On-the-job training, establishment size, and firm size: evidence for economies of scale in the production of human capital.

1. Introduction

In an important paper, Oi (1983) argued that the opportunity costs of monitoring employees increase with the value of the entrepreneur's time. If talented entrepreneurs are likely to have larger firms, then the costs of monitoring will increase with firm size. Garen (1985) and Barron, Black, and Loewenstein (1989) also contended that monitoring and evaluation costs rise with firm size, and large firms encounter informational problems not present for small firms. To economize on those monitoring costs, large employers can increase their capital stock, hire more able workers, and increase the on-the-job training of new employees. Barron, Black, and Loewenstein (1987), Hill (1989), Holtman and Idson (1991), and Frazis, Herz, and Horrigan (1995), using a variety of data sources, found that large firms and large establishments provided more training than their smaller counterparts. One explanation for higher levels of training found in large firms is the existence of internal labor markets. Idson (1996) found that larger firms provide employees greater opportunities for intra-firm job mobility. This internal mobility creates a greater expected duration of employment that makes larger firms more willing to provide higher levels of training. Baldwin, Gray, and Johnson (1995) found that, after controlling for technology, there is a negative relationship among training and establishment and firm size. Their findings suggest that the differences in the technology of large and small establishments may explain the differential training that earlier research has found.

In this paper, we argue that firm- and establishment-size differences in training, whether generated from differences in technology or not, result from cost advantages that arise at large firms and establishments. As Brown (1990) indicated in his survey of the literature, large firms appear to provide more training. One reason for this result is the economies-of-scale associated with the provision of formal training. Haber (1988), using SIPP data, found that employees of firms with at least 100 workers were about twice as likely to receive formal training as their smaller firm counterparts. Dunne and Schmitz (1995) examined whether plants that employ advanced technology require a skilled workforce. They hypothesize that because there are large fixed costs involved in using some advanced technologies, larger establishments will make greater use of these technologies. Dunne and Schmitz did find evidence that large plants are more likely to use advanced technologies than smaller plants. Because larger plants do use more advanced technology, it is likely that these plants will require training to use the technology. The cost advantages that arise in large establishments in the use of advanced technologies are similar to the cost advantages that arise in the provision of formal training. In both cases, larger firms are more able to spread these fixed costs across more output or more employees. Indeed, it is likely such cost advantages are reinforcing.

Another explanation for the difference in the provision of training is that larger employers have a greater opportunity to provide informal training through coworkers. Barron, Black, and Loewenstein (1987, 1989) found that larger firms have a higher probability of providing training through coworkers than their small firm counterparts. Because large firms are likely to have several workers performing the same job, they are more able to substitute relatively inexpensive coworker training for relatively expensive managerial training. In this case, coworkers are able to provide informal training to the newly hired worker. In smaller firms, the new worker may be the only employee assigned to that particular job. In that event, management must provide training. This scenario also suggests higher levels of training for large firm employees due to the greater opportunity to offer informal coworker training.

Because formal training programs will generally involve a considerable investment to set up the program, large firms and establishments have a cost advantage in the provision of the training. They are able to spread the fixed costs of these formal training programs over the greater numbers of workers that enter their training programs. For informal training, large establishments are more likely to have experienced workers who are already performing this task. Larger establishments may use these experienced workers to train newly hired workers, whereas smaller establishments may have to rely on management to provide the training to newly hired workers. If the opportunity cost of managers is higher than that of coworkers, then informal costs may be higher at smaller establishments. Because the cost of training is lower in large firms and establishments, they may adopt technologies that require more training; this allows workers at large firms and establishments to accumulate more human capital. Because human capital increases the productivity of employees, the lower training costs provide large establishments and firms with an inherent economy of scale in the production process.

Brown and Medoff (1989) examined several explanations for the positive relationship between employer size and wages. Although worker quality, working conditions, and other factors accounted for some of the firm-size wage differential, a large portion of the wage premium for employees of large firms still remained. Evans and Leighton (1989), Idson and Feaster (1990), Kruse (1991), Reilly (1993), and Even and Macpherson (1994) all observed that larger firms tend to pay higher wages even after controlling for worker heterogeneity. We contend that at least some of this observed difference in wages can be explained by the cost advantages with regard to training experienced by larger employers. We hypothesize that larger firms provide more training because these firms experience lower per unit costs of formal training due to the large number of new employees that enter the training programs. Larger firms also may experience lower informal training costs if they can substitute coworkers for managers when providing informal training. If larger firms do provide more training as a result of cost advantages, workers in these firms should have steeper wage profiles because of relatively larger increases in human capital (productivity). Holtman and Idson (1995) suggested that large firms have more information regarding the value of training because of better screening and the existence of internal labor markets. This asymmetric information essentially results in specific training. If firms bear a greater portion of specific training costs, this implies that large firms will have flatter wage profiles for a given level of training. The larger volumes of training that large firms provide, however, may result in steeper wage profiles despite the specificity of training. Thus, even after controlling for differing worker characteristics, the worker with more training, at the larger firm, will have higher wages. This is one possible explanation for the observed wage rate-firm size relationship found in the literature.

This paper examines the effects of firm and establishment size on training outcomes using a unique data set. In addition, we examine whether the training cost advantages of large firms result in steeper wage profiles. In the next section, we present a simple model to illustrate that lower per unit costs of formal training may be responsible for differences in training across establishments and firms of different sizes. In section 3, we discuss the data we use in this paper and present the results of our analysis, and section 4 offers some conclusions.

2. A Model of Training Cost Differences Across Firm and Establishment Sizes

Consider a firm or establishment that provides on-the-job training to newly hired employees. The cost of this training can be divided into two components, formal training and informal training. The cost of formal training is

[C.sub.FT] = A + BN,

where A is the fixed cost component of formal training, B is the variable cost component, and N is the number of workers to be trained. The component A reflects the necessary resource expenditure to establish the formal training program; B reflects the marginal cost of running the program including instructors' salaries, the trainees' salaries, and supplies. Similarly, we can define the costs of informal training as

[C.sub.IT] = DN,

where D denotes the variable cost component, including instructor's salary and the trainee's salary. We assume that there are no fixed costs associated with informal training, but we need only require that the fixed cost of informal training be lower than that of formal training and that the marginal cost of formal training be lower than the marginal cost of informal training.

Now suppose we have two firms of different sizes. Firm 1 is large and makes relatively more new hires than Firm 2, which is relatively small. Assuming that the two firms have access to identical training technologies, that is, [A.sub.1] = [A.sub.2] = A, [B.sub.1] = [B.sub.2] = B, and [D.sub.1] = [D.sub.2] = D, the larger firm will be able to provide formal training at a lower average cost because [N.sub.1] [greater than] [N.sub.2].

[Mathematical Expression Omitted],

If [N.sub.1] is greater than [N.sub.2], the average cost of formal training will be lower for Firm 1:

[Mathematical Expression Omitted].

The greater number of employees receiving training in a larger firm or establishment helps generate lower average costs of formal training by reducing the average fixed cost component of formal training. As a result, economies of scale can allow relatively larger firms and establishments to provide more formal training. Indeed, smaller organizations may not be able to provide formal training. In addition, lower average costs of formal training may suggest that small establishments or plants that are part of a larger firm may be able to send new employees off-site to a company-wide formal training program.

Larger firms and establishments may also have a cost advantage in the provision of some types of informal training. For instance, large firms and establishments may use coworkers instead of managers to provide this informal training. If the value of a coworker's time is less than that of a manager, then larger firms that have multiple workers performing the same job can generate a cost advantage in the provision of informal training. In this case the larger firm or establishment has the option of using coworkers instead of managers to train newly hired employees. If we refer to the cost of informal training equation, firms that use coworkers to train will have lower variable training costs because the manager's time is more valuable than that of the coworker. In this case, Firm 1, the larger firm that uses coworkers to provide informal training, will have a lower variable cost component for informal training. In this case [D.sub.1] [less than] [D.sub.2], and larger firms also will have lower cost with respect to informal coworker training.

The above examples suggest that larger firms and establishments can spread the fixed cost component of formal training across more newly hired employees. As a result, these firms and establishments have an inherent economy of scale advantage in the provision of formal training. In addition, large firms and establishments may have a cost advantage in the provision of some forms of informal training. Large establishments may be able to provide informal training using coworkers, whereas small establishments may not have coworkers to provide this training. These per unit cost advantages in the provision of training allow large firms and establishments to provide greater amounts of both formal and informal training.

3. The Results

Data Description

In this paper we use the 1992 Small Business Administration (SBA) Survey. The SBA commissioned the University of Kentucky to conduct a study of the recent training experiences of establishments. The survey asked the number of hours per week and the number of weeks of training for five types of training: formal training provided on-site; formal training provided off-site; informal management-provided training; informal coworker provided training; and informal training by watching others. In Table 1, we provide an exact statement of the questions asked.

Survey Sampling of Fairfield, Connecticut, drew a stratified random sample of 3600 establishments from their Comprehensive Business Database. Because the SBA wanted a comparison of the training activities of large and small establishments, we over-sampled large establishments to ensure that a sufficient number of large establishments were included in our sample to achieve statistically meaningful comparisons between large and small establishments. We stratified the sample by establishment size in the following manner: 1250 establishments with 0-19 employees, 1250 establishments with 20-99 employees, 550 establishments with 100-499 employees, and 550 establishments with 500 or more employees. Excluded were Agriculture, Forestry, and Fisheries (SIC 0-99) and Public Administration (SIC 900 and above). Except for these exclusions, we sampled establishments randomly within each size stratum, providing a representative distribution by industry and region.

The Survey Research Center (SRC) at the University of Kentucky conducted the survey in the summer of 1992. SRC first sent a letter to each establishment describing the survey. SRC tracked down the undeliverable letters using directory assistance and attempted to contact each of the 3600 establishments for a telephone interview. Of the original sample of 3600 establishments, 2561 were eligible to complete an interview. The 1039 ineligible establishments were out of business, had disconnected phones, did not answer in any of 15 attempts, could not be reached because of Hurricane Andrew, had no employees, or had other miscellaneous problems. We had 1288 establishments complete the survey. The 1273 noncompletions consisted of refusals, those who reported that answering surveys was against company policy, those who stated that the appropriate person was unavailable, and those who rescheduled the interview six or more times, which we believed to be implicit refusals. Barron, Berger, and Black (1997) provide a more detailed description of the data.

In Table 2, we provide the descriptive statistics for the sample used in this paper. We use only data elements collected in the SBA survey. The first variables are measures of hours per week of training by type. The second set of variables are measures of the number of weeks of training by type, and the third set of variables measure the fraction of training hours spent on each training type. Formal training accounts for about 21% of all hours of training. For formal training, on-site is about four times as great as off-site, regardless of the measure of training. [TABULAR DATA FOR TABLE 2 OMITTED] The data also show that among informal training, informal management is the most prevalent method.

The mean establishment size is 193 workers, and the average firm size is 1441 workers. The large difference is due to establishments that are plants or branches of large firms. Nearly 60% of the firms in the survey operate at more than one location. The establishment size variable is heavily skewed to the right. The median establishment size is 28 workers, and only 20% of the establishments employ at least 200 workers. The same is true of the firm size variable; only about 25% of the firms employ more than 1500 workers. Workers from the sample typically work 36.6 hours per week. The survey also indicates whether multiple employees were hired for the same position. Nearly 22% of all workers were hired at the same time as another worker(s). About 10% of the workers are union members. In addition, 13% of the workers are employed by not-for-profit organizations. Less than 20% of not-for-profit employees are union members.

In the regression analysis that follows, we consider three types of measures of training. First, we examine the hours per week that training is offered. This provides us with a measure of the intensity of training. Second, we examine the duration of each type of training in weeks. Thus, we can examine two margins on which firms might differ in their training behavior: intensity and duration. Finally, we examine the fraction of total training that each component of training provides. This allows us to focus on how the shares of training differ across firm sizes and to ignore variations in the total quantity of training.

For each measure of training, we estimate a model of the form

y = X[Beta] + [Epsilon], (1)

where y is the dependent variable (some measure of training), X is vector of covariates, [Beta] is a set of parameters to be estimated, and [Epsilon] is a disturbance term. For covariates we use the logarithm of the size of the establishment, the logarithm of the size of the firm, the number of hours worked that the position usually requires, a variable that indicates whether or not the position is covered by a union contract, a dummy variable indicating that multiple workers were hired at the time the position was filled, and a dummy variable indicating whether the firm is a not-for-profit concern.(1) Finally, we include a set of one-digit industry dummy variables, although their inclusion does not change the parameter estimates of other coefficients very much.(2) In addition, we also experimented with the use of a set of worker characteristics as additional covariates. These variables, however, did not materially affect the results of interest so we do not include these controls in the regressions presented in this paper.(3)

The inclusion of the controls for multiple hires is meant to account for demands on management time, although undoubtedly this outcome is correlated with establishment size.(4) Firms confronting a union may face much different incentives in the provision of training, although again it is likely that the union status is not independent of firm size. Not-for-profit firms may face much different incentives for training their workforces than for-profit firms.(5)

Intensity of Training: Hours per Week by Type

In Table 3, we present Tobit estimates for the number of hours per week of training for the five types of training. We use the Tobit model because there are numerous observations where training hours per week is reported to be zero. An increase in the size of the establishment increases training hours for all three measures of informal training, although the coefficient for the watching others equation is not statistically significant. The estimates suggest that, evaluated at the sample mean, a 10% increase in the size of the establishment would increase hours of informal management training by 2.5% and hours of informal coworker training by 2.7%. [TABULAR DATA FOR TABLE 3 OMITTED] Establishment size also has a positive impact on hours of formal on-site training, but it has a negative impact on formal off-site training. Interestingly, large firms provide more of both on-and off-site formal training. The reason for this difference appears to be that small establishments that belong to larger firms exploit the economies of scale by sending their employees to other sites within the firm to be trained. As the number of employees at a particular location rises, the establishment provides more of its training at the location.(6) Again evaluated at the mean, a 10% increase in the size of the establishment would reduce the number of hours of off-site training by 0.1% and increase formal on-site training by 3.7%.

Consistent with the economies-of-scale hypothesis, changes in firm size increase both types of formal training. The firm-size parameter estimates for both on-site and off-site training are positive and statistically significant. A 10% increase in firm size increases the hours per week of formal off-site training by 0.6%. The sign of firm size for off-site formal training supports previous research (e.g., Baldwin, Gray, and Johnson, 1995) that suggests larger firms will provide training elsewhere in the firm or from outside training sources. Also, a 10% increase in the size of the firm increases the number of hours of formal on-site training by 1.3%. Interestingly, there is an insignificant relationship between firm size and informal management training and only weak evidence that large firms use more coworker training and training by watching others. Because there are many large firms that consist of several small establishments, this result is not surprising. Large firms consisting of small establishments will not have as many managers and coworkers to provide informal training. Thus, any advantages in the provision of informal training by larger firms seemed to arise only at larger establishments.

Another variable that provides insight on the economies-of-scale issue is whether additional hires were made in the same position at the same time besides the individual observed. Multiple hires would lead to lower fixed costs per worker inasmuch as there are fixed costs associated with training. Fixed costs would more likely be associated with formal training, and we do find that multiple hires result in increased amounts of on-site formal training. Multiple hires also increase training time spent on informal coworker training and watching coworkers. When multiple workers are hired, firms provide less informal management training.

The other variables in the equation provide few surprises. The number of hours worked per week generally increases the quantity of training. This is to be expected. An individual working more hours provides the firm more work-time to recoup the firm's expenditure on training. The presence of a collective bargaining agreement does not have a significant impact on an individual's level of training. It is interesting to note, however, that the signs of the coefficients are positive for formal training measures and negative for informal measures. Nonprofit organizations do not train differently than a for-profit firm with regard to hours with one exception, off-site formal training.

The results of this Tobit model indicate that larger employers do train newly hired employees for a greater number of hours. This is particularly true for formal training, but it is also accurate for measures of informal training such as coworker training.

Duration of Training: Weeks of Training by Type

When deciding to offer a fixed number of hours of training, the firm can choose to train the worker more during a given week, changing the intensity of training, or the firm can reduce the intensity of training and increase the number of weeks of training that is provided. In this section, we examine how firm and establishment size affects the duration of training.

Training can be thought of in a hazard model framework. In this case we have a spell of training in which the number of weeks of training is the dependent variable. Han and Hausman (1990) developed a flexible parametric duration model that is based on an ordered logit model. Following Han and Hausman, the hazard function, the failure rate of time [Tau] conditional upon survival to time [Tau], is

[Mathematical Expression Omitted]. (2)

In words, the hazard function is the likelihood that a particular type of training will end in week [[Tau].sub.i] + 1, given that training had occurred until week t. Because Han and Hausman treated the logarithm of the integrated baseline hazards as constants in each period, the baseline hazards are estimated along with the parameters [Beta]. This allows estimation of all parameters simultaneously. If we let the indicator variable, [y.sub.it], equal one if failure (end of training) occurs in period t for worker i, and [y.sub.it] = 0 otherwise, the log-likelihood function takes the following form

[Mathematical Expression Omitted]. (3)

If the distribution of [Epsilon] is an extreme value distribution, the likelihood function is of an "ordered" logit form (Han and Hausman, 1990). Using the SBA data, the weeks of training are censored at 12 weeks. In this case, a term is added to the log-likelihood function specifying the cumulative probability of still receiving training beyond 12 weeks.

In Table 4, we present ordered logit estimates for an individual receiving each of the five measures of training where the dependent variables are the number of weeks of each type of training. Establishment size is correlated with longer spells of informal coworker training. Thus, larger establishments provide more coworker training by increasing both the intensity (hours per week) and duration (weeks) of training. There is also evidence that for on-site formal training, larger establishments train more intensively and provide training for a longer duration, although the duration result is significant only at the 10% (two-tailed) level. Finally, there is strong evidence that larger establishments offer off-site training less intensively and for a shorter duration. Again, this is consistent with the notion that small establishments that belong to larger firms exploit the economies of scale by sending their employees to other sites within the firm to be trained. As the number of employees at a particular location rises, however, the establishment provides more of its formal training at the location.

In contrast, larger firms offer both on-site and off-site training for longer durations than do smaller firms. There is some weaker evidence, with the estimated coefficients significant at 10%, that larger firms also provide coworker training and training by watching others for a longer duration. As is the case for training intensity, measured by hours per week, larger firms and establishments consistently provide more formal training in terms of duration, measured by number of weeks. Not only do these firms offer more formal training, they provide more informal training in many cases.

[TABULAR DATA FOR TABLE 4 OMITTED]

Again, the other covariates provide few surprises. The presence of additional people hired for the same type job once again increases the length of formal on-site training spells. The longer workweek, the longer the employee will be trained. Not-for-profit firms appear to offer informal management and informal coworker training for a longer duration. Interestingly, the presence of a collective bargaining agreement increases the duration of both measures of formal training, but there is no significant relationship among union status and the informal training measures. When we specify union firms as for-profit or not-for-profit, we find that both types of union firms provide more off-site formal training, whereas only for-profit union firms provide more on-site formal training than for-profit non-union firms. Similarly, both union and nonunion not-for-profit firms provide more informal management training.

Mix of Training: Fraction of Training Provided by Each Type of Training

Another training measure is the proportion of each type of training as a fraction of total training. In this manner we can see a firm's method of training response to different firm characteristics. By focusing on the fraction of training that each type provides, we can abstract from the differences in the quantity of training among firms and look at how the relative use of each type of training differs among firms. This approach allows us to see most clearly how the relative costs of training affect the mix of training. Thus, the question to be addressed in this section is how employer size affects the optimal composition of training methods, regardless of how much an employer trains its workforce.

In Table 5, we present double-limit Tobit estimates in which the dependent variables are the specific type of training as a fraction of the total training hours per week. Establishment size has a positive impact on the fraction of training that is formal on-site and informal coworker. Larger establishments, however, have lower fractions of formal off-site and informal management training. This suggests the mix of training is different for larger establishments, relatively more formal training occurs on-site and coworkers provide more informal training. For firm size, we find that the composition of training tends to be more in the form of formal training, both on- and off-site, for larger firms. Thus, it appears that, when holding the size of establishment is held constant, larger firms provide relatively more of their training from sources outside the firm or elsewhere from other sites within the firm. Moreover, the fraction of informal management training also falls as firm size increases.

The results of the other covariates are consistent with our earlier findings. The more hours worked per week, the presence of multiple hires at the time of hire, and the presence of a collective bargaining agreement all result in a training composition that is relatively more formal.

These results for the mix of training also seem to confirm the hypothesis that larger establishments and firms have a cost advantage in the provision of training. We specifically find that in situations where economies of scale are likely present with regard to training, for example in large firms or firms making multiples hires, the training mix is skewed toward more formal methods. These results also present an interesting relationship between establishment size and the mix of training: large establishments tend to substitute away from informal management training and into informal coworker and formal on-site training. This supports the contention that because a manager's time is more valuable than a coworker's time, larger establishments choose to train using coworker training. Smaller establishments do not have this option. This creates an informal training cost advantage for larger employers.

[TABULAR DATA FOR TABLE 5 OMITTED]

Implications for Wage Profiles

If larger firms have a comparative advantage in the provision of training, one would expect that the jobs larger firms offer should have steeper wage profiles. Large firms, with lower costs of providing training, should offer their workers more training, which should steepen their wage profiles. Importantly, this increase is independent of the specificity of the training and is simply the result of the cost advantage that large firms have in the production of human capital.

Because the SBA data are taken from a sample of newly hired workers, they provide little information about earnings-tenure profiles. Therefore, to get some idea about how earnings-tenure profiles differ by firm size, we use the Current Population Survey (CPS). In April of 1993, the Bureau of the Census conducted a Survey of Employee Benefits as a supplement to that month's CPS. Half of the April sample was eligible for the survey, resulting in a sample size of approximately 27,000. From the regular monthly survey we have measures of personal characteristics such as age, sex, race, marital status, veteran status, and education. Importantly, the supplement also provides measures of firm size. For the respondents to the April supplement, income and earnings data from the March 1993 CPS were merged to produce an April-March match for 1993. There were 27,268 valid responses to the April supplement. We excluded data with the following characteristics: workers aged less than 18 or greater than 64 (N = 1154), full-time students (N = 817), workers who did not work any weeks last year (N = 1539), no previous year earnings (N = 1676), missing observations on tenure (N = 1209), or missing firm size (N = 415). We also limited our analysis to workers with tenure of 30 years or less; this excluded 318 workers. Finally, because the earnings were with respect to the previous calendar year, we excluded everyone with less than one year of tenure at the firm because their earnings would not have been made at the firm (N = 3222). With these exclusions, we have a sample of 8844 males and 8190 females.

We used three categories of firm-size variables: less than 50 workers, 50-499 workers, and 500 and more workers. We estimated separate earnings equations for each of the firm size categories and for gender. For the smallest firms, we have samples of 2672 males and 2290 females. For firm with 50 to 499 workers, we have 1916 males and 1840 females, and for the largest firms, we have 4257 males and 4060 females. The form of the equation we estimate is

ln([y.sub.i]) = [X.sub.i][Beta] + [[Epsilon].sub.i], (4)

where [y.sub.i] is the ith worker's weekly earnings, [X.sub.i] is a vector of covariates, [Beta] is a corresponding vector of parameters to be estimated, and [[Epsilon].sub.i] is an error term. Our covariates include a quartic in age, an indicator for whether the worker is black, an indicator for whether the worker is not white or black, an indicator for whether the worker is not married, the number of children the worker has, and indicators for whether the worker has not completed high school, had attended college but had no degrees, had an associate degree, had a bachelors degree, or had a graduate degree.(7) We also include a control for the number of weeks worked last year Finally, we include a quartic in tenure.

By estimating separate equations for each firm-size category for both males and females, we allow every coefficient to vary with the firm size and gender. In Figure 1, we depict the relative wage-tenure profiles for the three categories of firm size for men. Although wage growth at the smallest firms does exceed wage growth at firms with 50 to 500 employees, wage growth at the largest firms is substantially higher than wage growth at smaller firms. In Figure 2, we depict the relative wage-tenure profiles for the three categories of firm size for women. For women, the growth rate of wages increases as firm size grows. The differences are substantial. For men, after 10 years on the job at a small firm wages would be about 23% above those at entry; at a large firm, after 10 years on the job wages would be about 36% above those at entry. For women, the differential in wage growth is even more pronounced. After 10 years on the job at a small establishment wages would be about 17% above those at entry; at a large firm, after 10 years on the job wages would be about 32% above those at entry.

As another way of judging the magnitude of the impact, we can pool the data across firm-size categories and reestimate Equation 2 with controls for firm size. In columns 1 and 3 of Table 6, we report the results of this estimation for male and female workers. For both men and women, wages increase with size of the firm. The estimates in columns 1 and 3 represent average wage premiums across all levels of tenure. To see how much the tenure differentials contribute to the average wage premiums, in columns 2 and 4 we add complete firm-size/tenure interaction and reestimate the model. With full firm-size/tenure interaction, the interpretation of the firm-size variables is the wage premium paid to a worker with 1 year of tenure. Thus, the ratio of the firm-size variables with and without the firm-size/tenure interactions provides an indication of how much the differential returns to tenure contribute to the average wage premium that larger firms pay. For instance, for men at firms with 50-499 workers, this ratio is 1.067, indicating that controlling for tenure increases the magnitude of the wage difference. For men at firms with 500 or more workers, however, this ratio is only 0.556. Thus, the differential returns to tenure explain about 44.4% of the average wage differential.

Similarly, for women at firms with 50-499 workers, the ratio of the coefficients is 0.713, which suggests that differential returns to tenure explain about 28.7% of the wage differential. For women at firms with at least 500 workers, the ratio is 0.587, which suggests that the differential returns to tenure explain about 41.3% of the wage differential. Moreover, for both men and women, we reject the model with a constant wage differential at better than a 1% confidence level. Thus, differences in the returns to tenure appear to explain a good bit of the firm-size wage differential, especially for workers at the largest firms.

Workers at large firms appear to have steeper wage profiles.(8) This is broadly consistent with our findings that large firms have a cost advantage in the production of training. Of course, there are reasons other than training for wages to slope upward. For instance, an entire literature has evolved from Lazear's (1981) work that suggests increasing wage profiles may represent a solution to agency problems. Obviously, agency problems may differ by firm size, and differences in agency problems may explain the differences in the returns to tenure. Similarly, another literature has evolved around the job matching literature that Jovanovic (1979) and Johnson (1978) initiated, and matching may differ by firm size. Nevertheless, these findings are broadly [TABULAR DATA FOR TABLE 6 OMITTED] consistent, with differences in the accumulation of human capital explaining a good bit of the firm-size earnings differential.

4. Conclusion

Regardless of the type of model of training measure implemented, intensity, duration, or mix, it appears that larger establishments and firms do indeed provide more formal training. Large establishments tend to provide more on-site training and less off-site training, whereas large firms generally provide more of both on- and off-site formal training. Consistent with our expectations, small firms are found more likely to train on the plant floor. Larger firms are more likely to train elsewhere in the firm or purchase outside training courses. Our finding that small establishments that are part of large firms tend to provide more formal off-site training also supports this view. In addition, larger firms tend to provide informal training through the use of coworkers rather than managers. Other studies indicate that the lower cost of coworkers' time might be only one reason that larger firms are more likely to use coworkers as a source of training. Troske (1997) found that more skilled workers tend to work together and that wages are highly related to the skill of other workers in the plant. Evidence from Dunne and Schmitz (1995) suggests that large employers tend to hire more skilled workers. If larger employers have more skilled coworkers who are relatively better at providing informal training than coworkers at small firms, these large firms will be more able to provide informal coworker training.

The cost of training advantages for large firms appear to be reflected in higher earnings-tenure profiles of large employees. This may be one explanation for the observed earnings-firm size relationship often found in related literature. The differences in human capital accumulation as a result of training economies of scale could be a substantial factor in explaining the existence of a positive wage rate and firm size relationship.

Table 1. Training Questions, 1992 SBA Survey

61. Is there formal training, such as self-paced learning programs or training done by specially trained personnel inside or outside the firm, for people hired in (NAME's) position, or is all the training done as informal on the job training?

1. formal training

2. all informal training

62. During the first 3 months of work what was the total number of weeks and hours per week (NAME) spent at on-site formal training such as self-paced learning programs or training or classes given by specially trained personnel?

63. During the first 3 months of work, how many weeks and hours per week did (NAME) spend on off-site formal training programs?

64. The next set of questions are about informal training provided to (NAME) by management, supervisors, and coworkers. During the first 3 months of work, what was the total number of weeks and hours per week that management and supervisors spent away from other activities giving informal individualized training or extra supervision to (NAME)?

65. During the first 3 months of work, what was the total number of weeks and hours per week that coworkers who are not supervisors spent away from their normal work giving informal individualized training or extra supervision to (NAME)?

66. During the first 3 months of work, what was the total number of weeks and hours per week that (NAME) spent observing coworkers in order to learn skills required for (his/her) position?

We thank Amitabh Chandra, John Garen, and two anonymous referees for helpful comments. D.A.B. thanks the Heinz School at Carnegie Mellon University for financial support.

1 The final estimations include the logarithm of firm size and the logarithm of establishment size as measures of employer size. Equations were also estimated including the logarithm of the number of employees at other establishments as a covariate instead of the logarithm of firm size. These estimations yielded results virtually identical to estimations presented in this paper.

2 For this reason, as well as for reasons of space, we do not report these results in the tables.

3 The worker characteristic variables include age, education, ethnicity, experience, and gender. These variables are not part of our final regressions for two reasons. First, their inclusion does not affect the other coefficients in the equation, and few of the results are systematic or significant. Only the education variable was consistently significant (positive). This is not surprising if education is a signal of capacity to learn. Second, and perhaps more importantly, inclusion of these worker characteristics may result in an endogeneity problem. Unlike, say, the NLSY, the SBA is a sample of newly hired workers. Because the firm gets to select the worker who will fill a position, it would not be appropriate to treat the worker's education level as exogenous to the firm's training decision. It seems likely that a firm would want to fill a position that would require a good bit of training with an educated worker. Thus, it is possible that education level does not cause more training, but that training causes more educated workers to be hired.

4 As an alternative measure of the demands on managers' time, we also estimated each of the equations including a variable measuring the ratio of new hires to the establishment size, where establishment size is a proxy for the number of managers at the establishment. Under this specification, we do not find that employers with a higher proportion of new hires tend to provide less informal management and more informal coworker training. The lack of similar results under this specification may have occurred because only about 20% of employers hired multiple workers.

5 We also disaggregate the union and not-for-profit dummy variables in an alternative specification. This creates dummy variables indicating whether the firm is either nonunion/not-for-profit, union/for-profit, union, or non-union/for profit. The last firm type is the omitted condition. Although this specification does not change the results, we include a discussion of significant impacts of the disaggregation in the text. In general, a union firm displayed the same training tendencies regardless of whether it was a for-profit or not-for-profit firm. Similarly, not-for-profit firms obtained similar estimates regardless of union status.

6 Haber (1988) found that larger firms are more likely to train on-site and less likely to train off-site. This suggests that small firms provide more general training and large firms provide more specific training. However, Haber did not examine both firm and establishment size. We find that large firms provide more of both on- and off-site formal training, but large establishments provide more on-site formal training and less off-site formal training. These results can be reconciled if it is the case that several small establishments are part of larger firms. Undoubtedly this is the case, considering the difference between mean establishment size (193) and firm size (1441). In this case, small establishments can be sending employees off-site for specific training at other locations within the firm.

7 Murphy and Welch (1990) suggest that a quartic in potential experience (age - 6 - education) describes the empirical distribution of the earnings-experience profile quite well.

8 This result differs from that reported by Brown and Medoff (1989), who found little evidence that employees in larger firms have steeper wage profiles. Brown and Medoff, however, used a tenure-firm size interaction; we estimate a separate equation for each firm-size category. In addition, we use a quartic in tenure to trace out the wage-tenure profile, and it appears that Brown and Medoff used a quadratic. Given the nonlinear relationship depicted in our Figures 1 and 2, the added flexibility may account for the difference. To test this possibility, we reestimated our model pooling the workers and used a quadratic in tenure. For both men and women, we reject the hypothesis that firm-size-tenure interactions may be constrained to be zero. Finally, Brown and Medoff (1989) used the 1979 CPS, whereas we use the 1993 CPS. If larger firms in 1993 are using relatively more advanced technologies that require more training than they were in 1979, we may observe a larger difference in the wage profiles between the two survey dates.

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