The impact of minimum wages on job training: an empirical exploration with establishment data.

Pedace, Roberto

1. Introduction

Human capital theory suggests that workers must contribute toward investments in job training and that one way in which they might do so is through reduced wages (Becker 1964). Minimum wage laws might be expected to reduce on-the-job training, then, to the extent they prevent workers from accepting lower wages (Rosen 1972). (1) Existing empirical studies of the relationship between minimum wages and job training yield divergent results. However, most of these studies utilize worker survey data that lack detailed measures of job training and establishment-level variables that are important determinants of training. In this paper, we overcome these problems by using an establishment data set that possesses both good measures of job training and good establishment-level control variables. The decision to offer training is ultimately made by the firm. Even if workers pay for some or all of their training through the acceptance of lower wages, their decision to undertake training is made largely by the choice of which firm to join. Thus, we believe the firm is the logical unit of analysis for exploring the issue of job training and minimum wages.

In the first section of the paper, we review the empirical literature on the impact of minimum wages on job training. The second and third sections discuss the empirical specification and data to be used in the analysis. The fourth section discusses the empirical results. We find little evidence linking minimum wages to reductions in the percentage of the establishment workforce receiving training and absolutely no evidence linking them to reduced hours of training per trained worker.

2. Review of the Literature

The empirical literature on the impact of minimum wages on job training is not voluminous. The earliest efforts focused primarily on wage growth as a proxy for training, producing mixed results. Two studies found age-earnings profiles to be significantly flatter for workers whose wages were bound to the minimum (Leighton and Mincer 1981; Hashimoto 1982), while a third study (Lazear and Miller 1981) found no statistically significant relationship between minimum wages and the slope of age-earnings profiles. Recent evidence has cast serious doubt on the validity of this entire approach.

Grossberg and Sicilian (1999) find that while minimum wages are indeed associated with reduced wage growth, they appear to have no significant impact on job training. Acemoglu and Pischke (1999) offer an insightful interpretation of these results. They claim that minimum wages eliminate part of the lower tail of the wage distribution, bunching workers around the wage minimum and thereby lowering the age-earnings profile quite independently of their impact on training. Thus, it seems clear that valid tests of the relationship between minimum wages and job training must be conducted with information on worker training and not simply wage growth.

There are only five empirical studies offering evidence on the impact of minimum wages directly on job training. The basic approach is to regress a measure of job training on a set of explanatory variables and a variable capturing the degree to which minimum wages act as a constraint on wage reductions. The hypothesis is that the more binding the minimum wage constraint, the less job training the worker and firm will undertake. There exist two levels of analysis in the literature, one operating at the state or regional level and the other operating at the level of the individual worker. Both have flaws.

Leighton and Mincer (1981) and Neumark and Wascher (2001) exploit variation in state wage minimums to explore the relationship between minimum wages and training. Both use data on individual workers, but their measures of the minimum wage exist at the state level. For example, Neumark and Wascher use the extent to which the state minimum wage exceeded the federal minimum over the previous three years. The results of both studies suggest that the higher the state minimum wage, the less likely it is that workers will receive on-the-job training.

However, there are several econometric problems plaguing this approach. First, these studies use state-level measures of minimum wages with individual-level data. Because the minimum wage variable exists at a higher level of aggregation than the unit of observation, the estimated standard error may understate the inaccuracy of the estimated coefficient (Moulton 1986), leading the researcher to perhaps mistakenly conclude that minimum wages reduce training when in fact they do not. A second concern is that the minimum wage variable may capture unobserved state effects on training that are correlated with minimum wages. (2)

Another approach to analyzing the impact of minimum wages on job training utilizes individual-level data only. Schiller (1994) and Grossberg and Sicilian (1999) adopt measures of the degree to which wages are bound by the minimum wage that vary at the level of the individual worker. Grossberg and Sicilian, for example, compare the impact on training of workers who are paid the minimum wage with those who earn both below the minimum and slightly more than the minimum. Schiller finds evidence that minimum wages reduce training, whereas Grossberg and Sicilian do not.

The problem with using minimum wage measures that vary at the level of the individual worker is that omitted determinants of training are likely to be correlated with the wage, which itself is used to assess the degree to which the minimum wage is binding. The estimated impact of minimum wages on training may well be biased as a result, the nature of the bias depending on the exact specification employed. For example, while it is possible that binding minimum wages reduce training, it is most probable that job training raises wages and thereby makes workers' wages less bound by the minimum wage. The wage component of the minimum wage measure is, therefore, likely to be correlated with left-out determinants of training, biasing the estimated impact of minimum wages on training. And here, the bias is likely to be upward. (3)

Acemoglu and Pischke (1999) conduct a first-difference analysis of the individual worker training equation using panel data. Fixed components of the error term will be eliminated in this approach, thereby reducing the possible bias found in cross-sectional levels regressions. Acemoglu and Pischke find no evidence of a training effect of minimum wages in their results. However, their measure of on-the-job training is also a particularly blunt one--namely, the change in whether the worker received job training at the current firm.

Indeed, poor measures of job training plague this literature more generally. Probably the most common measure of training is a dichotomous variable indicating its existence or lack thereof. An important exception is the Grossberg and Sicilian (1999) study, which utilizes data from establishments. The job training information they use refers to the amount of job training given to the last-hired worker. Specifically, their training measure is the number of hours devoted to training over the first three months of tenure of the most recently hired worker. However, Grossberg and Sicilian are unable to account for many important establishment-level determinants of training.

In this paper, we utilize a unique data set on establishments that offers an interesting alternative to the data used in most of the existing literature. First, we have good measures of job training--the percentage of the workforce receiving training and the average hours of training conditional on receiving training. Second, we possess good measures of a number of establishment-level control variables, including labor turnover and employee fringe benefits levels, that are absent from most existing studies.

Efficiency wage theory suggests that firms may reduce costly turnover by paying higher wages (Akerlof and Yellen 1986). Thus, wages (and therefore the extent to which wages are bound by the minimum wage) may be negatively correlated with turnover. But turnover reduction may also be a prerequisite for on-the-job training (Prendergast 1993) and so an important determinant in the training equation. If turnover is related to both the measure of the minimum wage and to job training in the way we have claimed, the failure to control for turnover may bias upward the estimated impact of minimum wages on training. It is important to control for fringe benefits in an analysis of the minimum wage impact on training because training could be financed by accepting lower benefits levels rather than by accepting lower wages.

Economies of scale in training and a host of other considerations suggest to us that job training is likely to exist as a matter of policy at the establishment or firm level, thereby making the establishment the appropriate unit of analysis for any investigation of job training. Workers receive training by virtue of the firm to which they attach themselves. Focusing on the determinants of training solely from the worker's point of view might make sense in a world of costless mobility, where the public-good nature of training poses no real problem for individual choice (Tiebout 1956). However, the very mention of job training typically suggests a context in which there is greater attachment between worker and firm than ideal microeconomics models posit and therefore in which firm policy and firm-level variables matter.

3. Econometric Specification

The empirical approach we take resembles that of the existing literature, but we use two different measures of job training and incorporate a wide range of establishment-level control variables into the analysis. We begin with a simple training equation of the following form:

(1) [t.sub.js] = [alpha] + [x'.sub.js][beta] + [m.sub.s][psi] + [[epsilon].sub.js]

where [t.sub.js] is a measure of the job training provided by establishment j in state s, [x.sub.js] is a vector of establishment characteristics (e.g., industry, workforee size, percentage of female workers, percentage of workers with a high school diploma, turnover, fringe benefits, and so on), and [m.sub.s] is the difference between the state minimum wage and the federal minimum wage. (4)

In order to employ this measure of the minimum wage, we identify states with minimum wages above the federal minimum and assign to establishments in those states the value of the difference between the state and federal minimums; all remaining establishments receive a zero for this variable. In this specification, the minimum wage variable is measured at a higher level of aggregation (the state level) than is the unit of observation (the establishment level). Under such circumstances, the standard assumption of uncorrelated errors across the observations is violated, and the error structure will have the following form:

(2) [[epsilon].sub.js] = [[lambda].sub.s] + [[phi].sub.js]

This may lead to possible downward bias in the standard errors of the estimated minimum wage effect, thereby allowing one to mistakenly find in favor of a statistically significant effect on training when no such effect exists. We therefore correct, in all of our results here, the standard errors for this "clustering" of observations at the state level using the technique recommended by Moulton (1986).

Another concern with this approach is that the minimum wage measure may capture state effects on training that are correlated with minimum wages. Suppose, for example, that states with higher minimum wages also possess policies--such as training subsidies or employment programs that yield better job matches--that lead to greater incentives for training by firms. In this case, the absence of state controls will tend to result in an underestimation of the negative effect of minimum wages on training.

To address this concern, we estimate the training equation utilizing a difference-in-difference estimation technique, similar to that of Neumark and Wascher (2001), that allows for the inclusion of state controls. Thus, the training equation becomes

(3) [t.sub.ijs] = [alpha] + [x'.sub.js][beta] + [s'.sub.s][gamma] + [d'.sub.ijs][delta] + [i'.sub.ijs][psi] + [[epsilon].sub.ijs]

where [t.sub.ijs] is a measure of training for occupation group i at establishment j in state s, [x.sub.js] is a vector of establishment characteristics as in Equation 1, [s.sub.s] is a vector of state dummy variables, [d.sub.ijs] is a vector of dummy variables representing the occupation from which the observation was drawn, and [i.sub.ijs] is a vector of interactions between the occupation dummies and the minimum wage measure used in Equation 1. Assuming that the training of managerial workers is unlikely to be affected by the minimum wage, they can be used as the base category in the vector of interactions. Controlling for state fixed effects, the causal effect of the minimum wage is captured by [psi], which reports the differential impact of the minimum wage on occupational categories that are more likely to be affected relative to an occupational category--namely, managerial workers--that is unlikely to be affected.

One drawback to this approach is that it assumes that the unobservables--state policy, for example--that are correlated with both the minimum wage and training have the same effect on all the occupational estimates of the minimum wage impact on training. This might be a quite restrictive assumption given that states with high minimum wages are also arguably more likely to possess active labor market policies that disproportionately affect the training needs of low-skill workers. In addition, we must also restrict all the establishment characteristics to have the same effect on training for all occupational groups.

Another drawback, one that the difference-in-difference approach shares with the specification in Equation 1, is that the minimum wage variable is a rather blunt measure of the extent to which minimum wages are binding on establishments. This measure varies only at the state level and indeed only among those states with minimum wages greater than the federal minimum.

Thus, in a final specification of the training equation, we utilize a measure of minimum wages that operates at the establishment and occupation level rather than the state level. This training equation is as follows:

(4) [t.sub.ijs] = [[alpha].sub.i] + [x'.sub.js][[beta].sub.i] + [s'.sub.s][[gamma].sub.i] + [m.sub.s]/[w.sub.ijs] [[psi].sub.i] + [[epsilon].sub.ijs]

where [t.sub.ijs] is a measure of training for occupation group i at establishment j in state s, [x.sub.js] is a vector of establishment characteristics as in Equations 1 and 3, [s.sub.s] is a vector of state dummies as in Equation 3, [m.sub.s] is the applicable state minimum wage, and [w.sub.ijs] is the average wage for the occupation in each establishment. (5) The i subscripts on the parameters indicate that the training equation is estimated individually for each occupational category.

This approach identifies the minimum wage impact on training by exploring whether establishments whose average establishment or occupation wage is closer to the state minimum wage offer less training. Unfortunately, this approach raises a number of challenging specification issues. Most important, it is plagued by the presence of the establishment wage on the right-hand side of the training equation. While the extent of job training may be related to how bound wages are to the minimum wage, it is also true that training affects wages. Thus, left-out determinants of training may be correlated with the establishment average wage. Where necessary, then, we must correct for endogeneity bias by instrumenting the average wage variable, raising all the attendant problems and pitfalls such a correction entails.

A final concern we have with all the estimated training equations stems from the high incidence of censoring among the establishment responses to the survey questions on training. Roughly 17% of the establishments in our sample report that they offer no training at all to their workers, and approximately 16% report that they train all their workers. This clustering of values for the dependent variable raises the possibility of censored regression bias in our results. To correct for this, we estimate both training equations with a Tobit maximum likelihood estimation technique and report these results as well. (6) The "hours of training" regressions are estimated with lower-limit censoring, and the "percentage trained" regressions are estimated with both lower- and upper-limit censoring.

4. Data

This study utilizes the 1997 National Employer Survey (NES), supplemented with Standard Statistical Establishment List (SSEL) data. The SSEL is the U.S. Census Bureau's master list of all establishments and enterprises in the United States. It provides the sampling frame for the Census Bureau's economic censuses and surveys, including the NES. We use the SSEL to establish the geographical location of firms in our survey, without which we would be unable to assign the relevant minimum wage level to each surveyed firm. The 1995 SSEL serves as the sampling frame for the 1997 NES.

Survey data were collected with a computer-assisted telephone interview (CATI). The sample was evenly divided between manufacturers and nonmanufacturers, with explicit oversampling of establishments that have 100 or more employees and implicit oversampling of manufacturers because they are greatly outnumbered by nonmanufacturers in the SSEL universe. Establishments in California, Kentucky, Maryland, Michigan, and Pennsylvania were also oversampled in order to support in-depth analysis of school reforms of interest to the survey sponsors (the National Center for Postsecondary Improvement, the Consortium for Policy Research in Education, and the National School-to-Work Office).

The survey was administered by the Census Bureau in the summer of 1997 and asked establishments about conditions in 1996. (7) It represents the responses of approximately 5400 establishments for a 78% overall response rate. This is higher than the response rate for other establishment surveys but is similar to that of the 1994 NES (Lynch and Black 1998). After deleting observations with missing values on the variables of interest, we were left with 1098 valid observations. All our descriptive statistics and regression results are calculated from this sample of firms. The presence of oversampled establishments requires the use of the provided weights in order to produce representative statistics and parameter estimates. Table 1 displays the minimum wage in cases where the state minimum exceeded the federal minimum. Table 2A provides descriptive statistics for the variables used in the analysis.

While previous studies often rely on dichotomous measures of training (e.g., whether the individual received training), the NES offers two detailed measures of job training: the "percentage of workers trained" and the "average number of hours devoted to training" in the establishment. The survey questions regarding job training begin with the following statement:

 I am now going to ask you some questions about structured or formal
 training that your employees experience. This training may be
 offered at your establishment or at another location, and may occur
 during working hours or at other times. Structured training includes
 all types of training activities that have a pre-defined objective.
 Examples of structured or formal training include seminars,
 lectures, workshops, audio-visual presentations, apprenticeships,
 and structured on-the-job training.

This is followed by specific questions regarding training:

 In the past year, how many workers received formal instruction, and
 what was the approximate average number of hours of training per
 employee?

The responses to this question are used to construct our dependent training measures.

Tables 2B and 2C provide descriptive measures of training by occupation and firm size, respectively. (8) While the support staff in the average establishment receives markedly less training than do supervisors, in general there is less variation across occupational categories in both the percentage of workers trained and the average hours of training than was expected. Training investments vary by establishment size in the expected way--namely, there exists more training in larger establishments.

The data set contains measures of labor turnover and a host of other variables that affect the firm's decision to offer training. Some, such as the gender and racial composition and average level of schooling of the workforce, mirror the kinds of variables one finds in estimated training regressions using worker-level survey data. Others, such as the quality of the local high school, are important worker-related determinants of job training that are rarely found in individual survey data. (9) And still others, such as whether the establishment has recently increased employment or is experimenting with new forms of workplace organization (e.g., self-managed teams or job rotation), are establishment-level variables that clearly impact training but are virtually impossible to obtain from worker survey data.

5. Results

In Table 3, we present the results of ordinary least squares (OLS) training regressions using the specification in Equation 1. (10) In Table 4, the results from the difference-in-difference specification in Equation 3 are presented, with managerial workers as the base occupation. The estimated coefficients for the various control variables are omitted in order to conserve space (see the Appendix for estimated coefficients of the other explanatory variables from the column 1, Table 4, results).

The results in the first row of column 1, Table 3, suggest that establishments in states with minimum wages that exceed the federal minimum train a smaller percentage of their workforce. The estimated effect is not only statistically significant but quantitatively significant as well. A 50-cent increase in the state minimum wage, holding the federal minimum wage constant, reduces the fraction of workers receiving training by over 15 percentage points. Evaluated at the mean, this translates into roughly a 25% reduction in the fraction of workers receiving training.

In the first row of column 2, we present the results for the "average hours of training" regression. In this regression, the estimated coefficient on the minimum wage variable is not statistically significantly different from zero. Thus, while minimum wages reduce the percentage of the workforce receiving training in this specification, they appear to have no impact on the average hours of training among trained employees.

Greater insight into these results may be achieved through an analysis of the job training impact of minimum wages on specific occupational groups. In the column 2 results, although average hours of training for the trained workforce as a whole do not appear to change in response to the minimum wage, it is possible that some occupational groups receive fewer hours of training while other occupational groups receive more hours of training as the minimum wage becomes more binding in a plant. This is entirely consistent with theory, which predicts that, in response to a minimum wage, employers may upgrade their technology of production and invest greater amounts of job training in fewer, more highly skilled workers. The lost training for those low-skilled workers who are finance constrained by the existence of minimum wages are merely transferred to more highly skilled, less-finance-constrained workers. While our occupational categories are rather broad and so may disguise training substitution effects of this sort within occupations, we find no evidence in the occupation-specific results of column 2 to suggest that some workers receive greater training as the result of more binding minimum wages.

Turning to the column 1 results, we see that the reduction in the percentage of workers trained as a result of greater minimum wages takes place across the occupational distribution: among frontline workers and technical workers but also among management, the highest paid of the occupational categories. Because we expect that minimum wages are unlikely to affect the training of managerial workers, this finding seems to us an indication that the results of this specification are tainted by omitted-variable bias.

In Table 4 we present the results of the difference-in-difference approach, which, because it focuses on relative training effects, allows us to net out the effect of unobservables that may be producing bias in the results of Table 3 by adding state effects. The results from column 1 of Table 4 suggest that the relative percentage of workers trained is not affected for any of the included occupational groups by a difference between the state and the federal minimum wage. In column 2, the results are presented for the "average hours of training" regression. In this regression, the estimated relative minimum wage effects are also insignificantly different from zero, and the quantitative impacts on training are extremely small. Possessing a state minimum wage that is higher than the federal minimum by 50 cents decreases the training of frontline workers relative to managers by roughly one percentage point.

While none of the estimated coefficients in Table 4 is statistically significant, the alternating negative/positive pattern is interesting and perhaps suggestive of substitution effects of the minimum wage on training. Interestingly, the alternating positive/negative pattern is exactly the opposite in the "percentage trained" and "average hours of training" regressions, which suggests that when the minimum wage causes firms to train fewer workers, firms increase the average hours of training of those workers who continue to receive training.

Ultimately, though, these results suggest that minimum wages have absolutely no effect on either the extensive (percentage of workers trained) or the intensive (hours of training per trained employee) margins. Thus, the difference-in-difference results offer considerable evidence to suggest that the Table 3 results are biased.

The integrity of the difference-in-difference results rests on the assumption that unobservables such as state policy affect the impact of minimum wages on training similarly for every occupational group. However, there are reasons to believe this assumption may be in error, suggesting that we attempt to identify the minimum wage impact on training separately for each occupation. Moreover, both the difference-in-difference specification and the simple state-level specification of Equation 1 utilize a minimum wage measure that is especially blunt in that it varies at the state level only and indeed only for states that have enacted a minimum wage higher than the federal minimum.

The results reported in Table 5 utilize an alternative minimum wage variable, one that measures the extent to which state minimum wages are binding for workers in a given firm and occupation and that incorporates state fixed effects whose impacts vary across occupational categories. The challenge posed by estimating this specification of the training equation is that the average wage variable must be instrumented in order to avoid endogeneity bias. We have used the "percentage of workers unionized" and the "natural log of total sales" in the establishment as identifying variables in this instrumental variables (IV) procedure. While unions affect wages and thereby training levels indirectly, they seldom have direct effects on training through collective bargaining agreements. Higher sales may affect wages through rent sharing but should not affect training directly.

Results from Generalized Method of Moments specification tests suggest that these are indeed valid identifying variables in the overall system of structural equations (Hausman 1978; Newey 1985). They are statistically significant determinants of average wages across establishments but have no independent effect on training other than through their impact on average wages. We have utilized the instrumental variables procedure only when a Hausman test revealed statistically significant evidence of endogeneity bias in the OLS regression results. (11)

The results in column 1 indicate that there are negative minimum wage effects on training for the workforce as a whole and that these negative effects are restricted to two of the occupational groups. Specifically, support staff and supervisory workers appear to witness statistically significant reductions in the percentage of workers trained as a result of higher minimum wages. A 50-cent increase in the minimum wage, ceteris paribus, reduces the fraction of support staff and supervisory workers receiving training by roughly eight and three percentage points, respectively. Evaluated at the mean, this translates into a 15% reduction for support staff workers and a 5% reduction for supervisory workers. The results in column 2 lend support to earlier findings suggesting that minimum wages have no effect on the hours that workers are trained.

The largest of the estimated minimum wage effects on training is for support staff workers, which is consistent with their economic position in the firm. Of the five occupational categories that can be identified with our data, this occupation has the lowest average wage and therefore should be most bound by the minimum wage. However, the negative estimated effect for supervisory workers, although smaller, is not as easily explained. The average wage of supervisory workers is significantly larger than that of either support staff or frontline workers.

While we believe this specification has several virtues that the other specifications lack, we are also less than fully satisfied with the IV procedures employed and with the robustness of our findings. The establishment unionization rate, for example, is an important determinant of frontline or technical workers' pay but less so of manager or supervisor pay, yet the minimum wage bindingness variable exhibited no signs of endogeneity bias in either of the former two occupational training regressions but did so in the supervisor training regression.

More important, the only two instances in which we find evidence of a negative training effect of minimum wages among the occupation regressions are the two cases in which Hausman tests revealed the need for an IV procedure. The OLS estimated coefficients on the bindingness variables in these two cases are far from statistically significant, and their magnitudes are smaller by 10-fold than the IV results. While we have followed strict statistical procedures in arriving at these estimates, the dramatic change in magnitudes when IVs are used, coupled with the fact that negative and statistically significant training effects are found only in those instances where instrumental variables are employed, leaves us with some concern for the integrity of these results.

In Tables 6 and 7, we replicate the regressions of Tables 4 and 5 but correct for the censored nature of the dependent variable using a Tobit estimation procedure. (12) Qualitatively, the results are entirely consistent with the regressions that ignore the censored nature of the dependent variable. As in Table 4, the Table 6 results suggest that minimum wages do not alter the percentage of the establishment workforce receiving training or the hours of training per employee. (13)

For the Table 7 regressions, in cases where the average wage must be instrumented, the nonlinear nature of the Tobit estimates requires that we give special attention to the standard errors. There are two instances where a two-stage estimation is required--the "percentage trained" regressions for support staff and supervisory workers. Murphy and Topel (1985) define a covariance matrix for the nonlinear least squares estimator that accounts for the variability in the explanatory variable that is introduced through the two-step procedure. (14) However, our first-stage regressions are used to obtain predicted values for the average establishment wage, which are then used to construct our establishment-level minimum wage measure. Consequently, the Murphy-Topel correction is not directly applicable in this case. In the two instances in which we utilize a two-stage Tobit estimation, we account for the variation in the first stage and correct the standard errors using a bootstrap procedure. This has been shown to produce reliable standard error estimates when these cannot be derived analytically (Johnston and DiNardo 1997). (15)

Nevertheless, we continue to find statistically significant negative minimum wage effects for support staff and supervisory workers. Moreover, quantitatively, the estimated impacts of minimum wages on training using the Tobit specification are larger. In the Table 5 results, for example, a 50-cent difference between the state and federal minimum wages reduces the fraction of support staff workers receiving training by eight percentage points. This compares with a 17-percentage-point reduction in Table 7. Once again, there are no significant minimum wage effects on hours of training. (16)

6. Conclusions

This study utilizes establishment-level data to explore the impact of minimum wages on job training. The decision to offer training ultimately rests with firms, and so we believe the firm is the logical unit of analysis for exploring this issue. Using establishment data provides the opportunity to control for establishment-level variables, such as turnover and the provision of fringe benefits, which have been absent from previous analyses of training because of the reliance on individual worker data.

In our view, problematic specification issues plague all existing approaches to the estimation of the impact of minimum wages on job training, ours included. Nonetheless, one finding that is consistent across all specifications of the training equation is that minimum wage policies have no significant impact on the average hours of training for workers who receive training. The evidence on whether minimum wages reduce the percentage of the workforce receiving training is more mixed. Among occupations for which it is plausible to expect a negative minimum wage impact on training, only support staff workers exhibited such an effect, and only in one of the three specifications of the training equation we estimated. Therefore, we think the most prudent conclusion to draw from this set of findings is that there is little evidence to suggest that minimum wages affect the percentage of the workforce receiving training.

Appendix
OLS Coefficient Estimates for "Percentage Trained" Regression of
Equation 3

 Standard
Variable Estimate Error

Employment and sales
 50-99 employees -1.5261 2.7524
 100-249 employees -0.0845 2.8994
 250-999 employees 0.7913 3.2128
 1000 or more employees 11.3054 3.7528
 Multiple-establishment firm 6.7397 2.0466
 Employment increased in past three years 3.4842 1.9556
 Employment decreased in past three years 8.3347 3.1884
 Turnover rate -0.1212 0.0423

Workforce characteristics
 % 18+ with a high school diploma 1.8782 0.3428
 18+ with a bachelors degree 1.1346 0.3512
 Number of permanent part-time workers -0.0244 0.0025
 Number of temporary workers 0.0047 0.0087
 % of female workers 0.1829 0.0561
 % of minority workers -0.0350 0.0498
 % of frontline workers 0.1094 0.1129
 % of support staff workers 0.2222 0.1397
 of technician workers 0.1455 0.1272
 % of supervisory workers -0.1280 0.2258
 Quality of local high school unacceptable -9.6451 7.4622
 Quality of local high school barely acceptable 26.5028 4.6127
 Quality of local high school acceptable 10.7400 3.9521
 Quality of local high school more than adequate 12.2541 4.1207
 Quality of local high school outstanding -2.4334 6.4764

Workplace organization
 % of nonmanagement in self-managed teams 0.2791 0.0315
 % of nonsupervisors in job rotation 0.0400 0.0346

Benefits
 Establishment contributes to pension or
 severance 6.8975 2.4343
 Establishment contributes to medical or dental -32.4541 11.9500
 Establishment contributes to child care or
 family leave 13.6998 2.1177
 Establishment contributes to life insurance 5.5753 4.3566
 Establishment contributes to sick pay or
 vacation -4.8653 7.4043

Occupation dummies
 Front line 0.4813 3.7696
 Support staff -5.1791 3.2538
 Technical 9.4531 4.1630
 Supervisory 3.0989 3.7876

This table excludes industry and state dummies.

Table 1. States with Minimum Wages That Exceeded the Federal
Minimum Wage

 Minimum Wage in 1996 Weighted Gap

Federal 4.25/4.75
Alaska 4.75 0.375
Connecticut 4.27 0.000
Delaware 4.65 0.275
District of Columbia 5.25 0.875
Hawaii 5.25 0.875
Iowa 4.65 0.275
New Jersey 5.05 0.675
Oregon 4.75 0.375
Rhode Island 4.45 0.075
Vermont 4.75 0.375
Washington 4.90 0.525

In 1996, the federal minimum wage was not implemented until
October 1. All other minimum wages were implemented at the beginning
of the calendar year. The minimum wage gaps are calculated using a
weighted average of the federal minimum wage (i.e., $4.375).

Table 2A. Descriptive Statistics for the Explanatory Variables

 Standard
Variable Mean Deviation

Employment and sales
 50-99 employees 0.1430 0.3502
 100-249 employees 0.2240 0.4171
 250-999 employees 0.3752 0.4844
 1000 or more employees 0.1494 0.3566
 Multiple-establishment firm 0.7031 0.4571
 Employment increased in past three years 0.4827 0.4999
 Employment decreased in past three years 0.2140 0.4103
 Turnover rate 19.0276 185.7143
 Average number of weeks to fill a position 3.3342 3.0289
 Natural log of total sales 17.4848 1.7816

Region
 Establishment located in West 0.1639 0.3704
 Establishment located in Midwest 0.2996 0.4583
 Establishment located in South 0.3770 0.4849

Workforce characteristics
 % 18+ with a high school diploma 31.2046 6.5922
 % 18+ with a bachelor's degree 12.5718 4.9626
 Number of permanent part-time workers 25.8315 143.4752
 Number of temporary workers 18.1521 105.4377
 % of female workers 38.5591 23.5415
 % of minority workers 25.9598 24.3694
 % of frontline workers 58.6984 23.9328
 % of support staff workers 12.7694 12.4860
 % of technician workers 10.5807 12.9012
 of supervisory workers 7.6821 5.0851
 % of nonsupervisors unionized 23.2995 37.6262
 Quality of local high school unacceptable 0.0219 0.1463
 Quality of local high school barely acceptable 0.1658 0.3720
 Quality of local high school acceptable 0.5692 0.4954
 Quality of local high school more than adequate 0.1821 0.3861
 Quality of local high school outstanding 0.0146 0.1199

Workplace organization
 % of nonmanagement in self-managed teams 17.7716 29.5405
 % of nonsupervisors in job rotation 22.4222 30.6450

Benefits
 Establishment contributes to pension or severance 0.8707 0.3357
 Establishment contributes to medical or dental 0.9927 0.0851
 Establishment contributes to child care or
 family leave 0.7514 0.4324
 Establishment contributes to life insurance 0.9517 0.2144
 Establishment contributes to sick pay or vacation 0.9945 0.0738

Minimum wage
 State minimum wage 4.4115 0.1381
 State minimum wage minus federal minimum wage 0.0365 0.1381

This table includes all the explanatory variables in the regressions
except the categorical industry and the establishment-and
occupation-specific minimum wage variables.

Table 2B. Descriptive Statistics for Training and Wage Variables
by Occupation

Variable Mean Standard Deviation

All
 % of workers receiving training 58.0761 36.9062
 Average number of hours trained 27.6146 43.8773
 Average wage 14.1039 4.2221

Front line
 % of workers receiving training 59.2058 40.8478
 Average number of hours trained 28.1876 48.9843
 Average wage 12.7150 7.2125

Support staff
 % of workers receiving training 54.2217 39.3727
 Average number of hours trained 20.4044 30.1949
 Average wage 12.2880 3.5758

Technical
 % of workers receiving training 61.7915 39.5289
 Average number of hours trained 30.9882 48.9026
 Average wage 16.0765 4.9419

Supervisory
 % of workers receiving training 65.0735 39.9918
 Average number of hours trained 27.5455 38.1044
 Average wage 16.7594 4.8256

Managerial
 % of workers receiving training 59.8867 40.1285
 Average number of hours trained 27.8470 49.2504
 Average wage 23.1587 7.8222

Table 2C. Descriptive Statistics for Training and Wage Variables
by Firm Size

Variable Mean Standard Deviation

1-49 employees
 % of workers receiving training 48.8899 42.3634
 Average number of hours trained 27.2904 72.7526
 Average wage 14.6345 4.2177

50-99 employees
 %o f workers receiving training 44.3509 39.6647
 Average number of hours trained 18.1832 24.6551
 Average wage 13.6102 3.6745

100-249 employees
 % of workers receiving training 55.2653 37.2239
 Average number of hours trained 25.0227 31.8413
 Average wage 13.6613 4.3466

250-999 employees
 % of workers receiving training 63.6000 33.9529
 Average number of hours trained 31.3155 43.2826
 Average wage 13.7479 3.9130

1000+ employees
 % of workers receiving training 68.2201 30.6076
 Average number of hours trained 31.4688 46.3714
 Average wage 15.7495 4.8356

Table 3. The Effect of Minimum Wages on Percentage of Workers
Trained and Hours of Training Using a State-Level Minimum Wage
Measure

 Dependent Variable: Average Hours
 Percentage of of Training
Occupational Group Workers Trained per Worker

All
 Estimate -33.2047 -6.4543
 Standard error (11.9402) (12.3958)
 [R.sup.2] 0.4296 0.1924

Front line
 Estimate -38.5873 -6.1059
 Standard error (13.5612) (14.3963)
 [R.sup.2] 0.4153 0.1985

Support staff
 Estimate -11.3607 -14.5429
 Standard error (12.1278) (10.9801)
 [R.sup.2] 0.4161 0.2447

Technical
 Estimate -40.0778 -0.0762
 Standard error (15.2753) (15.3427)
 [R.sup.2] 0.3602 0.1691

Supervisory
 Estimate -19.8936 -9.2563
 Standard error (13.0260) (9.0628)
 [R.sup.2] 0.4138 0.2027

Managerial
 Estimate -28.6259 -3.6990
 Standard error (13.2516) (8.4537)
 [R.sup.2] 0.3958 0.2288

The sample size is 1098 for all regressions. All equations include
the remaining variables in the table of descriptive statistics in
addition to 20 industry dummies. Standard errors, which are adjusted
for state group effects, are in parentheses.

Table 4. Difference-in-Difference Estimates of the Effects of
Minimum Wages on the Percentage of Workers Trained and Hours of
Training

 Dependent Variable: Average Hours
 Percentage of of Training
Occupational Group Workers Trained per Worker

Front line
 Estimate -2.342 0.2407
 Standard error (14.9700) (13.1012)

Support staff
 Estimate 6.5899 -4.7185
 Standard error (15.4666) (9.8664)

Technical
 Estimate -12.5184 8.7051
 Standard error (15.4672) (14.1721)

Supervisory
 Estimate 6.4784 -1.4752
 Standard error (16.3385) (9.3511)

[R.sup.2] 0.4338 0.2143
Hausman-Wu 0.29 0.50

The base category is managerial workers. All equations include the
remaining variables in the table of descriptive statistics in
addition to 20 industry dummies and state fixed effects. Standard
errors, which are adjusted for group effects, are in parentheses.

Table 5. The Effect of Minimum Wages on Percentage of Workers Trained
and Hours of Training Using Establishment- and Occupation-Level
Minimum Wage Measures

 Dependent Variable: Average Hours
 Percentage of of Training
Occupational Group Workers Trained per Worker

All
 Estimate -41.0771 10.7036
 Standard error (22.9898) (43.4677)
 [R.sup.2] 0.5336 0.2649
 Hausman-Wu 2.01 0.01

Front line
 Estimate -7.1464 -19.5497
 Standard error (16.6077) (14.8701)
 [R.sup.2] 0.5390 0.2805
 Hausman-Wu 1.68 0.96

Support staff
 Estimate -211.4745 10.7424
 Standard error (58.2997) (21.3342)
 Corrected standard error (77.1454)
 [R.sup.2] 0.5197 0.3945
 Hausman-Wu 3.63 ** 0.40

Technical
 Estimate 7.2278 22.7799
 Standard error (27.0670) (31.5805)
 [R.sup.2] 0.4720 0.2253
 Hausman-Wu 0.63 1.78

Supervisory
 Estimate -117.636 71.2078
 Standard error (50.4879) (41.4297)
 Corrected standard error (58.8394)
 [R.sup.2] 0.5449 0.2848
 Hausman-Wu 2.34 * 1.37

Managerial
 Estimate -1.5424 50.9651
 Standard error (29.6088) (36.1476)
 [R.sup.2] 0.5451 0.2806
 Hausman-Wu 0.97 0.07

All equations include the remaining variables in the table of
descriptive statistics in addition to 20 industry dummies and state
fixed effects. Standard errors, which are adjusted for state group
effects, are in parentheses. * and ** indicate that the Hausman-Wu
test statistic is large enough to reject the null hypothesis of
exogeneity at the 5% and 1% level of significance, respectively.
In those cases, the two-stage results are reported.

Table 6. Tobit Difference-in-Difference Estimates of the Effects of
Minimum Wages on the Percentage of Workers Trained and Hours of
Training

 Dependent Variable: Average Hours
 Percentage of of Training
Occupational Group Workers Trained per Worker

Front line
 Estimate -12.5407 0.4814
 Standard error (39.5420) (18.7843)

Support staff
 Estimate 6.4306 -5.7485
 Standard error (42.4360) (15.5504)

Technical
 Estimate -35.4213 10.3315
 Standard error (43.2113) (19.2656)

Supervisory
 Estimate 16.1544 -1.6631
 Standard error (46.4181) (15.3457)

[PHI](t/[sigma]) 0.7764 0.7224
Wald chi-squared 605.36 622.63

The base category is managerial workers. All equations include the
remaining variables in the table of descriptive statistics in addition
to 20 industry dummies and state fixed effects. Standard errors, which
are adjusted for group effects, are in parentheses. The degrees of
freedom for the Wald chi-squared statistics are 61 for the percentage
of workers trained regression and 104 for the average hours of training
per worker regression.

Table 7. Tobit Estimates of the Effect of Minimum Wages on Percentage
of Workers Trained and Hours of Training Using Establishment- and
Occupation-Level Minimum Wage Measure

 Dependent Variable: Average Hours
 Percentage of of Training
Occupational Group Workers Trained per Worker

All
 Estimate -95.6686 -10.0012
 Standard error (40.7012) (61.1640)
 Wald chi-squared 898.99 572.79
 [PHI](t/[sigma]) 0.9049 0.7291
 N left-censored 189 189
 N right-censored 172 0

Front line
 Estimate -24.7889 -26.5001
 Standard error (38.1088) (20.8376)
 Wald chi-squared 369.25 694.70
 [PHI](t/[sigma]) 0.8289 0.7357
 N left-censored 189 189
 N right-censored 423 0

Support staff
 Estimate -531.507 11.1665
 Standard error (133.4764) (29.3706)
 Corrected standard error (174.2821)
 Wald chi-squared 466.90 2528.92
 [PHI](t/[sigma]) 0.8238 0.7157
 N left-censored 189 189
 N right-censored 340 0

Technical
 Estimate -34.7793 32.1258
 Standard error (90.7214) (43.1963)
 Wald chi-squared 22.84 193.62
 [PHI](t/[sigma]) 0.7324 0.7054
 N left-censored 189 189
 N right-censored 430 0

Supervisory
 Estimate -281.2885 94.8657
 Standard error (141.6928) (53.5086)
 Corrected standard error (180.6712)
 Wald chi-squared 257.30 357.38
 [PHI](t/[sigma]) 0.8106 0.7486
 N left-censored 189 189
 N right-censored 491 0

Managerial
 Estimate -36.1474 45.3279
 Standard error (121.9013) (44.2573)
 Wald chi-squared 223.60 196.23
 [PHI](t/[sigma]) 0.8289 0.7454
 N left-censored 189 189
 N right-censored 399 0

All equations include the remaining variables in the table of
descriptive statistics in addition to 20 industry dummies and state
fixed effects. Standard errors, which are adjusted for state group
effects. are in parentheses. The degrees of freedom for the Wald
chi-squared statistics are 54 for the percentage of workers trained
regression and 95 for the average hours of training per worker
regression.

The authors thank Bill Carter, David Merrell, Mark Mildorf, Arnie Reznek, and Mary Streitlwieser for their help in acquiring and creating the data. Robert Breunig, Craig Gundersen, David Neumark, Paul Sicilian, Jeffrey Wooldridge, participants of the Claremont McKenna College and UC-Riverside seminar series, and two anonymous referees provided valuable comments and suggestions on previous drafts of this paper. Financial support was provided by the UC Institute for Labor and Employment. The data used are confidential under Title 13 and 26, United States Code. Access was obtained through the Center for Economic Studies (CES) at the U.S. Census Bureau. Researchers can access this version of the National Employer Survey with a CES-approved proposal (see hup://www.ces.census.gov/ces.php/home). A public-use version of the data is available (see http://www.irhe.upenn.edu/research/research-main.html). The findings and opinions expressed do not reflect the position of the institutions represented by the authors, the National Center for Postsecondary Improvement, the Consortium for Policy Research in Education. the National School-to-Work Office, or the U.S. Census Bureau.

(1) Workers and employers are likely to share in the costs of training, but the relative contributions depend on the type of training acquired. Typically, workers' relative contributions will be greater with general training because the rewards to these skills can be reaped with numerous employers. Firm-specific training, on the other hand, usually requires a smaller relative investment from workers. Minimum wages should therefore have a larger effect on general training, where the cost/wage contributions by workers are the greatest.

(2) Neumark and Wascher (2001) use a difference-in-difference approach that allows them to add state controls. We employ this technique in some of our empirical results later and discuss more fully at that time our concerns with this specification of the training equation. (3) The Grossberg and Sicilian (1999) results are not subject to this type of bias because they use the starting wage of the worker.

(4) Aside from the minimum wage measure, the specification of the training equation closely resembles that of Lynch and Black (1998), who utilize an earlier version of the NES data.

(5) Acemoglu and Pischke (1999) construct a similar variable that measures the ratio of the minimum wage to the average wage in the MSA (Metropolitan Statistical Area). However, since wages can vary considerably within MSAs, even less aggregation may be appropriate. We construct a minimum wage measure that captures the extent to which workers in given occupational groups are, on average, bound by the minimum wage at their place of employment.

(6) Papke and Wooldridge (1996) suggest the use of a quasi-maximum likelihood logit estimator (QMLE) for fractional response-dependent variables. In the case of our "percentage trained" variable, both the Tobit and QMLE provide different but reasonable functional forms for the conditional mean. The advantage of the QMLE is that it requires specification only of the conditional mean, while the Tobit requires the specification of the entire distribution and, therefore, relies heavily on the normality (and joint normality) assumptions. The Tobit estimates can be sensitive to specification, but the QMLE provides consistent estimates even in the presence of functional form misspecification (Papke and Wooldridge 1996; Johnston and DiNardo 1997). We check the robustness of our Tobit estimates by also estimating Equations 3 and 4 with a QMLE.

(7) In October 1996 the federal minimum wage increased from $4.25 to $4.75, so we assign a weighted average to represent the minimum wage for that year.

(8) Note, however, that we do not have the ability to distinguish general training from firm-specific training.

(9) The quality of the local high school may affect how much firms rely on in-house training programs for the transmission of basic skills. This effect will be less significant to the degree that workers migrate across district boundaries.

(10) Given Royalty's (1996) and Grossberg's (2000) results, we were concerned about possible endogeneity bias in the estimated coefficient on labor turnover. However, Hausman-Wu tests (Greene 2000) failed to reject the null hypothesis of exogeneity in any of the results we present here. Turnover was instrumented with the "percentage of workers unionized" as the identifying variable.

(11) We reject the null hypothesis of exogeneity in only 2 of the 10 regressions. In all but these two cases, then, we are able to treat the average wage as exogenous.

(12) In order to compare the Tobit results to the uncensored estimates, they must be multiplied by an adjustment factor. The estimated effect is given by [delta]E[t|*]/[delta]m = [PHI](t/[sigma])[PSI], where [PHI] is the standard normal cumulative distribution function and t is calculated using the mean values for the explanatory variables. For ease of interpretation, this adjustment factor is included in each of the relevant tables.

(13) Our QMLE results yield the same conclusions--there are no significant minimum wage effects on training.

(14) Generally, this adjustment leads to an increase in the computed standard errors.

(15) Jeong and Maddala (1993) have argued that most applications using standard errors for the purpose of hypothesis testing are useless because of unreliable distributional assumptions and should, therefore, use the bootstrap method directly.

(16) The QMLE results also indicate negative minimum wage effects only on the percentage of support staff and supervisors trained. Moreover, the QMLE magnitudes are nearly identical to those using the Tobit procedure.

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Received March 2002; accepted February 2003.

David Fairris * and Roberto Pedace ([dagger])

* Department of Economics, University of California, Riverside, CA 92521, USA: E-mail dfairris@ucracl.ucr.edu.

([dagger]) Department of Economics, University of Redlands, Redlands, CA 92373, USA; E-mail roberto_pedace@redlands.edu; corresponding author.