More detail on the pattern of returns to educational signals.

1. Introduction

Spence (1973) and Arrow (1973) formalized the idea that education can be used as a signal for innate productivity. If correlated with innate productivity, education alleviates an informational asymmetry between employers and workers concerning the productivity of a worker. Thus, employers use educational signals in the hiring process as a means of predicting expected worker productivity. This process is formally known as signaling.

In search of evidence for the signaling hypothesis, researchers began to investigate how returns to educational signals change with labor market experience. It was conjectured that returns to educational signals should decline with work experience as employers learn about the true productivity of their employees, therefore depreciating the signal's value. However, the analysis of Layard and Psacharopoulos (1974) failed to reveal such a pattern. Riley (1979) argued that employers must be fight in predicting the true productivities of a group of workers on average. As information about worker productivity is revealed, members of a particular educational signaling group will see their wages improve and others will earn lower wages. However, if average group productivity remains constant, the predictive value of educational signals is confirmed and returns to educational signals remain unchanged. Farber and Gibbons (1996) present research that incorporates Riley's point. Their theoretical model of employer learning predicts constant returns to educational signals over time. They (like Riley) assume that the productivity of a worker does not depend on the quality of the match between job and worker, implying constant average group productivity. Using National Longitudinal Survey of Youth 1979 (NLSY79) data, they find evidence generally in favor of their theoretical results. Altonji and Pierret (2001) further develop the model of Farber and Gibbons (1996) but arrive, after relaxing informational assumptions, at the conclusion that the value of an educational signal should decrease over time. (1) They also use NLSY79 to substantiate their results. Belman and Heywood (1997) depart from earlier models by assuming that the quality of the match between workers and jobs affects worker productivity and argue that a sufficient proportion of all job-worker matches are not perfect at the time a worker is hired. This implies that (group) productivity increases over time as the quality of the job-worker match improves. In their framework, workers acquire educational signals and are hired by firms that use those signals to estimate expected productivity. Jobs require a specific level of productivity. However, a high-productivity worker matched with a low-productivity job will not be able to achieve his full productivity. He faces a job productivity constraint insofar as the job keeps him from realizing his full productive potential. Over time, as information about the true productivity of the employees becomes available, mismatched workers are reassigned to appropriate jobs, and job-worker matches become perfect. Belman and Heywood (1997) find that their model produces declining returns to educational signals over time. They provide empirical evidence using Current Population Survey (CPS) data.

However, none of the aforementioned models addresses the important question of how and when workers' true productivities are revealed, which potentially affects the time paths of returns to educational signals. This paper addresses that shortcoming using a multiperiod version of the Belman and Heywood (1997) model, which was chosen because it incorporates the sensible assumption of improved job-matching over time. In the model, information in the first period is imperfect but symmetric (neither the worker nor the firm has knowledge of the worker's true productivity). From period two onward, the informational structure of the model changes as workers become privately aware of their true productivities. At this point, information becomes asymmetric since firms are still unsure about worker productivities. It is easy to imagine this situation in a real life setting where imperfect monitoring of workers limits the ability of the firm to generate information about workers' true productivities. The worker, better able to compare his ability to requirements of the job, gathers private information. How do workers use this private information and how do firms react as they expect this informational asymmetry?

Stiglitz (2002, p. 463) identifies the ability to appropriate returns from information as one of the key issues in information economics: "Someone who knows his abilities are above average has an incentive to convince his potential employer of that, but a worker at the bottom of the ability distribution has an equally strong incentive to keep the information private." This paper adopts Stiglitz's view of the behavior of firms and workers in the current context. Workers who are currently overpaid (with productivities less than the job requires) have an incentive to keep this information private. Workers who are underpaid (face job productivity constraints) have an incentive to reveal their true productivity publicly and earn higher wages. Similarly, firms have an incentive to detect overpaid workers.

The main result of the paper is that returns to (above median) educational signals initially increase, a new finding in the literature. Data from the Current Population Survey (CPS) are used to produce empirical support for this hypothesis. The paper adds an important dimension to the existing literature on the time pattern of returns to educational signals. Previous research studies found the returns to educational signals to be either decreasing or constant over time. The results here imply that focusing on a general trend between states with complete uncertainty and certainty likely leads to the omission of important details.

The rest of the paper is organized as follows: Section 2 describes the model, provides a description of the revealing/detection process, and concludes with the presentation of the main theoretical result. Section 3 describes the data set and presents the empirical results. Section 4 provides concluding remarks.

2. The Model

Assume N ordered worker types consisting of equal numbers of workers, [T.sub.i], i = 1 ... N with true productivities (2) [v.sub.i], i = 1, 2, 3 ... N. There are N job types [t.sub.i], i = 1 ... N, with corresponding productivity requirements [v.sub.i], i = 1 ... N. To simplify the model each firm [F.sub.i] only offers jobs of type [t.sub.i]. Each worker acquires an ordered educational signal [S.sub.i], i = 1 ... N. Agents are assumed to observe their own productivity with noise and base their decisions about the acquisition of educational signals on unbiased estimates of their own productivity. This results in signaling groups that potentially contain workers of all types and whose heterogeneity depends on the sampling distribution of the estimator used by the agents. Let [alpha] measure the proportion of workers who acquired signal [S.sub.i] and are of type [T.sub.i] (have true productivity [v.sub.i]). (3) For simplicity, I assume that workers who acquire a signal [S.sub.j] and are not of the corresponding true productivity [v.sub.j] are represented in equal proportions in each signaling group. Thus, the share of workers of any given true productivity in a signaling group [S.sub.i] that are not of true productivity [v.sub.i] is (1 - [alpha])/(N - 1).

After hiring is completed, both employers (profit maximizers) and employees (utility maximizers) are trying to improve their position. There will be perfect matches, undermatched workers (workers who have higher productivity than the job requires), or overmatched workers (workers who have lower productivities than the job requires).

Workers who are constrained by the job match (undermatched) have an incentive to reveal their true productivity and earn a higher wage in a different firm. (4) Firms have an incentive to detect workers who have a lower productivity than the job requires (overmatched). The ability of workers to reveal their true productivity (firms to detect workers) is assumed to depend on time elapsed since hiring and the means workers (firms) possess to reveal (detect) mismatches. A sensible assumption seems that both depend on how misplaced a worker is (quality of the job-worker match). Therefore, the model assumes that the most undermatched workers are able to reveal their true productivity first, and that the firm is able to detect the most overmatched workers first. (5) Both types of workers move to their appropriate firms where the match is perfect. (6) In addition to the theoretical considerations in Stiglitz (2002), empirical evidence on job matching supports the proposed mechanism. Bartel and Borjas (1981) and Mincer (1986, Part A) find that the wages of quitters (undermatched in the model) usually increase, and that the wages of workers who get laid off (overmatched in the model) usually decrease.

Although the chosen mechanism appears sensible, a cautious reminder seems appropriate. It is evident that the results in this paper may depend critically on the particular process of generating information assumed here; other processes may lead to different conclusions. The remainder of the section outlines the effect of the revealing/detection process on firm wages, wages to educational signals, and, finally, on returns to educational signals and their time paths.

Firms are assumed to operate in competitive labor markets. In period 1, the firm [F.sub.j]'s profit-maximizing choice is to hire workers who purchased the signal [S.sub.j]. (7) The job match determines the productivity of each worker. A worker matched with a job [t.sub.j] has maximum productivity [v.sub.j] even though his true productivity might be higher. His productivity is constrained by the job match. Workers who are assigned to a job [t.sub.i] and have productivity [v.sub.j], with i > j, realize productivity [v.sub.j]. Therefore, the first period wage in firm j is equal to the expected productivity of the group that purchased the signal [S.sub.j].

w[F.sup.t.sub.j] = [alpha][v.sub.j] + [[1 - [alpha]]/[N - 1]] ([N - j][v.sub.j] + [j-1.summation over (i=1)] [v.sub.i]) = [v.sub.j] - [[1 - [alpha]]/[N - 1]] [j-1.summation over (i=1)]([v.sub.j] - [v.sub.i]). (1)

The first part of Equation 1 shows that the expected productivity of workers with educational signal [S.sub.j] depends on the share of workers with the correct signal ([alpha]), workers facing a job productivity constraint (first part inside parentheses), and workers with tree productivities less than required by the job. The second part of Equation 1 shows an alternative formulation in which expected productivity depends on the productivity of the group of workers for which the job match is perfect and is negatively affected by workers with lower productivity.

From the second period onward, the revealing/detecting process potentially changes firm wages. Assume a model with 10 worker types, 10 firms, and 10 educational signals. In period two, workers with educational signal [S.sub.10] (working in firm [F.sub.10]) who are of true productivity [v.sub.1] are detected. Similarly, workers with educational signal [S.sub.1] (working in firm [F.sub.1]) who are of true productivity [v.sub.10] are assumed to be able to reveal their true productivity. Both switch to their appropriate firm. In period three, the process continues with workers that are most overmatched/undermatched in that period (i.e., workers that signaled [S.sub.10] [[S.sub.1]] and are of true productivity [v.sub.2][[v.sub.9]]). This affects the composition of the workforce in firms [F.sub.1] and [F.sub.10] and increases the wage in firm [F.sub.10]. (8) The general formulation for firms whose wages increase because of the revealing/detection process is

w[F.sup.t.sub.j] = [v.sub.j] - [[1 - [alpha]]/[N - 1]] [j-1.summation over (i=j-(N-t))] ([v.sub.j] = [v.sub.i]). (2)

The intuition behind Equation 2 is largely the same as in period one, except that some workers have been removed from the firm (as the lower bound of the summation indicates), and workers who are perfect matches were added.

The wage for an educational signal is equal to the average wage of the group possessing that signal. Note that, in period one, the wages to the educational signals are equal to the firm wages because all members of a particular signaling group [S.sub.j] are in firm [F.sub.j], thus

w[S.sup.t=1.sub.j] = w[F.sub.t=1.sub.j]. (3)

As soon as an educational signaling group is affected by the revealing/detection process (members change firms) the equality shown in Equation 3 ceases to hold. The main result of the paper applies to above median educational signals, where reference is made toward the ordinal ranking of the educational signals. For this reason, the paper focuses on wages and returns to above median educational signals. (9) In general, the wage to an above median educational signal [S.sub.j] that is affected by the revealing/detection process ([S.sub.10] in period 2, [S.sub.9] in period 3) can be written as

w[S.sup.t.sub.j] = w[F.sup.t.sub.j] - [[1 - [alpha]]/[N - 1]] [j-(N-t+1).summation over (i=1)] (w[F.sup.t.sub.j] = w[F.sup.t.sub.i]). (4)

Equation 4 shows that wages to educational signals depend on two countervailing effects. A rising firm wage (w[F.sup.t.sub.j]) positively affects the wage to the signal. However, some of the workers of the signaling group had true productivities below the job requirements and will, after being detected, work in lower order firms, putting downward pressure on the wage to the signal. As shown below, the relative magnitude of the two effects is crucial to the main result of the paper.

As Equation 5 shows, returns to educational signals are defined as the difference between the wages of two adjacent educational signaling groups at a given point in time

r[S.sup.t.sub.j] = w[S.sup.t.sub.j] - w[S.sup.t.sub.j-1]. (5)

Note that, as an educational signaling group enters the revealing/detection process (continuing the above example, [S.sub.10] in period 2), the adjacent signaling group (i.e., [S.sub.9]) does not. Therefore, as shown in Equation 6, the change in returns to educational signals over time equals the change in the wage to the higher order signal ([DELTA]w[S.sup.t.sub.j]).

r[S.sup.t.sub.j] - r[S.sup.t-1.sub.j] = (w[S.sup.t.sub.j] - w[S.sup.t.sub.j-1]) - (w[S.sup.t-1.sub.j] - w[S.sup.t-1.sub.j-1]), = (w[S.sup.t.sub.j] - w[S.sup.t-1.sub.j] = [DELTA]w[S.sup.t.sub.j], (note: w[S.sup.t-1.sub.j-1] = w[S.sup.t.sub.j-1]). (6)

PROPOSITION: The returns to above median educational signals first affected by the revealing/ detection process increase for any formulation of differences in true productivities that preserves the order of revealing in the model.

PROOF: Equation 7 shows the change of the wage to an educational signal first entering the revealing/detection process (see Appendix A for a derivation). The summation is unambiguously positive.

[([1 - [alpha]]/[N - 1]).sup.2] [j-1.summation over (k=2)]([v.sub.j] - [v.sub.k]) > 0. QED. (7)

Intuitively, improved matching makes one group unambiguously better off relative to the adjacent group if the adjacent group does not improve their match. This is the case for each signaling group when it first enters the revealing/detection process. Owing to their ability to reveal at an earlier date, above median educational signaling groups have a first-mover advantage compared to their adjacent signal ([S.sub.10] reveals before [S.sub.9], etc.). Before moving on to the empirical section, the generality of the result has to be addressed, since it applies to above median educational signals only. However, in real life this means that it is valid for most postsecondary educational signals. Given the growing importance of postsecondary education in industrialized societies, it is this specificity that should be seen as a strength, not a weakness, of the result.

3. Empirical Results and Data

The estimation uses five cross sections (1979, 1985, 1990, 1994, 1998) of the outgoing rotation files of the Current Population Survey (CPS). The full sample includes individuals aged 16-65 with valid observations. A second (sub)sample consists of a synthetic panel data set spanning the period from 1979-98. The range of ages selected in the five years of the synthetic panel were selected to simulate a cohort in the early stages of its work life (16-41 age range). (10)

Data limitations do not allow a complete stratification of diploma effects. The estimations will focus on the bachelor's degree and especially on its interaction(s) with potential experience. The CPS started reporting actual degrees in 1992. (11) All preceding years (1979, 1985, 1990) use years of education to construct indicator variables for degrees. (12) The other categories used are LOW (high school degree, associates degree, some college) and PROF (includes PhDs, law degrees, MDs, etc.) and contain the remaining diplomas. Table 1 shows descriptive statistics of the samples.

The main hypothesis derived from the theoretical section is that above median returns to educational signals increase in the early part of the model. This section forwards empirical evidence for this hypothesis by evaluating the time pattern of diploma (sheepskin) effects popularized by Hungerford and Solon (1987). It should be pointed out that, in doing so, the paper implicitly assumes that diploma effects (higher returns to education in diploma years) are returns to educational signals, a contention that is not universally accepted. (13)

The model used regresses the natural log of the real wage on measures of years of education and potential labor market experience and a set of controls. Also included are diploma dummies measuring the diploma (sheepskin) effect and interaction(s) between the diploma effect and potential experience. The latter variable is included to test the prediction of rising returns to educational signals. The basic specification is given in Equation 8.

In wage = [[beta].sub.1] + [[beta].sub.2] edu + [[beta].sub.1] exp + [[beta].sub.2] [exp.sup.2] + [[beta].sub.3]X + [summation over (i)] [[beta].sub.i] [dipl.sub.i] + [summation over (j)] [[beta].sub.j] [dipl.sub.i] + [summation over (j)] [dipl.sub.j] exp. (8)

X includes controls for gender, race, marital status, part time, region, and appropriate year dummies. The first set of estimations uses four samples created from pairs of cross sections (79/85, 85/90, 90/94, 94/98). For each sample, two regressions are run. To elicit the effect of being in an early stage of one's career on the time path of the diploma effect, the first regression restricts the sample to individuals with limited experience (three years or fewer in first and corresponding experience in the second cross section). The second regression uses the unrestricted sample. Both regressions use a year dummy. The theoretical results would suggest that the sample restricted to individuals with less potential experience exhibits larger increases in their returns to educational signals. Table 2 contains the regression results. All estimations display the predicted pattern. The coefficients on the BACH variable are smaller in the restricted samples and indicate an increase over time. Moreover, the coefficients on the interaction between the diploma effect and potential experience are positive and statistically significant for the restricted sample while negative and significant for the unrestricted sample. The latter result correlates closely with the results of Belman and Heywood (1997) and indicates that returns to educational signals rise in the early part of an individual's work life but decrease afterward. In other words, they seem to indicate nonlinearities in the time paths of returns to educational signals, with concavity as one of the (simpler) options. To provide evidence of concave time paths, I use the synthetic panel and add interactions of diploma effects and the square of potential experience to the model. The expectations are that the coefficient on the interaction of the BACH variable with experience should be positive while the second interaction (with potential experience squared) should be negative. The results (including a set of year dummies) are presented in column (6) of Table 3 and confirm expectations.

Earlier studies using CPS data used only white, male samples and did not include any further controls. The section concludes with testing the sensitivity of the results to the inclusion of other controls and the division by gender summarized in Table 3. The first four regressions estimate the sample with and without controls and also by gender. The results indicate that the inclusion of other controls changes the level of diploma effects but does not affect the interactions between the diploma effects and potential experience (squared). Thus, they do not weaken the results presented earlier. The results further indicate that women experience higher increases in their returns to educational signals than men. To compare the results to earlier studies, the diploma effect for the BACH variable is calculated (14) at mean potential experience using the estimates of the full specification in columns 5 and 6. The diploma effect for the model without further controls is 38%, which is slightly lower than the effect estimated by Jaeger and Page (1996), who estimated a diploma effect for the bachelor's degree of 46%. The difference is most likely attributable to the fact that the current study partially includes data in which the exact degree is not reported, lowering the diploma effect as reported by Jaeger and Page (1996). Including other controls lowers the diploma effect of the BACH variable to 31%.

One final caveat needs to be addressed. The theoretical model measures returns to educational signals by comparing the returns of adjacent signals. However, while estimating sheepskin effects, one measures the premium generated by a diploma with respect to a base group (in this case individuals without a diploma). To address this, I examine the difference of coefficients on the interactions between the BACH variable and potential experience, and the LOW variable and potential experience. The BACH variable represents an above median signal, and the LOW variable contains the adjacent signal. A positive difference would indicate that the return to the BACH variable increases relative to the LOW variable--in line with the theoretical model. The equality of these two coefficients is rejected in every equation at conventional levels of significance. (15)

4. Conclusion

This study provides new insight into the relationship between returns to educational signals and work experience. The paper uses a multiperiod model in which additional information about employees' productivity becomes available over time, improving the quality of the job matches between workers and firms. In contrast to earlier studies, the returns to above median educational signals are found to increase in the early part of the revelation process. This result suggests that the simple view that returns to educational signals decline once complete information is known must be augmented to include a dynamic process with time periods in which returns do not decline. The empirical results are supportive of this finding and indicate periods in which the time paths of returns to educational signals increase.

Appendix A: Derivation of Equation 7

When an educational signal is first affected by the revealing detection process (period 2 for the highest educational signal), its firm wage ([w[F.sup.t.sub.j]) and its wage to the signal (w[S.sup.t.sub.j]) change. This is not the case for the wages to signals of lower order. Thus, the change in the return to the educational signal can be expressed as the difference between the wages to the signal before and after entering the revealing/detection process (as Eqn, 6 in the text shows). Algebraically, the difference can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (A1)

with

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Substitution yields

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (A2)

Canceling terms yields

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (A3)

with

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Substituting back into Equation A3 yields

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (A4)

After the initial period, the highest educational signal ([S.sub.N]) enters the revealing/detection process in period 2, the second highest ([S.sub.N-1] in period 3, and so on. In general, the period when a return to an above median educational signal is first affected by the revealing process is j = N - t + 2. This implies that j - (N t + 1) = 1. Thus Equation 6 can be simplified to

[([1 - [alpha]]/N - 1).sup.2] [j-1.summation over (k=2)] ([v.sub.j] - [v.sub.k]) > 0. (A5)

This summation is unambiguously positive.

Appendix B: Data

The data used come from the 1979-1998 Current Population Survey (CPS) outgoing rotation files (ORG). The full sample includes all individuals aged 16-65. The five cross sections (age ranges in parentheses) for the synthetic panel data set were drawn from 1979 (16-22), 1985 (22-28), 1990 (26-33), 1994 (30-37), and 1998 (34-41). If not reported, hourly wages were constructed using weekly wages and usual hours worked. The resulting hourly wage was deflated using the Consumer Price Index (CPI-U, base 1982-1984). Other variables used are region, education (highest grade completed), potential experience (age--education--6), marital status, year dummies, part time status, gender, and race. For the years 1979, 1985, and 1990, educational variables are coded as LOW (highest grade completed greater or equal than 12 and smaller than 16), BACH (highest grade completed equals 16), and PROF (highest grade completed greater than 16). For the years 1994 and 1998, educational variables are coded as LOW (high school diploma, GED, some college, associate's degree), BACH (bachelor's degree), and PROF (master's degree, professional degree, doctorate degree).

I would like to thank Keith A. Bender, Scott Drewianka, and especially John S. Heywood for comments and suggestions on earlier drafts of this paper. I would also like to thank two anonymous referees for their insightful comments. Any remaining mistakes are my responsibility.

Received December 2003; accepted October 2005.

References

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Spence, A. Michael. 1973. Job market signaling. Quarterly Journal of Economics 87:355-74.

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(1) Consider a vector of variables Z that is correlated with true productivity and is observable by the researcher but is not available to the employer. Farber and Gibbons (1996) assume that the educational signal is correlated with the part of Z that is orthogonal to the employer's information at the time of hiring. Altonji and Pierret (2001) relax this assumption so that the educational signal is correlated even with information contained in Z that is available to the employer at the time of hiring. This subtle difference in assumptions produces decreasing returns to educational signals over time.

(2) The term, true productivity, refers to the worker's maximum productivity. Owing to job productivity constraints, the actual on-the-job productivity might differ from the true productivity of the worker.

(3) It is assumed that [alpha] > 1/N. This assumption is necessary to ensure that educational signals have informational content. Consider picking a worker with a bachelor's degree. A share smaller or equal to 1/N would imply that it is more likely/equally likely that the worker you picked is not of the corresponding true productivity, and the signal would contain no information. The magnitude of [alpha] depends on the ability of individuals to estimate their own true productivity.

(4) The process by which workers reveal their productivity is based on employer learning. As in Waldman (1984), the current employer learns directly by observing the workers. Other firms learn indirectly from observing the actions of the worker's current employer and base wage offers on those observations.

(5) This implies that the model does not necessarily follow a cardinal time scale. A change from one period to another occurs whenever enough time has elapsed for a worker to be able to reveal his true productivity or be detected by the firm. For simplicity it is also assumed that, for workers with the same displacement, detection and revealing happen in the same period.

(6) For simplicity it is assumed that firms follow a one wage rule.

(7) Hiring workers with a higher educational signal will not change the expected average productivity in the firm because of the job productivity constraints, which is not tree in a firm with higher job requirements. Thus, even if the firm attempts to hire from a higher educational signal, it will be outbid by firms with higher job requirements. Therefore, the profit-maximizing choice is to hire workers from the corresponding educational signaling group.

(8) Firm [F.sub.1]'s wage does not change because it replaces a worker whose productivity was constrained to [v.sub.1] with a worker whose true productivity is [v.sub.1].

(9) The full model covering all educational signaling groups and all time periods is available from the author on request.

(10) The ranges of ages are 1979 (16-22), 1985 (22-28), 1990 (26-33), 1994 (30-37), and 1998 (34-41).

(11) See Jaeger and Page (1996) for a detailed examination of the impact of this change on the level of diploma effects.

(12) The BACH variable contains individuals with exactly 16 years of completed education (before 1992) and individuals with a bachelor's degree (after 1992).

(13) It can be argued that the diploma effect represents a return to human capital. This view holds that it is necessary to complete all four years of courses of a degree to get all benefits. Thus, a single year of education doesn't account for one-quarter of the worth of the acquired degree and the increased return to the fourth year of college is actually a human capital return to completing the degree. An alternative human capital interpretation of diploma effects is offered by Chiswick (1973) and adopted by Lange and Topel (2006). In their view, diploma effects are generated by a selection process that leads students with low returns to education to drop out of school. Only students with high returns to education remain to complete the diploma year.

(14) The mean potential experience level for individuals with a bachelor's degree is 9.06 years. Using the estimated coefficients on the BACH variable and its interactions with potential experience (Table 3, column 5) the cumulative diploma effect is calculated as 0.162 + (9.06 X 0.036) + ([9.06.sub.2] x -0.002) = 0.0324. The percentage increase in wages is calculated as exp (diploma effect) - I.

(15) Result available from the author on request.

Steffen Habermalz, University of Nebraska--Kearney, Department of Economics, College of Business and Technology, West Center 306C, 905 East 25th Street, Kearney, NE 68849, USA; E-mail [e-mail].

Table 1. Descriptive Statistics

                                         Synthetic
                       Full Sample         Cohort

Variable              Mean      SD      Mean     SD

Wage                  10.47     9.54    10.31   8.59
Real wage              8.23     6.63     7.75   5.56
Log real wage          1.94     0.58     1.90   0.54
Years of education    13.09     2.59    13.22   2.35
Experience            17.61    12.51    10.47   6.20
Age                   36.76    12.28    29.74   6.16
LOW                    0.62     0.49     0.65   0.48
BACH                   0.15     0.35     0.17   0.37
PROF                   0.08     0.28     0.07   0.25
Part time              0.21     0.40     0.19   0.40
Married                0.60     0.49     0.55   0.50
Sex                    0.52     0.50     0.52   0.50
Black                  0.10     0.29     0.09   0.29
Other race             0.04     0.20     0.04   0.20
Observations         395,966           88,218

SD, standard deviation.

Table 2. OLS Estimation (Full Sample)

                          79/85                      85/90

                    Low Exp.       All        Low Exp.       All
Variable              (1)          (2)          (3)          (4)

Education           0.062 ***    0.058 ***    0.076 ***    0.067 ***
  (years)           (19.98)      (51.34)      (26.30)      (58.33)
Pot.                0.06 ***     0.035 ***    0.049 ***    0.034 ***
  experience        (12.69)      (83.50)      (10.95)      (88.57)
Pot.               -0.003 ***   -0.001 ***   -0.003 ***   -0.001 ***
  experience (2)   -(6.67)      -(64.99)     -(5.59)      -(67.22)
LOW                 0.04 ***     0.113 ***   -0.065 ***    0.076 ***
                    (3.24)       (20.04)     -(6.01)       (13.97)
LOW x               0.008 ***   -0.004 ***    0.017 ***   -0.003 ***
  experience        (3.52)      -(17.93)      (6.87)      -(15.27)
BACH                0.037        0.232 ***    0.05 **      0.245 ***
                    (1.61)       (23.99)      (2.23)       (25.48)
BACH x              0.026 ***   -0.005 ***    0.024 ***   -0.006 ***
  experience        (8.53)      -(13.78)      (6.62)      -(17.37)
PROF                0.058 *      0.274 ***    0.078 **     0.278 ***
                    (1.87)       (21.99)      (2.33)       (22.36)
PROF x              0.025 ***   -0.007 ***    0.023 ***   -0.007 ***
  experience        (6.30)      -(14.31)      (4.46)      -(15.08)
Other Controls      Yes          Yes          Yes          Yes
[R.sup.2]           0.353        0.402        0.438        0.406
Observations        22,848       145,341      24,268       178,862

                          90/94                     94/98

                    Low Exp.       All        Low Exp.       All
Variable              (5)          (6)          (7)          (8)

Education           0.066 ***    0.065 ***    0.054 ***    0.062 ***
  (years)           (21.46)      (54.12)      (15.39)      (52.32)
Pot.                0.034 ***    0.036 ***    0.047 ***    0.036 ***
  experience        (6.57)       (87.09)      (8.17)       (81.41)
Pot.               -0.001       -0.001 ***   -0.003 ***   -0.001 ***
  experience (2)   -(1.35)      -(67.10)     -(4.70)      -(65.34)
LOW                -0.034 ***    0.09 ***    -0.014        0.092 ***
                   -(3.05)       (15.42)     -(0.97)       (14.85)
LOW x               0.024 ***   -0.002 ***    0.023 ***    0.0004 *
  experience        (6.62)      -(10.02)      (5.44)      -(1.82)
BACH                0.15 ***     0.327 ***    0.228 ***    0.374 ***
                    (6.09)       (32.61)      (8.44)       (37.33)
BACH x              0.029 ***   -0.006 ***    0.029 ***   -0.004 ***
  experience        (5.91)      -(14.88)      (5.25)      -(10.25)
PROF                0.123 ***    0.389 ***    0.372 ***    0.509 ***
                    (3.57)       (28.63)      (7.27)       (34.76)
PROF x              0.049 ***   -0.005 ***    0.025 **    -0.005 ***
  experience        (6.78)      -(10.00)      (2.53)      -(8.42)
Other Controls      Yes          Yes          Yes          Yes
[R.sup.2]           0.402        0.381        0.397        0.363
Observations        20,890       173,141      18,271       160,198

The numbers in parentheses are t values. Regressions also include
dummy variables for year. Other controls are part time, region,
married, gender, and race. Odd numbered columns use samples limited to
zero to three years of potential experience in the first year and
corresponding years in the second year of the sample. Even numbered
columns use all observations (aged 16-65).
All estimations use robust standard errors.

* Statistically significant at the 10% level.

** Statistically significant at the 5% level.

*** Statistically significant at the 1% level.

Table 3. OLS Estimation (Synthetic) Panel Regressions and Sensitivity
Analysis

                                  Male                Female

                            (1)           (2)           (3)

Education (years)        0.071 ***     0.068 ***     0.073 ***
                         (28.20)       (28.11)       (26.28)
Pot. experience          0.07 ***      0.048 ***     0.028 ***
                         (21.30)       (14.88)       (8.74)
Pot. experience (2)     -0.001 ***    -0.001 ***     0.0003 ***
                        -(11.38)      -(7.65)       -(2.86)
LOW                      0.072 ***     0.013         0.08 ***
                         (4.90)        (0.92)        (4.87)
LOW x experience         0.01 ***      0.013 ***     0.017 ***
                         (3.23)        (4.25)        (5.60)
LOW x experience (2)     0.0005 ***    0.0005 ***   -0.001 ***
                        -(3.58)       -(3.51)       -(6.76)
BACH                     0.154 ***     0.067 ***     0.156 ***
                         (5.96)        (2.69)        (6.20)
BACH x experience        0.03 ***      0.032 ***     0.05 ***
                         (5.82)        (6.51)        (10.48)
BACH x experience (2)   -0.001 ***    -0.001 ***    -0.002 ***
                        -(4.72)       -(4.32)       -(9.45)
PROF                     0.224         0.13          0.13
                         (5.75)        (3.38)        (3.54)
PROF x experience        0.035 ***     0.037 ***     0.064 ***
                         (4.09)        (4.44)        (8.24)
PROF x experience (2)   -0.002 ***    -0.001 ***    -0.003 ***
                        -(3.57)       -(3.23)       -(6.36)
Other controls           No            Yes           No
[R.sup.2]                0.244         0.285         0.25
Observations             45,981                      42,237

                          Female                 All

                            (4)           (5)           (6)

Education (years)        0.073 ***     0.067 ***     0.07 ***
                         (27.34)       (35.07)       (38.87)
Pot. experience          0.016 ***     0.054 ***     0.034
                         (5.10)        (22.69)       (14.85)
Pot. experience (2)      0.0001       -0.001 ***    -0.001 ***
                        -(0.50)       -(12.01)      -(6.61)
LOW                      0.014         0.07 ***      0.016
                         (0.86)        (6.25)        (1.49)
LOW x experience         0.02 ***      0.01 ***      0.014 ***
                         (6.62)        (4.21)        (6.49)
LOW x experience (2)    -0.001 ***    -0.001 ***    -0.001 ***
                        -(6.74)       -(5.17)       -(6.05)
BACH                     0.047 *       0.162 ***     0.072 ***
                         (1.88)        (8.99)        (4.15)
BACH x experience        0.055 ***     0.036 ***     0.04 ***
                         (11.66)       (10.01)       (11.47)
BACH x experience (2)   -0.002 ***    -0.002 ***    -0.002 ***
                        -(9.38)       -(8.59)       -(8.61)
PROF                     0.04          0.196         0.094
                         (1.11)        (7.21)        (3.59)
PROF x experience        0.064 ***     0.048 ***     0.047 ***
                         (8.42)        (8.17)        (8.25)
PROF x experience (2)   -0.002 ***    -0.002 ***    -0.002 ***
                        -(5.84)       -(6.81)       -(5.74)
Other controls           Yes           No            Yes
[R.sup.2]                0.284         0.226         0.306
Observations                           88,218

The numbers in parentheses are t values. Other controls are part time,
region, married, gender, and race. The regression uses a synthetic
panel data set constructed from 1979 (ages 16-22), 1985 (22-28), 1990
(26-33), 1994 (30-37), 1998 (34-41) to simulate a cohort early in its
work life. All estimations use robust standard errors.

* Statistically significant at the 10% level.

** Statistically significant at the 5% level.

*** statistically significant at the 1 level.