure, and 6.19 years of task tenure. Notice that these numbers a considerably lower than the corresponding ones for the medium-skilled. This is because the high-skilled are more likely to move in and out of the sample than the medium-skilled, possibly because of spells as self-employed or civil servants.
switchers, task-speci…c human capital accounts for more than 80 percent of the overall wage growth due to human capital accumulation.
Our estimates can also provide insights into the costs of job displacement due to the loss of occupation- and task-speci…c skills. We base our calculation on the OLS estimates for the displaced sample (Table 8, column (6)).13 Since our calculation excludes the loss in task match quality, our wage losses are a lower bound for the true wage loss of job displacement. Consider a high-skilled worker who is displaced after 10 years in his occupation and …nds employment in similar occupation (e.g. in the 10th percentile of the distribution of moves). The predicted wage loss of this worker is 12.3 percent,
10.0 percent from occupation-speci…c skills but only 0.7 percent from task-speci…c skills. In contrast, if he would move to a distant occupation (e.g. in the 90th percentile of the distribution of moves), he would lose 30.1 percent, 10.0 percent from occupation-speci…c skills and 20.1 percent (0.9 0.230) from task-human capital. The basic pattern holds for all education and experience groups: wage losses of displacement vary with the type of the occupational move after displacement.
Our estimates also imply that wage losses after displacement are low to the extent that workers are able to …nd employment in a similar occupation after displacement. For instance, for high-skilled workers who switches occupations following plant closure, the mean observed distance between the preand post-displacement occupation is 0.177, while it would be 0.466 if he were randomly assigned to an occupation. Hence, for a high-skilled a worker who has been displaced after 10 years in his occupation and moves to a new occupation, the average predicted wage loss due to task-speci…c human capital is
4.1 percent (0.177 0.230), but would be more than twice as high (10.7 percent) if he were randomly allocated to a new occupation.
These calculations show that task-speci…c skills are important for wage growth and costs of displacement.
The OLS speci…cation yields lower estimates for the return to task-speci…c, and higher estimates for the return to occupation-speci…c human capital, than the control function estimates in Table 9. Calculations based on this speci…cation may therefore be thought of as conservative estimate for the importance of task-speci…c human capital.
5.4 Further Robustness Checks Our wage speci…cation (3) does not incorporate job search over …rm matches which has been shown to be an additional source of wage growth (e.g. Topel and Ward, 1991; Pavan, 2005; Yamaguchi, 2007b).
How would …rm matches a¤ect our …ndings? Neal (1999) proposes a model in which workers search over both …rm and occupation matches. He shows that it is optimal for workers to …rst search for a good occupation match, and then for a good …rm match. For a sample of young workers like ours, he then provides empirical support for such a search strategy. Under the two-stage search strategy, our estimates will be little a¤ected by search over …rm matches. The reason is that the majority of young workers in our sample has been in the labor market for less than 8 years so their decision whether to switch occupations and to which occupation to move should be predominantly driven by the task match, and not by the …rm match.
another reason why in an OLS regression the return to task tenure may be downward biased, although the bias still cannot be signed. This is because some workers may have moved to a distant occupation because of a high …rm match, despite a low task match.
As a robustness check, we estimate …rst di¤erence regressions, using a sample of …rm switchers.14 Due to censoring, we cannot estimate …rst di¤erences for university graduates. Instead, we use Honoré’s trimming estimator (1992) for the censored regression (Type 1 tobit model) with …xed e¤ects. Since the estimator is semiparametric, no functional form assumption on the error term is required. However, we do require pairwise exchangeability of the error terms conditional on the included regressors, see Honoré (1992) for details.
Results can be found in Table 9, columns (5) and (6). As expected, …rst di¤erence estimates of the return to occupation- and task tenure are smaller than the OLS and control function estimates.15 Task There is a compelling reason for why …rst di¤erence estimates result in a downward bias in the return to occupationand task-speci…c human capital. Workers who choose to switch occupations, or choose to move to a distant occupation, do so for a reason and therefore have typically less to lose than a randomly selected worker. However, there is also a reason why …rst di¤erence estimates may not provide a lower bound to the return to task tenure: Some workers may have moved to a distant occupation because of a high return to human capital. These workers earn low current wages, but expect a higher than usual wage growth in the future.
Note that due to di¤erences in the econometric model, the results for the low- and medium-skilled cannot be directly tenure continues to be a signi…cant source of individual wage growth even in the …xed e¤ects model.
In addition to …rm matches, we have so far also abstracted from occupational mobility along a job ladder (see Gibbons et al., 2005; Jovanovic and Yarkow, 1997; Yamaguchi, 2007a). Within our framework, job ladders can be modeled by relaxing the restriction that the occupation-speci…c weights add up to one. We would expect occupations that have a higher analytic and manual weight to be higher up the job ladder, and workers should move along the ladder as they become more experienced. While we do not explicitly analyze hierarchical occupation mobility in this paper, our control function estimates is consistent even in the presence of career mobility. This is because the validity our instruments, in particular the deviation of occupation tenure from its occupation-speci…c mean, does not rely on the assumption that the occupation-speci…c weights add up to one.
In sum, the robustness of our results to alternative estimation techniques suggests that task-speci…c human capital is indeed an important source of individual wage growth.
6 Conclusion How general is human capital? The evidence in this paper demonstrates that speci…c skills are more portable than previously considered. We show that workers are much more likely to move to occupations that require similar skills and that the distance of occupational moves declines over the life-cycle.
Furthermore, wages and occupation tenure at the source occupation have a stronger impact on current wages if workers switch to a similar occupation.