Minimum wages, on-the-job training, and wage growth.

Sicilian, Paul

1. Introduction

It has long been recognized that firms may react to imposition of a legal minimum wage by reducing nonpecuniary attributes of jobs. Hashimoto (1982) and Leighton and Mincer (1981) suggest that, since human capital models predict workers will pay for at least part of any on-the-job training through reductions in wages, a binding minimum wage will reduce training opportunities. They present similar empirical tests of this hypothesis that, they argue, support the theory.

Though routinely cited as examples of the effects of binding minimum wage constraints (e.g., Ehrenberg and Smith 1997), their tests are unconvincing for theoretical reasons and because of data limitations they faced. In fact, neither researcher had direct evidence on training. Instead, they inferred the amount of on-the-job training received by observing wage growth over a fixed period of time without accounting for the possibility that individuals may change jobs during the period of observation. Thus, the data they use do not allow one to be sure that wage growth within the firm is lower on jobs starting at the minimum wage. Lazear and Miller (1981) also attempt to measure the effects of minimum wages on wage growth. Like the other researchers, they expect that binding minimum wages may inhibit wage growth, though they do not insist that reduced training is the only explanation for the expected lower wage growth. based on their empirical work, they conclude that, "There are no obvious retardation effects of the minimum wage on wage growth" (p. 350). Comparing their empirical method and findings to those of Hashimoto (1982) and Leighton and Mincer (1981), they argue that, "The lack of robustness of results across studies suggests that the issue raised is one worthy of study, but one that has not been shown to be important conclusively" (p. 378).

This paper uses data from the Employment Opportunities Pilot Project (EOPP) to examine directly the relationships between minimum wages, wage growth, and on-the-job training. We find that wage growth is slower on minimum wage jobs than on other jobs. However, the amount of training provided to workers on minimum wage jobs is not significantly different than the amounts of training other low-wage workers receive. Thus, the EOPP data indicate that, while workers on minimum wage jobs do experience slower wage growth than other low-wage workers, this outcome is not due to reduced on-the-job training.

The remainder of the paper is organized as follows. The next section provides a critical review of the research on minimum wage effects on wage growth and training. Section 3 discusses the EOPP data and defines the variables used in our empirical procedures. Section 4 presents the results of our estimation, and the final section presents our conclusions and suggestions for further research.

2. Previous Research

As mentioned above, there are three existing studies of the effects of minimum wages on wage growth - Hashimoto (1982), Leighton and Mincer (1981), and Lazear and Miller (1981).(1) All three use samples of young men from the 1960s and/or early 1970s. Hashimoto uses the National Longitudinal Survey (NLS), Lazear and Miller use both the NLS and the National Longitudinal Study of the High School Class of 1972, and Leighton and Mincer use both the NLS and the Panel Study of Income Dynamics (PSID).

Hashimoto (1982) and Leighton and Mincer (1981) explicitly attempt to measure the effects of minimum wages on training. Their method - using wage growth to proxy the amount of on-the-job training - has been used by other researchers studying the effects of training (Lazear 1976; Landes 1977). While this method is an ingenious attempt to get around data limitations regarding on-the-job training, there are several shortcomings to this research. First, human capital theory suggests that the rate of wage growth for a given amount of training depends on the proportion of that training that is specific and on the relative bargaining power of the employer and employee (Hashimoto 1981). Thus, different rates of wage growth do not necessarily imply different amounts of on-the-job training. Moreover, several theories of compensation suggest that wage growth may be independent of increases in productivity. For example, Salop and Salop (1976) develop an adverse selection model, which suggests that firms will offer back-loaded compensation packages to attract workers with lower turnover propensities. Also, principal-agent models argue that inclined earnings profiles provide incentives for greater employee effort on the job (Lazear 1979). As Lazear and Miller (1981) point out, even if there is convincing evidence that wage growth is retarded by minimum wages, it may not be because of reduced investments in human capital. Instead, "the current retardation in wage growth may reflect minor shifting of the age-earnings profile, paying out more of lifetime wealth to young workers" (p. 353). Card and Krueger (1995) present evidence to this effect using data from surveys of fast food restaurants in Texas. They show that these employers neither delayed the time of the first raise nor reduced the size of the raise in response to increases in the minimum wage.

Finally, in both the Hashimoto (1982) and Leighton and Mincer (1981) studies, wage growth is measured as the change in wages observed over the same fixed calendar time period for all individuals. Thus, wage growth is observed at potentially very different points in each person's tenure and, in fact, may represent wages at two different jobs. Since human capital theory suggests that most training will occur at or near the beginning of a job, the best test of the training hypothesis would be to observe workers at the start of employment spells. Because the EOPP includes direct and relatively detailed measures of on-the-job training, we are able to avoid the disadvantages of the indirect method described above.

3. Data

The EOPP is a two-wave survey of approximately 3000 firms conducted in 1980 and 1982. This study uses the 1982 data. The firms in the EOPP are concentrated in the South and Midwest(2) and are predominately small and low-wage employers. Given the well-known differences in pay and personnel policies between large and small employers, one should be circumspect in generalizing the results presented in this paper.(3) The survey directs the employer to consider "the last new employee your company hired prior to August 1981" and asks questions dealing with both "that person and the position he or she was hired to fill." Wage information includes the current wage of the employee (or, if the worker has left the firm, the wage at the time of the separation) and the starting wage. Thus, we are able to measure wage growth within the firm precisely. Moreover, we are able to determine whether the employee started at the minimum wage.(4) The dummy variable MINIMUM WAGE is equal to one if the individual started at the minimum wage. Also, to differentiate minimum wage jobs from other low-paying jobs, we include two other starting wage dummy variables. BELOW MINIMUM WAGE is equal to one if the starting wage is less than the minimum wage, and JUST ABOVE MINIMUM WAGE is equal to one if the starting wage is no more than 25 cents above the minimum wage.(5) Table 1, which presents tabulations of starting wages by occupation and industry, shows that both minimum wage and other low-wage jobs are concentrated in the service and clerical occupations and in the service and retail industries.

The EOPP provides relatively detailed information regarding on-the-job training. Specifically, we know, during the first three months the number of hours management, supervisors, and coworkers devote to formal and informal training of the newly hired worker. TRAINING INTENSITY is the sum of the first three months of training activities.(6) Since not all workers [TABULAR DATA FOR TABLE 1 OMITTED] in our sample have completed three months with the firm, we include in our training regressions a dummy variable - JOB TENURE MORE THAN 3 MONTHS - equal to one if the individual's tenure is greater than or equal to three months.

Demographic variables contained in the EOPP include the worker's SEX and his or her AGE at the time of hiring. EDUCATION is defined as years of schooling completed when hired, while RELATED EXPERIENCE is defined as the answer to the question "How many [years] of experience in jobs that had some application to the position did (name) have before (he/she) started working for your company?" TENURE in years for those workers who are no longer with the firm is given in the data. For those still employed by the firm, tenure can be calculated using information regarding the worker's starting month and year and the date of the survey.

Firm-wide data in the EOPP include the extent of unionization within the firm and the firm's standard industrial classification code. UNION is the "current percentage of nonsupervisory workers that are covered by collective bargaining." We control for industry in some specifications through use of dummy variables corresponding to one-digit SIC codes and for occupation using dummy variables corresponding to the job's Dictionary of Occupational Titles code. While the EOPP does not provide an exact measure of plant size or firm size, it does report the number of employees in all the firm's establishments within the geographic site defined by the EOPP The log of this number, FIRM SIZE, is included in our regressions.

We know at the time of the hiring whether the job was permanent, temporary, or seasonal. PERMANENT is a dummy variable equal to one if the job was permanent. The variable WEEKLY HOURS contains the individual's usual weekly hours worked. Barron, Black, and Loewenstein (1993) suggest that wages and on-the-job training are likely to be affected by the amount of physical capital available to the worker. The EOPP includes the question, "If it were purchased today what would be the cost of the most expensive machine people in [this] position work on or with?" The firm's answer can fall into one of five categories: under $2000, $2000-$10,000, $10,000-$50,000, $50,000-$200,000, over $200,000. We follow Barron and Bishop (1985) in defining CAPITAL as the geometric mean of the interval given by the firm.(7)

The major weakness of the EOPP is some missing demographic variables for the worker. In particular, the data set has no information regarding race, marital status, or the size of the worker's family, if any. There is ample evidence in the existing empirical literature of gender differences with regard to the determinants of and the returns to training (e.g., Holtmann and Idson 1991; Lynch 1992; Barron, Black, and Loewenstein 1993). Thus, we estimate separate equations for men and women. We are somewhat concerned about how the omission of marital status and family size data affects our ability to control for labor force attachment, particularly since attachment to the labor force is likely to be an important determinant of on-the-job training. We believe that RELATED EXPERIENCE serves as a proxy for historical labor force attachment. An additional control comes from the fact that the firm is asked "How many weeks does it take a new employee hired for this position to become fully trained and qualified if he or she has no previous experience in this job, but has had the necessary school-provided training." We follow Barron, Berger, and Black (1993) in using responses to this question as a measure of JOB COMPLEXITY. As O'Neill and Polachek (1993, p. 210) note, ". . . investments requiting lengthy or otherwise costly training are less likely to be undertaken by those who do not anticipate a long period of market work." Hence, we use JOB COMPLEXITY as a proxy for labor force attachment. Since Brown (1989) finds that nearly all wage growth occurs during the training period, we include in the wage growth equations the dummy variable TRAINING DONE, equal to one if the individual's TENURE is greater than the number of weeks needed to become fully trained in the job.

To create samples from the EOPP, we keep only those observations in which the individual is between the ages of 16 and 65. Hires prior to 1978 are dropped to avoid problems associated with retrospective information.(8) These restrictions leave us with 2984 observations. Finally, for each regression, we drop all observations for which there is not a complete set of variables.(9) This leaves us with samples of between 1006 and 1188 for men and between 817 and 949 for women. Table 2 presents descriptive statistics for our sample. Since our sample restrictions eliminate nearly a third of the original sample, we compare the summary statistics of the excluded workers - found in Appendix 1 - to our final sample of workers.(10) We find no appreciable differences between our sample of workers and the excluded group.

Although the EOPP has more detailed training information than most other data sets, it is useful to examine their validity.(11) In particular, it would be reassuring to know whether our TRAINING INTENSITY variable relates to other variables in our data in ways that conform to our expectations. Our examination of the data reveals that, as expected, TRAINING INTENSITY [TABULAR DATA FOR TABLE 2 OMITTED] is positively correlated with EDUCATION (r = 0.0697), TENURE (r = 0.0571), and JOB COMPLEXITY (r = 0.1094) and negatively correlated with RELATED EXPERIENCE (r = -0.0750) and AGE (r = -0.0568). Moreover, it is worth noting that Lynch (1992) finds a relatively high degree of consistency between the EOPP training data and similar data contained in the National Longitudinal Survey of Youth.

In Table 3, we present, for various ranges of the starting wage, mean levels of training, wage growth, and tenure, as well as the means of some key worker characteristics such as age, education, and experience. On average, men who start work in low-wage jobs are in less complex jobs and are likely to receive fewer hours of training than other workers. Wage growth for men in minimum wage jobs is considerably less than the wage growth of other men. Both more years of education and more years of previous experience are associated with higher starting wages.

Women who start work at the minimum wage also seem to have somewhat slower wage growth than other workers, though the difference is not as pronounced. However, it appears that women who start at the minimum wage are no less likely than other workers to receive training and that they receive no fewer hours of training than other workers. In what follows, we investigate these relationships more fully. Ultimately, we find the patterns suggested by Table 3 to be quite consistent with our overall conclusions.

4. Estimation

Wage Growth Equations

We start our formal analysis by estimating the effect of minimum wages on wage growth. To estimate wage growth, we use a standard human capital specification augmented by both the [TABULAR DATA FOR TABLE 3 OMITTED] starting wage dummy variables and, in some specifications, our direct measure of on-the-job training. There is some controversy in the literature regarding the proper measure of wage growth. Hashimoto (1982) and Lazear and Miller (1981) both use percentage wage growth as their dependent variable. Leighton and Mincer (1981), on the other hand, argue that it is more proper to use absolute wage growth. They give two reasons for this. First, the return to an amount of investment in human capital (in this case, the amount of training) should be measured in dollars rather than in percentages. Second, even if all workers in a sample experienced identical levels of absolute wage growth, those hired at the minimum wage and other low wages would tend to experience the highest percentage gains in the wage. Thus, the use of percentage wage growth on the left-hand side would increase the likelihood of finding a minimum wage effect. The result is that "dollar growth provides a more convincing test of the effect of the minimum wage on wage growth than percentage growth" (Leighton and Mincer 1981, p. 164). In fact, while they concentrate their discussion on the results from estimating absolute wage growth, Leighton and Mincer also estimate models using percentage wage growth as well as models with the current wage as the dependent variable and the starting wage as a control variable. Their conclusions are robust to their measure of wage growth. We also estimate regressions using percentage wage growth and models of the current wage, in levels and logs, on the starting wage, inter alia. As described below, our conclusions are robust to the different specifications.

We focus first on ordinary least squares (OLS) estimates of wage growth regressions omitting TRAINING INTENSITY. This allows us to directly compare our findings to the previous research. Column 1 of Table 4 presents these estimates for the men in our sample. We find that [TABULAR DATA FOR TABLE 4 OMITTED] men in minimum wage jobs experience significantly less wage growth than men in other jobs. Calculated at the means of the sample, the estimates in column 1 suggest that men with starting wages equal to the minimum wage experience 47% lower wage growth than men starting well above the minimum wage. Thus, our findings are in line with Hashimoto (1982) and Leighton and Mincer (1981) rather than Lazear and Miller (1981).

For women (Table 4, column 4), wage growth is significantly lower on all low-wage jobs than on jobs starting well above the minimum wage. With industry and occupation controls included, we estimate that wage growth is about 52% lower for women in MINIMUM WAGE jobs than for women in jobs with starting wages more than 25 cents above the minimum wage. While the point estimates imply that women on minimum wage jobs experience slightly less wage growth than women on other low-wage jobs, the estimated coefficients are not significantly different from one another. Thus, while men in minimum wage jobs seem to have retarded wage growth relative to men in other low-wage jobs, this difference is not apparent for women.

To explore further the relationship between minimum wage legislation and wage growth, we add TRAINING INTENSITY to the specification. One potential problem with OLS estimation of wage growth equations that include on-the-job training as an explanatory variable is that on-the-job training is a choice variable. The training decision is partially due to the employer and partially due to the worker through his/her occupational and other preemployment choices. If, as a result, unmeasured characteristics of jobs or workers associated with the determination of on-the-job training are correlated with our measure of the TRAINING INTENSITY, then the estimated coefficient on the training variable will be biased, as it will be correlated with the error term.(12)

To correct for this potential heterogeneity bias, we estimate our wage growth equations using instruments for TRAINING INTENSITY. These instruments are estimated from each of the Tobit specifications in Table 5 as the expected value of TRAINING INTENSITY conditional on receiving training and are used in the corresponding wage growth equations. Because this instrumental variable estimator is inefficient, we test for the existence of heterogeneity bias using a Hausman (1978) specification test.(13)

While the IV estimates, reported in Appendix 2, show a significant negative effect of MINIMUM WAGE on the wage growth of both men and women, TRAINING INTENSITY is never significant at the 10% level.(14) Moreover, in each case, we fail to reject the null hypothesis of equality between the OLS and IV coefficients. Given the lack of evidence of unobserved heterogeneity in our estimates, we assume from this point on that our sample is homogeneous and we concentrate on the OLS estimates.(15)

[TABULAR DATA FOR TABLE 5 OMITTED]

Columns 2 and 3 of Table 4 present estimates of wage growth equations for men with TRAINING INTENSITY included. On-the-job training is a positive and significant determinant of wage growth. This finding is consistent with the bulk of empirical research on the wage effects of on-the-job training (e.g., Lynch 1992; Booth 1993).(16) The estimates in column 2 imply that every 10% increase in TRAINING INTENSITY is expected to result in a 1.27% increase in wage growth, calculated at the means.

Including TRAINING INTENSITY in the wage growth equation attenuates the estimated effect of minimum wages, though only marginally. Nonetheless, minimum wage jobs continue to exhibit significantly less wage growth than other jobs. The estimates in column 2 suggest that minimum wage jobs experience 37% lower wage growth than jobs starting well above the minimum wage.

For women, the estimated effects of minimum wages on wage growth are essentially unchanged by including TRAINING INTENSITY. The point estimates in column 6 of Table 4 imply that wage growth for women on minimum wage jobs is about 44% lower than for women in jobs starting well above the minimum wage, but once again, the estimated coefficient on MINIMUM WAGE is not significantly different than the coefficients on the other low-wage dummy variables. We find no significant effect of TRAINING INTENSITY on women's wage growth. Apparently, therefore, even if minimum wage legislation reduced women's training opportunities, the estimates from Table 4 suggest that this would not significantly impact women's wage growth.

As stated above, we estimated the wage growth equations using percentage wage growth as well as regressions of the current wage on the starting wage and our other control variables. Appendix 3 presents the estimated coefficients for the starting wage dummy variables from these regressions as well as the F-tests for significant differences between MINIMUM WAGE and the other low-wage dummy variables. As can be seen, these specifications tell essentially the same story as the absolute wage growth regressions reported in Table 4. Namely, minimum wage jobs exhibit significantly less wage growth for men but not for women.(17)

On-the-Job Training

Having established that the minimum wage is indeed associated with reduced wage growth, particularly for men, we now use the direct measures available in the EOPP to determine whether there is also an observable relationship between holding a minimum wage job and the quantity of on-the-job training received. We want to be confident that these estimates focus on the correct question, namely: For otherwise similar jobs, do training and wage growth differ for minimum wage versus nonminimum wage jobs? Failing to control for potential sources of individual-specific heterogeneity may cause our point estimates to be seriously biased. Thus, we make every effort in our estimation to avoid unobserved individual-specific heterogeneity.

It is likely that employers will respond to a minimum wage by hiring better qualified applicants. These workers would need less training since they presumably bring with them human capital obtained in previous jobs. If we did not control for RELATED EXPERIENCE, our estimates could potentially overstate the negative impact of minimum wages on training.

As discussed above, JOB COMPLEXITY is included as a control for labor market attachment. This is an important control if workers in less complex jobs are, on average, more weakly attached to the labor force. If these workers tend to end up in low-paying jobs, then omitting JOB COMPLEXITY would cause the effects of the starting wage dummy variables to be overstated.

To the extent that these variables capture what would otherwise be unobserved worker heterogeneity, omitting them from the training equation would seriously bias our estimated coefficients. Our model, therefore, tests for differences in on-the-job training even when we hold constant prior accumulations of human capital and labor force attachment.

Other variables in the TRAINING INTENSITY regression include human capital variables, EDUCATION, and AGE and firm-specific and position-specific variables, MINIMUM WAGE, BELOW MINIMUM WAGE, JUST ABOVE MINIMUM WAGE, PERMANENT, In(FIRM SIZE), CAPITAL, UNION, WEEKLY HOURS, and JOB TENURE GREATER THAN 3 MONTHS.

Because a substantial portion of our sample received no training, we use Tobit regressions to estimate on-the-job training equations.(18) The estimated equations are reported in Table 5. For men, MINIMUM WAGE is estimated to have a significant negative effect on on-the-job training. Importantly, however, F-tests (reported at the bottom of Table 5) show there is no significant difference between the quantity of on-the-job training received by workers in minimum wage jobs and the amount of training received by workers in other low-paying jobs. Apparently, what we observe is a low-wage effect on on-the-job training rather than just a minimum wage effect. For women, MINIMUM WAGE is estimated to have no effect on TRAINING INTENSITY, even with the occupation and industry control variables omitted.

JOB COMPLEXITY is a significant determinant of training for both men and women, though the magnitude of the effect of JOB COMPLEXITY is considerably larger for women. This is consistent with our interpretation of this variable as a measure of labor force attachment. We expect labor force attachment to be a less important determinant of men's on-the-job training since there is less variability in men's attachment to the labor force. It is worth noting that the women in our sample are represented disproportionately in jobs that are less complex, which is an indication of women's weaker labor force attachment.

Our estimates lead us to tell very different stories about the relationships between minimum wage jobs, on-the-job training, and wage growth for men and for women. For men, it appears that being in a minimum wage job - or in any other low wage job - means that a worker will receive fewer hours of on-the-job training than more highly paid workers and that this leads to lower wage growth since hours of TRAINING INTENSITY is an important determinant of wage growth. Moreover, it appears that, even when the effect of TRAINING INTENSITY on wage growth is accounted for, workers in minimum wage jobs experience slower wage growth than other workers. For women, we find that workers in minimum wage jobs receive as much training as other workers and that, in any event, TRAINING INTENSITY does not influence wage growth.

5. Summary and Conclusions

We find that minimum wage jobs exhibit less wage growth than other jobs. This finding is stronger for men than for women. Our results are consistent with the research of Hashimoto (1982) and Leighton and Mincer (1981). Nonetheless, our conclusions are more in line with Lazear and Miller (1981), that is, we find no evidence of a unique minimum wage effect on training opportunities. The process of wage determination for men appears to be consistent with human capital theory in that on-the-job training has a significant impact on wage growth. However, we find no evidence that training has an impact on women's wages.

Our conclusions suggest that the indirect method of proxying training with wage growth can be misleading, as it fails to distinguish whether the reduced wage growth of workers in minimum wage jobs results from their receiving less training than other low-wage workers or whether it is strictly a result of the wage determination process. Future research should attempt to gauge the determinants of wage growth on the job. In particular, empirical studies into the exact relationship between on-the-job training and wage growth and the causes for gender differences would be valuable.

[TABULAR DATA FOR APPENDIX 1 OMITTED]

[TABULAR DATA FOR APPENDIX 2 OMITTED]

Appendix 3

Minimum Wage Effects Using Alternative Wage Growth Measures (White
standard errors)

Dependent
Variable Men Women

% [Delta] Wage(a) MINIMUM WAGE -0.0169 0.0114
 (-1.253) (-0.702)

 BELOW MINIMUM WAGE 0.0914 0.0291
 (3.164) (1.326)

 JUST ABOVE MINIMUM WAGE 0.0363 0.0008
 (1.774) (0.061)

 F-test: p-value: MINIMUM
 WAGE = BELOW
 MINIMUM WAGE 0.0001 0.0790

 F-test: p-value: MINIMUM
 WAGE = JUST ABOVE
 MINIMUM WAGE 0.0116 0.4772

Current Wage(a) MINIMUM WAGE -32.338 -23.081
 (-4.178) (-2.244)

 BELOW MINIMUM WAGE -5.997 -22.317
 (-0.498) (-2.082)

 JUST ABOVE MINIMUM WAGE -15.289 -20.196
 (-1.398) (-2.581)

 F-test: p-value: MINIMUM
 WAGE = BELOW
 MINIMUM WAGE 0.0135 0.9455

 F-test: p-value: MINIMUM
 WAGE = JUST ABOVE
 MINIMUM WAGE 0.0930 0.7600

ln(Current Wage)(a) MINIMUM WAGE -0.0678 -0.0447
 (-4.658) (-2.461)

 BELOW MINIMUM WAGE 0.0263 -0.0288
 (0.994) (-1.330)

 JUST ABOVE MINIMUM WAGE -0.0138 -0.0290
 (-0.660) (-1.899)

 F-test: p-value: MINIMUM
 WAGE = BELOW
 MINIMUM WAGE 0.0003 0.4640

 F-test: p-value: MINIMUM
 WAGE = JUST ABOVE
 MINIMUM WAGE 0.0096 0.3623

t-statistics are in parentheses.

a The set of control variables is the same as in Table 5 with
starting wage and industry and occupation controls included.

This is a revised version of a paper presented at the Western Economic Association International meetings. The authors wish to thank Mark Schweitzer, William Ferguson, William Boal, two anonymous referees, and the editor for helpful comments on earlier drafts.

1 Note that, in their paper, Lazear and Miller (1981) refer to prepublication versions of both the Hashimoto (1982) and Leighton and Mincer (1981) papers.

2 Survey sites included firms from Alabama, Colorado, Florida, Kentucky, Louisiana, Ohio, Texas, Washington, Wisconsin, and Virginia.

3 On the differences between large and small firms, see inter alia. Brown, Hamilton, and Medoff (1990).

4 The NLS and PSID, by contrast, do not provide information on starting wages.

5 Alternatively, we defined ABOVE MINIMUM WAGE as equal to one if the starting wage was no more the 50 cents above the minimum wage. No conclusions were changed by this alternative definition.

6 We note that this variable has a maximum value of 1200 hours for women and 1400 hours for men, implying a maximum of about 100 hours of training per week for women and 117 hours per week for men during the first three months of employment. We assume that these large values imply that several employees spent time with the trainee simultaneously, though we are still circumspect about their validity. To limit the effect of the few extremely large values of TRAINING INTENSITY on our results, we estimated equations using the full sample and, alternatively, with the sample truncated above 480 hours of training. This truncation eliminates less than 2% of the sample for both women and men and has no effect on our findings.

7 For the largest category, CAPITAL is set equal to $250,000.

8 Thus, the sample consists of workers who started their jobs between 1978 and 1981. The minimum wage was increased in January in each of these years. It was raised to $2.65 from $2.30 in 1978, to $2.90 in 1979, to $3.10 in 1980, and to $3.35 in 1981. Approximately 2% of workers in the sample started their jobs in 1978, 8% in 1979, 17% in 1980, and 73% in 1981.

9 There is one exception: Because of the large numbers of missing values for the variable WEEKLY HOURS, rather than drop observations, we use the modified zero-order regression method described in Maddala (1977); that is, in our regression analysis, we set missing observations on weekly hours to zero and include a dummy variable equal to one if weekly hours is missing and equal zero otherwise.

10 The variables with the most missing observations are STARTING WAGE (286 missing), CURRENT WAGE (307 missing), and TRAINING INTENSITY (363 missing).

11 See Barron, Berger, and Black (1997) for evidence on the validity of data regarding on-the-job training.

12 Another potential problem is that, since the minimum wage was increasing during the period of observation, individuals who were hired at the minimum wage and who were still earning the minimum wage in 1981 (or at the time of separation) may have received wage increases simply because of increases in the minimum wage. In an alternative specification (not presented here), we estimated wage growth equations omitting these individuals. None of our conclusions were affected by this omission.

13 The null hypothesis is that plim([[Beta].sub.OLS] - [[Beta].sub.IV]) = 0, where [[Beta].sub.OLS] and [[Beta].sub.IV] are alternative estimators of the parameter vector [Beta]. Under the null, [[Beta].sub.OLS] is consistent and efficient with asymptotic covariance matrix [V.sub.OLS]. [[Beta].sub.IV], with asymptotic covariance matrix [V.sub.IV], is consistent under both the null and alternative hypotheses, though it is inefficient. The test statistic suggested by Hausman (1978), ([[Beta].sub.OLS] - [[Beta].sub.IV])[prime]([V.sub.IV] - [V.sub.OLS]) 1([[Beta].sub.OLS] - [[Beta].sub.IV]), is asymptotically chi-square with degrees of freedom equal to rank([V.sub.IV] - [V.sub.OLS]).

14 While the wage growth equations omit CAPITAL, AGE, and JOB COMPLEXITY and are aided by the nonlinearity of the estimation procedure for the instruments, we suspect that collinearity between our instruments and the other right-hand side variables may be at least partially responsible for the insignificance of TRAINING INTENSITY.

15 As an alternative check for heterogeneity, we follow Lynch (1992). Booth (1993), and Veum (1995), among others, by using a Heckman correction for self-selection (Heckman 1979). This procedure uses the inverse Mills' ratio from a probit regression estimating the probability of receiving training as a proxy for the unobservables in the subsequent wage growth regression. Our findings using this method are consistent with those discussed above: The inverse Mills' ratio is never significant, which suggests that sample heterogeneity bias is unlikely to affect our estimates.

16 A recent exception to this general conclusion, however, is Levine (1993). who finds no evidence that high returns to tenure are associated with higher than average levels of training.

17 In fact, two of the specifications tell exactly this story. The percentage wage growth equation is a bit different. MINIMUM WAGE in this specification is negative but statistically insignificant. BELOW MINIMUM WAGE and JUST ABOVE MINIMUM WAGE are positive and significant. Nonetheless, F-tests indicate that minimum wage jobs exhibit significantly less wage growth than other low-wage jobs.

18 About 8% of men and 7% of women in our sample received no formal or informal training during their first three months of employment.

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