Optimal 'mismatch' and promotions.

Hersch, Joni

I. INTRODUCTION

A substantial proportion of workers are employed in jobs for which they appear to be either overqualified or underqualified. For instance, using data from the Panel Study of Income Dynamics, Sicherman [1991] finds that 40 percent of his sample are overeducated, and another 16 percent are undereducated. Rumberger [1987] reports similar values using data from the Quality of Employment Surveys. Other studies which find substantial education mismatch include Duncan and Hoffman [1981], Verdugo and Verdugo [1989], and Hersch [1991]; and evidence that a single firm hires both under- and overqualified workers is presented here.

This paper provides an explanation for why firms hire both overqualified and underqualified workers. Firms hire overqualified workers because these workers require less training for their initial positions. Such workers also form a pool from which promotions are made, which lowers hiring costs for higher level positions within the firm. Workers accept positions for which they are overqualified to enhance their probability of promotion and because of search and mobility costs, but if they fail to be promoted to a position that better matches their qualifications, they are more likely to quit. Firms hire underqualified workers, despite their longer training requirement, since such workers are less likely to quit and provide continuity of the labor force over time. Thus, contrary to job matching arguments that would explain these hires as a result of imperfect information, hiring of seemingly mismatched workers is optimal and these matches are made with perfect information.

The model developed in this paper yields three testable hypotheses: (1) training time for entry level jobs is inversely related to overqualification at the time of hire; (2) workers who are overqualified on their current job are those who have failed to be promoted to a job which better matches their qualifications, and such workers are more likely to quit; and (3) workers overqualified at time of hire are more likely to be promoted.

To test these hypotheses, I use new data collected for this purpose. Previous empirical research, such as that cited above, was restricted by data availability to examining only the match between education and the worker's current job. Thus, the quality of the match with the worker's initial job, and the match between worker qualifications other than education, has gone unexplored. However, various worker characteristics in addition to education are often substituted for each other in determining a worker's qualification for a job. Thus, I examine additional qualifications including the match between the worker's experience, level of previous job, and use of skills. Information on the match between the worker's qualifications and those required for the initial job with the employer is particularly important, since entry level qualifications determine training time for the initial job, as well as the likelihood of promotion. Further, individual-specific training time for the initial job is necessary, but typically not available, since data sets providing information on training such as the Panel Study of Income Dynamics and Quality of Employment Surveys request information on training time for the average worker, and not for the individual worker.

The data set reveals several interesting statistics. Qualification mismatch at hire is fairly common for this firm: 29 percent of the sample report themselves overqualified for their first job with the firm, while 13 percent report themselves as underqualified. Lateral intra-firm mobility is common and occurs far more frequently than promotions. Workers in the sample average 1.3 promotions but four different jobs with the employer. This suggests that the job matching process occurs not only by turnover but through intrafirm mobility.

Consistent with the assumptions and implications of the model, the empirical results indicate that workers who are overqualified at hire receive less training and more promotions, and that workers overqualified for their current job are more likely to quit. Workers underqualified at hire receive more training, and workers underqualified for their current job are less likely to quit.

II. THE MODEL

The theoretical framework is an overlapping generations model. Assume there are n types of firms in the economy, with a number of firms of each type. Firms are competitive and infinitely lived; workers work two periods. Workers differ in their level of qualifications. Each period, firms decide how many workers of each type to hire and how many, and which, of its incumbent workers to promote. Promoted workers receive a higher wage, and may also be more productive after promotion. However, firms may promote workers even if doing so does not make workers more productive, since as in Carmichael [1983], one purpose of promotion in this model is to induce optimal turnover.

After promotion decisions are announced, workers choose whether or not to quit, in order to maximize lifetime earnings, based on their placement with the firm and outside wage offers. Firms know the distribution of outside wage offers but do not know a particular worker's outside opportunity.

Workers are characterized by a vector of observable qualifications such as education and work history. For now, assume that search and mobility costs do not vary among workers. More qualified workers face a "better" distribution of outside wage offers, in the sense that the distribution of their outside wage offers stochastically dominates that of less qualified workers.

For simplicity assume that firms face a common distribution of job seeker qualifications. Also assume that skills required of workers in all firms are similar enough that workers are eligible to work in a firm of any type.

To derive the optimal hiring and promotion rules for a representative firm, it is sufficient to assume that there are two types of workers, labelled "H" and "L."(1) Workers are endowed with one unit of time per period. All training takes place in a worker's first period with a firm. A firm decides how many of each type of worker to hire and sets the promotion policy to maximize profits. Firms can commit to a particular promotion policy.(2)

Let [N.sub.j] denote the number of workers of each type hired with j = H, L. The term "young workers" refers to those in their first period with the firm, while "experienced workers" are in their second period. Further, let

[h.sub.1] = total work time of young workers in starting level job, net of training time,

[Mathematical Expression Omitted] = total work time of experienced workers who are not promoted (and remain in starting level job),

[Mathematical Expression Omitted] = total work time of experienced promoted workers.

Wages are determined exogenously, with

[w.sub.1] = starting wage for young workers,

[Mathematical Expression Omitted] = wage rate of experienced workers in the starting level job,

[Mathematical Expression Omitted] = wage rate of experienced promoted workers.

Wages will have the property that [Mathematical Expression Omitted].

At each period t, the firm's production function is of the following form:

[Mathematical Expression Omitted]

where f is assumed to be strictly concave, with [f.sub.1] [greater than] 0, [f.sub.2] [greater than] 0. Assume also that the firm values both young and experienced workers; that is, [f.sub.1](0, [center dot]) and [f.sub.2]([center dot], 0) are sufficiently large. The increased productivity of promoted workers is indicated by the function [Mathematical Expression Omitted] which multiplies the total work time of promoted workers. Note that the value of this function depends on the number of workers promoted. If [Mathematical Expression Omitted] for all values of [Mathematical Expression Omitted], promoted workers are no more productive than workers not promoted. For it to be optimal for the firm to promote some but not all workers of the same type, we must have [Mathematical Expression Omitted] after some point. The rapidity of the decrease in the marginal product of promoted workers and the effect of promotion on deterring turnover determine the number of workers promoted.

The profit function for a representative firm can be expressed as

[Mathematical Expression Omitted],

where [Beta] is the discount factor and the price of output is normalized to equal 1.

Let [T.sub.j] denote training time of type j, j = H, L. Workers of different types differ in required training time to achieve a given level of productivity, with [T.sub.H] [less than] [T.sub.L]; overqualified workers require less training time. This assumption is tested in section IV.

Since each worker is endowed with one unit of time each period, total work time of young workers, net of training time, is

[h.sub.1] = [N.sub.L](1 - [T.sub.L]) + [N.sub.H](1 - [T.sub.H]).

Let [P.sub.j] be the fraction of type j promoted, with j = H, L, and [F.sub.j]([center dot]) the conditional distribution function of outside wage offers for experienced workers. [F.sub.j](w) is the probability that an individual of type j stays with the firm, given wage w. [F.sub.H](w) [less than or equal to] [F.sub.L](w), that is, more qualified workers are more likely to quit for a given wage offer. This assumption is also tested in section IV.

Total work time of experienced workers is

[Mathematical Expression Omitted]

for workers not promoted; and

[Mathematical Expression Omitted]

for promoted workers. The firm's objective is to choose [N.sub.H] and [N.sub.L], the number of over- and underqualified workers, and [P.sub.H], and [P.sub.L], the fraction of each type promoted to maximize (1) subject to (2a)-(2c). We focus on stationary equilibrium, where [Mathematical Expression Omitted] and [Mathematical Expression Omitted].

The most important notion derived from this model is that firms may optimally hire, and promote, both over- and underqualified workers. The intuition is that if the training time of underqualified workers is much greater than that of overqualified workers, the firm will hire overqualified workers to assure output in the first period. If overqualified workers are sufficiently more likely to quit than underqualified workers, the firm will hire underqualified workers to assure the presence of experienced workers. Firms generally promote some, but not all, workers; although promoted workers are more productive, the marginal productivity of promoted-workers decreases as more are promoted.

To show that firms may optimally hire both over- and underqualified workers, consider the case where [T.sub.L]= 1 and [Mathematical Expression Omitted]. Since underqualified workers produce no output when young, the firm must hire overqualified workers. Since all overqualified workers quit after one period, whether or not they are promoted, the firm must hire underqualified workers. By continuity of the profit function, firms also hire both over- and underqualified workers when the training time for underqualified workers is 1 - [Epsilon], for [Epsilon] sufficiently small, and positive probabilities of overqualified workers staying: [Mathematical Expression Omitted], with k sufficiently small. Phrased differently, the results extend to the case where underqualified workers are productive when young and overqualified workers do not automatically quit when old.

To show that firms may optimally promote none, some, or all workers of a given type, consider the case where no underqualified workers are promoted ([P.sub.L] = 0) and the productivity of promoted workers [Mathematical Expression Omitted], where c is constant for all values of [Mathematical Expression Omitted]. It is now easy to show that either all or no overqualified workers are promoted ([P.sub.H] = 1 or [P.sub.H] = 0), since promotion only serves to deter turnover of overqualified workers - if the production function and parameters of the model are such that if it is efficient to deter turnover of any overqualified workers by promotion, it is efficient to do so for all overqualified workers. Next consider [Mathematical Expression Omitted] after some point, so that the marginal productivity of promoted workers declines. Firms may now wish to promote fewer workers, so that 0 [less than or equal to] [P.sub.H] [less than] 1, with the value depending on the particular function [Mathematical Expression Omitted].

Most of the implications of the model are obvious. It is clear that firms will promote more highly qualified workers before less qualified workers, and only promote less qualified workers if all highly qualified workers are offered promotion; firms hire fewer underqualified workers, the greater is the difference in training time between under- and overqualified workers; and firms hire more underqualified workers, the greater is the likelihood that an underqualified worker who is not promoted will stay with the firm relative to an overqualified worker who is not promoted.

Differences among firms

Differences among firms in their production technology lead to hiring and promoting different proportions of over- and underqualified workers. In general, training and hiring costs depend on characteristics such as firm size and production technology used by the firm. For example, monitoring costs differ with firm size, suggesting that hiring costs will also vary with firm size, as more resources are spent screening workers prior to hire in firms in which monitoring costs are high, as in Mellow [1982] and Oi [1983]. Large firms may have rigid production processes requiring longer employer search for a suitable employee, and more training of that employee for the firm's specific production process [Oi 1983]. Training costs will vary with firms' production technology, with even firms in the same industry differing in the organization of production, as Oi discusses.

Turnover will be more costly in industries or firms with large capital stock that will be underutilized until a new hire is trained (e.g., Lang [1991], Montgomery [1991], Barron, Black and Loewenstein [1993]). Similarly, turnover is more costly when the production process is interdependent among workers, since specific capital of the existing work force will be underutilized until the new hire is trained. Such differences among firms are captured in the model by differences in the production function [f.sub.2], with firms that value experienced workers more having a greater [f.sub.2].

Differences among workers. Differences in characteristics of workers in the labor pool also lead to hiring and promoting different proportions of over- and underqualified workers. Workers with high search and mobility costs are more likely to accept a first-period job for which they are overqualified, and to stay with the firm in the second period even if they are not promoted. A familiar example is highly educated and skilled university secretaries.

Firms may hire more overqualified workers who choose to be overqualified in the first period as part of a long-run career path strategy. As Sicherman [1991] and Sicherman and Galor [1990] demonstrate, it is optimal for some workers to seek jobs for which they are overqualified in the early part of their career, to acquire skills that will enhance their long-run career profile or to improve their probability of promotion. Since firms promote overqualified workers first, workers may maximize their lifetime earnings by taking a lower wage job when young in order to increase their probability of promotion later.

III. DATA

Since existing data sets lacked information on job match quality, length of on-the-job training provided to individual workers, number of promotions, and intended turnover, I collected new data by survey from employees of a private firm in a regulated industry in Wyoming in 1991. As discussed below, use of any existing national data set to address the questions of this paper would result in severe errors-in-variables problems that would obfuscate the interpretation of the empirical findings. In addition, data from employees of a single firm are probably more appropriate for studying the determinants of training time and number of promotions than are data from workers employed in a cross-section of firms. Firms vary in the fixed amount of training time provided to all new hires, as well as in their internal labor market rules governing promotion and in the growth rate of the firm which may determine promotion opportunities.(4)

To generate the data set, a four-page questionnaire, accompanied by a stamped return envelope, was distributed through the company's mail system. All respondents were guaranteed confidentiality, with no names requested on the survey. The response rate was extremely high for a mail survey, with 62 percent of the firm's 758 employees responding.(5)

The sample consists of 451 male and female workers who provided information on all variables used in the analysis. Variables unique to this study are described below. The data set also contains information on standard human capital and demographic variables, such as experience, tenure, education, marital status, race, and so forth, found in other data sets.

Descriptive statistics are provided in Table I. Compared with a national sample, on average the workers are somewhat older, better educated, and have higher hourly wages. The average value of tenure of seventeen years is particularly high relative to a national sample. The rate of unionization is high, since non-exempt employees were covered by a union contract.(6) While the sample is not representative of the general population of workers, the results may generalize to firms with similar employment policies and to other regulated or highly unionized firms.

The key variables in this study are the qualification match variables, on-the-job training, number of promotions, and quit intentions. The match questions were designed to elicit information on both the qualification match at time of hire, as well as qualification match of the worker's current job. The questions addressing qualification match at time of hire asked respondents to indicate how their entry level qualifications matched requirements of their first job with their current employer - whether they were underqualified, exactly qualified, or overqualified. Workers indicating that they were overqualified were asked to indicate the reasons - whether they had more education than necessary, whether they had more experience than necessary, and/or whether their previous job was at a higher level. About 58 percent reported an exact qualification match at hiring, while 29 percent considered themselves overqualified. The form of overqualification was excess education for 21 percent of the sample and excess experience for 13 percent. Seven percent reported their previous job had been at a higher level (multiple responses were permitted). Interestingly, about 13 percent reported themselves underqualified at time of hire.(7)

Qualification match with the worker's current job is measured by education match, by whether the worker's job gives the worker the opportunity to use his or her skills, and by reported job satisfaction. To obtain information on education match, workers were asked to select one of seven categories in response to the question, "What is the level of education you feel is actually needed by the average person to do your job, not just to be hired? (This can be more or less than the level specified in the job description.)." Each category (ranging from no formal education necessary to graduate degree) was converted to a single year equivalent. Surplus or deficit education was defined as the difference between the worker's actual education and that required for the job.

Whether the worker's current job provides opportunity to use his or her skills is elicited by two questions. First, workers were asked, "How much chance does your job give you to do the things you are best at?" with five response choices ranging from "no chance" to "a very good chance." Second, workers were asked if they have "any skills, training, and/or education that they are not using on their current job" but wish they could use, and to specify what they are.

The final question measuring current match quality requests job satisfaction, where workers were asked "How do you feel about the kind of work you do?" and given six choices from "don't like it" to "it's exactly the kind of work I like best."

On-the-job training for the worker's initial job is measured by the response to the question, "Did you receive any formal on-the-job training for your first job with your current employer? If yes, how many weeks?" Formal training time in the sample averaged 4.3 weeks, with 75 percent of the sample receiving formal training.(8)

The training question in this survey differs from the training questions on the Panel Study of Income Dynamics (PSID) and the Quality of Employment Survey (QES), which request information on how long it would take the average new person to become fully trained and qualified Panel Study or to do the job reasonably well Quality of Employment. These questions on the Panel Study and Quality of Employment were designed to minimize bias in reported training time for the worker's job resulting from individual differences in skills and background. However, testing the hypothesis that firms optimally hire overqualified workers in order to reduce individual training time requires a measure of training actually provided to that worker. There is great variation in training time even within a narrow job classification. For instance, network technicians in my sample report training time ranging from zero to fifty-two weeks.

The number of promotions is measured as the response to the question, "How many promotions have you received since you began working for your current employer?" Fifty-seven percent of the workers in the sample were promoted at least once, with the average number of promotions for the sample equalling 1.3. Lateral within-firm job mobility is far more common than upward mobility. Respondents report an average of four different jobs with this employer.(9) TABLE I

Variables and Descriptive Statistics(a)

Human Capital and Individual Characteristics Mean and Std. Dev.

Previous Experience 4.53 (5.66)

Tenure with Employer 17.10 (6.55)

Tenure on Job 8.72 (5.68)

Education 13.39 (1.65)

White-Collar .62 (.49)

Job Covered by Union Contract .81 (.39)

Physical Condition Limits Work .05 (.22)

White .90 (.30)

Male .50 (.50)

Age 41.48 (7.08)

Married .75 (.43)

Hourly Wage 14.94 (3.28)

Weeks of Formal on-the-Job 4.32 Training for First Job (TRAINING) (8.64)

Number of Promotions (PROMOTIONS) 1.29 (1.57)

Number of Different Jobs with Employer 4.03 (2.53)

Job Match for First Job with Current Employer Mean and Std. Dev.

Under-Qualified for First Job .13 (.34)

Exactly Qualified for First Job .58 (.49)

Over-Qualified for First Job .29 (.45)

More Education than Necessary for First Job .21 (.41)

More Experience than Necessary for First Job .13 (.34)

Previous Job at Higher Level .07 (.26)

Job Match for Current Job with Employer Mean and Std. Dev.

Would Quit for any Job Paying at Least as Well .16 (QUIT INTENTION) (.37)

Required Education to Perform Job 12.83 (not just to be hired) (1.52)

Surplus Education .96 = actual education - required education (if positive) (1.51)

Deficit Education .40 = required education - actual education (if positive) (.79)

Uses Best Skills = ranking of extent job gives 3.62 worker a chance to do things worker is best at, (1.11) from 1 = no chance, to 5 = very good chance.

Other Skills = 1 if worker would like to use .37 other skills, training, and/or education in (.48) current job.

Satisfaction = ranking of job satisfaction from 3.95 1 = don't like, to 6 = exactly the kind of work (1.19) liked best.

Sample size 451

a. Sample consists of respondents to survey administered by author to employees of a private firm in Wyoming

Since the data are cross-sectional, actual quit behavior is not observed. Reported quit intention is used instead, which should be interpreted as a "pressure" variable related to actual quits. Quit intention is measured as a dummy variable equalling one if the worker reports that he (she) is likely to quit his (her) job for any other job, regardless of pay, or for any other job paying as much as the current job. Given the high tenure of workers in the sample, it is not surprising that only 16 percent of the workers report that they are likely to quit.

IV. EMPIRICAL SPECIFICATION AND RESULTS

This section presents the results of three empirical tests: (1) training time for entry level (e.g., first-period) jobs is inversely related to overqualification; (2) probability of quitting is positively related to over-qualification; and (3) workers overqualified at time of hire are more likely to be promoted.

Training

Since the training time variable refers to training time for the worker's initial job with the employer, training time is regressed on the worker's initial qualifications at time of hire. These are worker's education, previous work experience, and dummy variables for whether the worker was overqualified or underqualified for the first job. The relation between education and training, and between previous experience and training, are unclear. As Barron, Black, and Loewenstein [1989] hypothesize, if ability and training are complementary and human capital is positively correlated with ability, then workers with greater amounts of human capital will be placed into jobs which require more training. However, what is of interest here are not levels of human capital, but match between the worker's qualifications and those needed for performance on the job. Thus, we expect to see that overqualified workers receive (or require) less training, and underqualified workers receive more.

Quit Intention. The second empirical test is that workers overqualified for their current job are more likely to quit, since their alternative wage based on their level of human capital will be higher than their current wage, while the opposite is expected for underqualified workers. Workers overqualified on their current job will be workers who started off overqualified, yet failed to be promoted to a job that better matched their qualifications.(10)

Four variables are included as measures of match between the worker's qualifications and those required for their current job: years of surplus education, years of deficit education, whether the job uses the worker's best skills, and whether the worker possesses other skills he would like to make use of on the job. Reported job satisfaction is included to control for nonpecuniary aspects of the job that may influence turnover plans. The equation also includes years of previous experience and tenure. Since the question eliciting information on quit intention controls explicitly for wage, the worker's current wage rate is not included in this estimation (although the results are essentially identical if wage is included as a regressor).

Promotions. Finally, the promotions equation follows a specification similar to that for training time, since the hypothesis is that workers who are overqualified at time of hire constitute a pool from which promotions are made, and workers that are overqualified but not promoted are more likely to quit. The number of promotions with current employer is regressed on qualification match at hire, controlling for tenure with firm and previous work experience.

Results. Table II presents the results of estimating these equations. Column 1 presents OLS estimates of length of training provided for the worker's first job with employer. More educated workers receive more training, suggesting that ability and training are complements. However, workers overqualified for their first job receive an average of 2.5 fewer weeks of training than exactly qualified workers, and underqualified workers 3.2 weeks more training. No other variables are significant determinants of training duration at the 5 percent level.

Column 2 presents probit estimates of the quit intention equation.(11) As predicted, workers who have not been promoted into [TABULAR DATA FOR TABLE II OMITTED] a good match, as indicated by their over-education for their current job, express a significantly greater likelihood of quitting, while the opposite is true for workers with less education than required for their current job.(12) Note this effect is distinct from the effect of education on reducing quit intention. The results indicate an independent effect of education on quit intention, significant at the 5 percent level (one-sided test).

Workers in jobs that make use of their best skills would seem to be in a good match, and indeed these workers indicate that they are less likely to quit. As expected from matching models, workers with more previous experience are also less likely to quit their job. It is noteworthy that tenure with employer is not significantly related to quit intention. White workers express a greater likelihood of quitting than nonwhite workers, which may be due to greater concern of nonwhite workers over restricted alternative job opportunities due to discrimination.

Column 3 presents estimates of number of promotions received by a worker since joining the firm, using a negative binomial regression model. This specification was chosen since number of promotions is count data, taking on discrete values. Estimates using the Poisson regression model are similar, but indicate that the assumption of equal mean and variance should be rejected at the 1 percent level, using the test for overdispersion recommended by Cameron and Trivedi [1990].

Controlling for tenure with employer (which is positively related to the number of promotions, as expected), workers who were overqualified for their initial job receive an average of .35 more promotions than exactly qualified workers. The difference between the number of promotions of workers underqualified at hire is not significantly different from those exactly qualified.

White collar workers have a significantly higher number of promotions than blue collar workers. Workers covered by a union contract have significantly fewer promotions, perhaps because unionized jobs have shorter job ladders.

As a check on the robustness of the negative binomial regression model, the promotions equation was also estimated by Tobit. The results were similar to the negative binomial estimates, with the exception of the significance of the coefficients on physical condition. The Tobit results suggest that workers with physical limitations receive more promotions (p-value = .05).

Alternative Specifications and Selection Bias. As hypothesized in the theoretical development, training time should not have an independent effect on number of promotions after controlling for initial job qualifications. In addition, neither training time nor number of promotions should have an independent effect on quit intention after controlling for current qualification match quality. These hypotheses were tested by including both training time and number of promotions in the quit intention equation, and by including training time in the promotions equations. The results strongly supported exclusion of these variables. A likelihood ratio test of the joint significance of training time and number of promotions in the quit equation overwhelmingly failed to reject the hypothesis that the coefficients on these variables are jointly zero, with individual t-values of -.11 and -.66, respectively. Similarly, a likelihood ratio test indicated that training time is not a significant determinant of number of promotions. The t-statistic on training time in the promotions equation was -.66.(13)

Selection bias may arise since only workers employed by the firm at the time of the survey are observed in the sample; workers that left the firms are not represented. If there is a systematic relation between the dependent variables and the probability of inclusion in the sample, the parameter estimates may be biased. As the model predicts, workers not promoted are more likely to leave the firm, hoping to find a better match and thereby enhance their probability of promotion. While this will not necessarily bias the estimated coefficients, the average number of promotions observed may be biased upward.(14) Unfortunately, however, testing and correcting for possible selection bias is impossible with the available data.

V. CONCLUDING REMARKS

This paper demonstrates that firms may optimally hire workers that are seemingly mismatched. Turnover may be higher for an overqualified worker, but training costs will be lower. Further, overqualified workers are more likely to be promoted. Training costs will be higher for underqualified workers, but turnover may be lower, since such workers will have fewer higher-wage alternative opportunities. Empirical support for these hypotheses are provided, using new data designed to measure qualification match.

While the standard view of job matching is that turnover is the primary mechanism by which a better job match occurs, it is noteworthy that lateral job moves are fairly common within this sample. This suggests that much of the job matching process takes place within a firm, rather than through turnover, which further reduces the costs of seeming mismatches. Note that the firm in this study is relatively small, and thereby offers relatively little opportunity for lateral mobility. Intrafirm mobility as a mechanism for achieving high-quality job matches may be prevalent within large firms. More research on the within-firm match process is necessary.

1. In the empirical tests, H and L will correspond to overqualified and underqualified workers, respectively.

2. I make the conventional assumption that the firm commits to a promotion policy because it values its reputation as an honest employer (e.g., Lazear [1981], Shapiro and Stiglitz [1984]).

3. Since firms can distinguish between the two types of workers ex ante, it is not necessary that all workers be offered the same wage in the first period. This assumption is made to simplify the notation. What matters is that workers with different qualifications who are offered the same job be paid wages more similar than would be predicted by their differences in qualifications. This is consistent with the empirical evidence from studies of the effect of education mismatch on wages. These studies typically find that over-(under) educated workers earn more (less) than their exactly educated co-workers, but less (more) than similarly educated workers holding jobs for which they are exactly educated (e.g., Duncan and Hoffman [1981], Rumberger [1987], Sicherman [1991], Hersch [1991]).

4. While by design this data set meets the purpose of providing information to examine qualification mismatch and promotions, it is vital to note that these data are far from perfect. The ideal data set would be a long panel data set on a random sample of workers, which includes the required information on job match quality at hire and on current job, and individual-specific on-the-job training, as well as the timing and number of promotions and actual turnover behavior. Lacking this information on any existing data set, the researcher has three options: not testing the theoretical implications; using an existing data set with its known deficiencies and consequent biases; or generating new data, which overcomes a number of problems which would result from the use of any existing data set but is subject to other limitations. I chose the third option, recognizing that the results of this study may not generalize beyond the sample considered here. However, these findings provide evidence on the likely importance of observable components of match quality in the employment relation, suggest directions for future data collection efforts, and help to identify the means by which qualification match may be quantified.

5. As an incentive to respond to the questionnaire, workers that returned their completed survey were placed in a lottery, which awarded three prizes ($100, $50, and $25).

6. However, the workers in the sample are more similar on average to workers employed in the same industry group (transportation, communications, and public utilities) than to the general population of workers. Calculations from the 1988 May Current Population Survey yield average values of tenure, age, and hourly wage that are significantly greater for workers in transportation, communications, and public utilities than in other industries. In transportation, communications, and public utilities, the average values of tenure, age, and hourly wage (in 1988 $) are 9.55, 38.65, and $11.93, respectively. The corresponding values for all other industries are 6.53, 36.93, and $9.69.

7. The correlations between tenure and over- and underqualification are not significantly different from zero, indicating that there is no systematic relation between time of hire of incumbent labor force and qualification match.

8. Informal training is also quite common among the employees of the finn, with 87 percent of the sample reporting that they learned to do their job through informal training. Although a measure of training that includes both informal and formal training would be preferable, a quantifiable measure of informal training is extremely difficult to attain. As long as the length of time in informal training and formal training are positively correlated, the substance of the results will be unaffected by including only formal training time in the analysis.

9. By asking information on both number of different jobs and number of promotions, workers were less likely to report lateral moves as promotions. However, nearly 8 percent of the full sample of 471 workers reported the same value for number of promotions and number of jobs. I reduce the reported number of promotions by one for those reporting number of promotions equal to number of jobs.

10. As long as there is a positive correlation between quit intention and realized quits, the use of quit intention will provide a test of the assumption that overqualified (type H) workers have higher realized quits because they face better alternatives.

11. Although quit intentions typically exceed actual quits, it is not clear that this will bias the estimated coefficients on the qualification match variables. However, if the relation between actual and intended quits differs between under- and overqualified workers, inferences of actual quit behavior derived from quit intentions may be misleading.

12. This finding is consistent with Sicherman and Galor [1990] who show that workers who have a high probability of promotion but are not promoted are more likely to quit the firm.

13. The coefficient estimates derived from equation-by-equation estimation are clearly unbiased, but it is possible that efficiency could be improved by estimating the equations of the model using a seemingly unrelated regressions method. However, the efficiency gain over equation-by-equation estimation is likely to be slight, since the expected relations generally proved to be statistically significant. Note that the presence of a dichotomous dependent variable (quit intention) and a count data dependent variable (number of promotions) clearly complicates estimating the system by a seemingly unrelated regressions method.

14. This effect is doubtlessly mitigated by the fact that the wages paid by this firm are relatively high for the region, so even workers who are not promoted are unlikely to improve their wages by moving to another firm in the region. A national labor market would not be the relevant labor market for the vast majority of workers in this sample.

REFERENCES

Barron, John M., Dan A. Black, and Mark A. Loewenstein. "Job Matching and On-the-Job Training." Journal of Labor Economics, January 1989, 1-17.

-----. "Gender Differences in Training, Capital and Wages." Journal of Human Resources, Spring 1993, 342-64.

Cameron, A. Colin, and Pravin K. Trivedi. "Regression-Based Tests for Overdispersion in the Poisson Model." Journal of Econometrics, December 1990, 347-64.

Carmichael, Lorne. "Firm Specific Human Capital and Promotion Ladders." Bell Journal of Economics, Spring 1983, 251-58.

Duncan, Greg J., and Saul D. Hoffman. "The Incidence and Wage Effects of Overeducation." Economics of Education Review, Winter 1981, 75-86.

Hersch, Joni. "Education Match and Job Match." Review of Economics and Statistics, February 1991, 140-44.

Lang, Kevin. "Persistent Wage Dispersion and Involuntary Unemployment." Quarterly Journal of Economics, February 1991, 181-202.

Lazear, Edward P. "Agency, Earnings Profiles, Productivity and Hours Restriction." American Economic Review, September 1981, 606-20.

Mellow, Wesley. "Employer Size and Wages." Review of Economics and Statistics, August 1982, 495-501.

Montgomery, James D. "Equilibrium Wage Dispersion and Interindustry Wage Differentials." Quarterly Journal of Economics, February 1991, 163-80.

Oi, Walter Y. "Heterogeneous Firms and the Organization of Production." Economic Inquiry, April 1983, 147-71.

Rumberger, Russell W. "The Impact of Surplus Schooling on Productivity and Earnings." Journal of Human Resources, Winter 1987, 24-50.

Shapiro, Carl, and Joseph E. Stiglitz. "Equilibrium Unemployment as a Worker Discipline Device." American Economic Review, June 1984, 433-44.

Sicherman, Nachum. "Overeducation in the Labor Market." Journal of Labor Economics, April 1991, 101-22.

Sicherman, Nachum, and Oded Galor. "A Theory of Career Mobility." Journal of Political Economy, February 1990, 169-92.

Verdugo, Richard R., and Naomi Turner Verdugo. "The Impact of Surplus Schooling on Earnings." Journal of Human Resources, Fall 1989, 629-43.