APPENDIX 2
HETEROGENEITY AND THE RETURNS TO TRAINING

One interpretation of the training returns presented in Table 3 is that they may, at least in part, be driven by worker or job heterogeneity. That is, training may be more common among better workers or those in "better" jobs or matches, and regardless of the effect of training, these workers enjoy higher earnings. Dealing with such heterogeneity has been a central concern for researchers attempting to estimate the returns to training and schooling.

The National Longitudinal Surveys offer a variety of means to control for this problem. For example, the NLSY data provide measures that allow for some direct control for job and worker attributes that are correlated with both training and earnings. First, the NLSY includes measures of the number of employees working for each respondent's employer. Employer size is known to be correlated with the probability a worker receives training (Barron, Black, & Loewenstein, 1987). Additionally, each of the NLSY sample members took the Armed Services Vocational Aptitude Battery (ASVAB) of tests. [16] From this battery, an Armed Forces Qualifying Test (AFQT) percentile score is calculated, which the U.S. Department of Defense uses as a general measure of trainability. The AFQT score has recently received considerable attention as a measure of skill (e.g., Neal & Johnson, 1996), and offers promise as a control for the possibility that the higher earnings of workers participating in training are due to higher than average skill levels.

As a first attempt to control for the possibility that more skilled, or trainable workers receive the most training, I estimated the earnings effect of training in a model which includes AFQT scores for the NLSY sample. I also included an indicator of whether a sample member worked for an employer with one thousand or more employees to limit the joint effect of job characteristics on training and earnings. The results of this estimation are included in Table A1. The first column presents estimates of the effects of the principal human capital measures, including job training on earnings. These are the results of Model 2 presented in Table 3. In the second column I present the results of the model that include individuals' AFQT percentile scores and the firm size measure.

Table A1
Returns to Training, with Test-Score and Firm-Size Controls: NLSY Cohort

While employer size does not have a significant effect on earnings, clearly the AFQT percentile score is a powerful predictor of wages. Each unit increase in percentile ranking on the AFQT score is associated with a 0.41% increase in wages. This suggests that, after controlling for other factors, a worker scoring in the highest percentile on the AFQT will earn 41% more than the worker scoring in the lowest percentile.

Once these measures of skill and employer size are included, training still appears to have a sizable effect on earnings. Using these direct controls for heterogeneity, workers participating in training are estimated to earn 9.6% more than workers who never engaged in training. This estimate is lower than the previous estimate, although not significantly so. Interestingly, the inclusion of the AFQT and employer size measures has a more substantial effect on estimated returns to formal schooling. For example, the college premium falls from 43% to 26% and the earnings penalty for dropping out of high school falls from 30% to 18% upon inclusion of the skill and employer size measures. These results suggest that heterogeneity plays a marginal role in shaping observed returns to training for this group. This is consistent with several recent attempts to control for heterogeneity in the estimation of the earnings effects of training (see Constantine & Neumark, 1996, for a review).

For my purposes, the issue of heterogeneity concerns not only the extent to which point estimates are biased, but also whether any bias has become more or less severe over time. If the value of training as a signal of worker quality has changed, or if firms have changed the manner in which they allocate training resources, the bias associated with heterogeneity may have changed over time. Any change in the influence of heterogeneity could confound real changes in the returns of training in Table 3.

In order to examine this possibility, I make use of the longitudinal aspect of the NLS data and estimate fixed-effects models of the impact of training on the earnings of both the NLS-OC and NLSY cohorts. The principal results of this analysis are presented in Table A2. The fixed-effects models estimate that for the original cohort, participation in training increased wages by 10.6%. For the NLSY cohort, training was associated with a 12.5% increase in earnings.

Table A2
Alternative Estimates of the Returns to Training

These results suggest that heterogeneity played a minor role at best in determining observed returns to training. Even after controlling for firm size; measurable worker skill; and now unmeasured, time-invariant worker characteristics, participation in training earns high returns for both cohorts. Moreover, the fixed-effects results confirm those presented in Table 3, that the returns to training were of similar magnitudes for both cohorts.

[16] The ASVAB includes ten tests designed to measure skill and knowledge in areas such as general science, arithmetic reasoning, word knowledge, and mechanical comprehension (Center for Human Resource Research, 1995).