Experience, Tenure, and the Perceptions of Employers.

Terrell, Dek

Danielle Lewis [*]

Dek Terrell [+]

This paper examines how group-based assessments concerning employee ability impact employee compensation. The employer learns about worker ability through Bayesian updating, creating an additional channel for wage growth that is not available to those workers with only general labor market experience. Consistent with the model's predictions, results from National Longitudinal Survey of Youth (NLSY) indicate that black workers fare much better relative to white workers in returns to tenure than in returns to experience. Finally, parameter estimates in the structural model suggest that employers initially undervalue black males but that their wages rise with learning by employers over time.

1. Introduction

On average black males earn lower wages than white males, just as average wages differ across many groups. This paper examines one explanation for this wage gap: the possibility that employers underestimate the ability of workers in one or more groups. In particular, this paper proposes a model that provides explicit predictions about the affect of employer's perceptions on workers' returns to general experience and tenure on the job. We then examine the wage growth of young males to see whether patterns are consistent with the model.

Economic theory provides many other explanations for differences in wages across groups. One possible explanation is that, on average, the marginal product of labor is lower for one group than other groups. There are many possible explanations for the disparity in the marginal productivity across groups. Card and Krueger (1992) argue that differences in the quality of education between black and white workers have been a key factor in generating the wage gap over time. However, wages may also differ due to some unobservable factors. Herrnstein and Murray's (1994) controversial Bell Curve asserts that wage differences simply reflect differences in average intelligence across groups. Lundberg and Startz (1998) offer a dynamic model where one group possesses lower ethnic capital, perhaps as the result of past discrimination, which leads to persistent wage gaps.

Discrimination offers another explanation for observed wage gaps. Dainty and Mason (1998) summarize the theories and empirical evidence of discrimination. In Becker's (1971) neoclassical "taste for discrimination model," discrimination occurs because employers, managers, or customers prefer not to associate with the members of a specific group. Statistical discrimination provides another explanation. In these models, the variance of ability is higher for one group than another group. It is interesting to note that the implications of statistical discrimination vary across models. In Phelps's (1972) original model, some individuals in the high-variance group earned higher wages than the other group, while others earn lower wages. However, the average wage of the high-variance group and low-variance group was equal. Lundberg and Startz's (1983) extension of this model generates lower average wages for the high-variance group. However, Berk (1999) offers an alternative model where the high-variance group earns higher wages.

Still another potential explanation for wage differences is that employers inaccurately perceive some groups as less productive. The literature contains both survey evidence and experiments that suggest that employers perceive blacks negatively in terms of one or more attributes that affect worker productivity. [1] Furthermore, learning may not quickly eliminate misperceptions. Almeida and Kanekar (1989) and Wong, Derlega, and Colson (1988) provide evidence that agents tend to attribute positive outcomes to good luck if they begin with negative opinions about a group. Given these results, Farmer and Terrell (1996) suggest the possibility that employers underestimate the ability of workers in some groups.

Farmer and Terrell (1996) examine the impact of inaccurate perceptions of ability in a model with two types of learning. In their model, employers learn about individual ability through observing individual output but use group averages to estimate group ability. A key result of that model is that employers' perceptions of average group ability do not always converge to the true average. This result is driven by the fact that perceptions affect the return to investment in human capital.

This paper proposes a variant of the Farmer and Terrell model that provides explicit predictions about wage growth of undervalued workers as they accumulate tenure on the job and experience. Implicitly, we take employer perceptions of group ability as given and do not allow them to change with observations of individual ability. [2] Clearly, the output of a single worker tells the employer much more about her ability than the average ability of a group of millions. Thus, we focus exclusively on the problem of learning about individual ability. The key prediction of our model is that undervalued employees benefit from employer learning, which boosts the returns to tenure on the job.

To investigate the empirical content of this model, we analyze the returns to general labor market experience and tenure on the job for black and white workers in the National Longitudinal Survey of Youth (NLSY). Then we estimate the parameters of the employer's prior distribution. The prior mean summarizes the extent to which the employer's prior assessments undervalue black workers and the prior variance measures the strength of these beliefs and ascertains the rate of learning.

Section 2 of this paper specifies the theoretical model, and section 3 summarizes the data. Section 4 contains estimates of the returns to general labor market experience and tenure on the job for blacks and whites and examines returns across groups stratified on the basis of occupation and AFQT score. Section 5 includes the structural model's prior parameter estimates, and section 6 contains some final remarks.

2. The Model

We assume a competitive labor market where a worker supplies one unit of labor each period and is paid his expected marginal product. The output of the worker is determined by the Cobb-Douglas production function:

y = [A.sup.[alpha]][X.sup.[beta]][J.sup.[gamma]][e.sup.[epsilon]], (1)

where y denotes worker output, A denotes worker ability, X denotes general labor market experience, J denotes job specific experience, and [epsilon] is a stochastic error component. We assume that [epsilon] [sim] IID N(O, [[sigma].sup.2]). Following, Becker's (1975) and Mincer's (1974) human capital models, workers accumulate general human capital with general work experience and specific human capital with tenure on the job. We assume that the parameters [alpha], [beta], and [gamma] are constant over time and add subscripts to y, X, J, and [epsilon] to denote values for specific time periods. Adding subscripts and taking the natural logarithms implies that the employee's output in period t is

ln [y.sub.t] = [alpha] ln A + [beta] ln [X.sub.t] + [gamma] ln [J.sub.t] + + [[epsilon].sub.t]. (2)

We assume that worker ability (A) remains constant over time. However, wages are determined by the employer's perception of worker ability, which does change with observations of output. We summarize the employer's initial belief about employee ability with the prior distribution:

P([alpha] ln A) [sim] N([[micro].sub.prior], [[[sigma].sup.2].sub.prior] (3)

As in most applications, the mean of a normal prior distribution reflects the best guess about the parameter, and the variance is a measure of the certainty of beliefs. Because prior opinions depend on the employee's group, [[micro].sub.prior] and [[[sigma].sup.2].sub.prior] vary across worker groups. [3] For new employees, the employer has no other information regarding ability; thus, E[[alpha] ln A] = [[micro].sub.prior], and the employee's initial log wage is 1n [w.sub.0] = E[ln [y.sub.0] = [[micro].sub.prior] + [beta] 1n [X.sub.0]. [4] In later periods, the employer updates priors on the basis of observations of output. [5] Thus, after T observations of output, the employer sets the wage in T + 1 based on the conditional expectation:

ln [w.sub.T+1] = E[ln [y.sub.T+1]\[y.sub.1],[y.sub.2],...,[y.sub.T]] = E[[alpha] ln A]\[y.sub.1],[y.sub.2],...,[y.sub.T]] + [beta] ln [X.sub.T+1] + [gamma] ln [J.sub.T+1]. (4)

The key problem is to determine E[[alpha] ln A]\ [y.sub.1], [y.sub.2],...,[y.sub.T]], the employer's perception of ability conditional on T observations of output. We approach the problem by assuming that the employer updates priors using Bayesian updating. In this approach, the first step requires finding the distribution of output conditional on ability. Based on Equation 2, we know that

P(ln [y.sub.t]\[alpha] In A) [sim] N([alpha] ln A + [beta] ln [X.sub.t] + [gamma] ln [J.sub.t], [[sigma].sup.2]) or (5)

f(ln [y.sub.t]\[alpha] ln A) = 1/[sigma][square root]2[pi] exp [[-1/2[[sigma].sup.2][(ln [y.sub.t] - [alpha] ln A - [beta] ln [X.sub.t] - [gamma] ln [J.sub.t]).sup.2]]. (6)

Assuming independence of the errors over time, we can summarize the distribution for these T observations of output, conditional on ability, as

f(ln [y.sub.t], ln [y.sub.2], ..., ln [y.sub.T]\[alpha] ln A)

= [(2[pi][[sigma].sup.2]).sup.-T/2] exp[-1/2[[sigma].sup.2] [[[sigma].sup.T].sub.t=l] [(ln [y.sub.t] - [alpha] ln A - [beta] ln [X.sub.t] - [gamma] ln [J.sub.t]).sup.2]]. (7)

We combine the employer's prior information with the observed levels of output to summarize the employer's assessment of worker ability after T periods using Bayes's rule:

P([alpha] ln A\ln [y.sub.1],..., ln [y.sub.T]) = P(ln [y.sub.1], ..., ln [y.sub.T]\[alpha] ln A)P([alpha] ln A)/P(ln [y.sub.t], ..., ln [y.sub.T]) (8)

This problem simply combines a normal prior with known variance with a normal likelihood function with known variance and implies the following posterior density function: [6]

P([alpha] ln A\ln [y.sub.1], ..., ln [y.sub.T]) [sim] N([[micro].sub.T], [[[sigma].sup.2].sub.T]). (9)

where

[[micro].sub.T] = [[[sigma].sup.2].sub.T][[[[sigma].sup.T].sub.t=l] (ln [y.sub.t] - [beta] ln [X.sub.t] - [gamma] ln [J.sub.t])/[[sigma].sup.2] + [[micro].sub.prior]/[[[sigma].sup.2].sub.prior]], and [[[sigma].sup.2].sub.T] = [(T/[[sigma].sup.2] + 1/[[[sigma].sup.2].sub.prior]).sup.-1].

A closer look at Equation 9 reveals some interesting features of the model. The mean perceived log ability level of the worker conditional on T observations is a weighted average of two components. The first component consists of the level of ability that would be predicted from observed output by solving the production function for [alpha] ln(A) and assuming that the error term has mean zero. This predicted ability is the employer's best guess of the worker's ability from the T observations of output. The second term is the employer's prior assessment of worker ability. The posterior mean log ability is a weighted average of the prior about ability and the level of ability predicted on the basis of job performance. The weights of the two terms are the inverse of the respective variances. The variance of the updated distribution for log ability is a combination of the prior variance and the variance of the average log ability calculated from observed output.

The link between updating and tenure occurs because the employer learns only whether the employee accumulates tenure on the job. More observations of employee output reduce the influence of prior beliefs, thereby raising the weight on observed output. This implies that undervalued employees will benefit from increased tenure with the same employer because of more observations of the employee's productivity. Likewise, for employees whose ability is initially overvalued, the learning process will partially offset any increases in job-specific human capital and retard wage growth.

To further clarify the link between tenure, learning, and wages, consider the simplest case where the employer observes output once for every period of tenure. In this case, we can simply replace T with the employee's current level of tenure on the job (J) in Equation 9 to get [7]

[[micro].sub.J] = [[[sigma].sup.2].sub.J][[[[sigma].sup.J].sub.t=l] (ln [y.sub.t] - [beta] ln [X.sub.t] - [gamma] ln t)/[[sigma].sup.2] + [[micro].sub.prior]/[[[sigma].sup.2].sub.prior]], and [[[sigma].sup.2].sub.J] = [(J/[[sigma].sup.2] + 1/[[[sigma].sup.2].sub.prior]).sup.-1]. (10)

Plugging Equation 10 in for [alpha] ln A in Equation 2 provides the employee's wage rate after J + 1 periods of tenure on the job:

ln [w.sub.J+1] = [[[sigma].sup.2].sub.J][[[[sigma].sup.J].sub.t=1] (ln [y.sub.t] - [beta] ln [X.sub.t] - [gamma] ln t)/[[sigma].sup.2] + [[micro].sub.prior]/[[[sigma].sup.2].sub.prior]] + [beta] ln [X.sub.T+1] + [gamma] ln(J + 1). (11)

From Equation 11, we see that tenure plays two roles in the model. The last term in the equation, [gamma] ln(J + 1), reflects the return to specific human capital. The first term indicates that tenure also affects wages by influencing the employer's assessment of worker ability through learning. If a worker is initially undervalued, additional years of tenure lead to increases in perceived ability and thus a second channel for wage growth. Notice that there is no learning with only general experience. Knowledge of past output is not transferred to new employers, and thus the prior again determines the initial wage in each new job. [8]

Clearly, the next issue is whether there is any empirical evidence to support the model. We investigate this issue on the basis of a comparison of wages for black and white male workers. The earlier discussion suggests that employers may systematically underestimate the ability of black workers. If this indeed occurs, the model suggests that returns to tenure for black workers should include a learning component not included for white workers. We investigate this possibility first by computing estimates of the returns to tenure and experience for black and white workers in section 4. In section 5, we return to the model to directly estimate the structural parameters.

3. Data

The empirical portion of this paper is based on wage growth analysis for young black and white males using panel data taken from the 1979--1994 NLSY. The NLSY consists of individuals who were between the ages of 14 and 21 as of January 1, 1978. The goal of our analysis is to determine whether there is any evidence that black workers are initially undervalued and, if so, to determine how fast employers update inaccurate assessments of ability.

Following Wolpin (1992) and Bratsberg and Terrell (1998), we address these questions using a sample of terminal high school graduates. We define a terminal high school graduate as someone whose last month enrolled in school coincides with the month he graduated from high school. [9] The NLSY data provide information concerning the respondent's last month and year enrolled in school as well as the month and year the respondent graduated from high school. We assume that graduation and the last date of enrollment occur on the 15th of each month.

Eliminating agricultural, military, and government workers leaves a sample of 339 black respondents and 703 white respondents who were terminal high school graduates. Each individual in our sample has up to 16 observations corresponding to the years 1979-1994. The sample respondents enter the sample during the year following graduation. This leaves a final sample of 2653 observations for black workers and 5985 observations for white workers. [10] Each observation focuses on information related to the job reported as the Current Population Survey (CPS) job in the NLSY data set. Bratsberg and Terrell (1998) find that potential experience exaggerates actual experience for black workers and that using potential experience lowers the estimated return to experience. For this reason, we construct a measure of experience using the NLSY work history data. In particular, the data set includes a variable summarizing each worker's employment status for each week after January 1, 1979. Our algorithm adds one week of expe rience for every week the individual worked between high school graduation and the interview date for the observation. [11] For tenure, we use the NLSY tenure variable that is also based on actual weeks of work. Table i contains summary statistics for the data that reveal substantial differences in many attributes across groups.

4. Estimates of the Return to Tenure and Experience from Wage Regressions

The first goal of the empirical analysis is to search for evidence that employers' priors initially undervalue black workers. The most basic prediction of the model is that returns to tenure for black workers reflect an employer learning component not present in returns to experience. Thus, the model predicts that black workers will fare better in returns to tenure than in returns to general experience.

This section estimates the wage growth attributable to tenure and experience for black and white terminal high school graduates. Our initial approach is to estimate returns for both groups, with and without AFQT in the model. The remainder of this section investigates whether patterns of wage growth differ in subgroups, divided on the basis of occupation and AFQT score. After investigating general patterns in returns, we turn to the problem of estimating the parameters of the employer's prior distribution for both races in section 5.

Many studies (Abraham and Farber 1987; Altonji and Shakotko 1987; Marshall and Zarkin 1987; Topel 1991) note that estimates of tenure and experience may be biased because of the correlation between tenure and experience and unobservable determinants of wages. Our initial wage regression is identical to a model used by Bratsberg and Terrell (1998). However, this paper has the advantage of using three more years of data than the Bratsberg and Terrell (1998) study. Although Bratsberg and Terrell (1998) find that the returns differed substantially across the estimators, the relative returns to tenure and experience for black and white workers did not appear very sensitive to the estimator choice. Given this result, we focus on ordinary-least-squares (OLS) estimates for the model parameters.

Table 2 contains the results of a regression of log wages on individual characteristics, including tenure and experience. Following Bratsberg and Terrell (1998), we include a quadratic term in tenure and experience to allow for a diminishing return to both types of human capital. Columns 1 and 2 contain OLS estimates for the model considered in the previous study with three additional years of data. These results correspond closely to the OLS results reported by Bratsberg and Terrell (1998).

The critical question is whether the returns to tenure and experience, defined by the coefficients on experience, experience squared, tenure, and tenure squared, differ across the two groups. Table 3 contains the cumulative wage growth attributable to tenure and experience for both groups of workers, and Figure 1 graphs these returns. The top left panel contains a graph of the cumulative wage growth due to tenure over an eight-year period of tenure for black and white workers, computed from the numbers in columns 1 and 2 of Table 2. The results show very similar returns to tenure for black and white workers, with black workers earning a slightly higher return to tenure. Black workers earn 37.7% (exp[0.320] - 1) cumulative wage growth due to eight years of tenure, while wages of white workers rise by 31.0% with eight years of tenure. Moreover, a t-test fails to reject the hypothesis that cumulative wage growth due to two, four, six, or eight years of tenure is equal for both groups at the 5% significance level. [12] Thus, the difference in returns to tenure might be attributable to sampling variation.

Below this graph is a similar graph for experience. White workers earn much higher returns to general labor market experience than do black workers. This difference in returns to general experience translates into much higher wage growth over time for white workers. The cumulative return to eight years of experience is 24.1% for white workers but only 9.4% for black workers. Not surprisingly, a t-test using standard errors in Table 3 rejects the hypothesis of equal wage growth due to experience across races at all time horizons considered.

Several other studies also find this pattern of results in a comparison of returns for black and white workers. Altonji and Shakotko (1985) focus on returns to tenure and experience for workers in the Panel Study of Income Dynamics. They find roughly equal returns to tenure for black and white workers but find that the white worker's returns to general experience greatly exceed those of black workers. Wolpin (1992) estimates the parameters of a structural model and finds similar results for terminal high school graduates in NLSY data. Likewise, Bratsberg and Terrell (1998) obtain similar results for NLSY wage regressions using several alternative estimators.

In the context of the model derived in section 2, this stark contrast is easily explained. We would assume that if learning did not occur, the disparity between the returns to tenure and experience for black and white workers would be the same. This suggests that black workers would trail in returns to both experience and tenure. The fact that the returns to tenure are equal across groups reflects the employer's learning that boosts the returns to tenure for the undervalued black workers.

Neal and Johnson (1996) suggest including the Armed Forces Qualification Test (AFQT) in the wage regression to proxy for such unobserved skills and find that this variable eliminates much of the racial gap in wages. Columns 3 and 4 in Table 2 address this issue by adding the AFQT score to the basic regression. Some coefficients are affected by the variable--notably the intercepts appear to converge in these models. However, the tenure and experience coefficients are virtually unaffected by the addition of the AFQT to the model, and Table 3 shows that the profiles do not change at all. Controlling for AFQT does not change the fact that black workers experience lower wage growth and that the gap stems from lower returns to general experience for black workers.

Another question lies in the source of these gaps. Perhaps black workers simply work in occupations that generate lower growth in wages with experience. To address this issue, we divide the sample into worker subsamples based on occupation using Boston's (1990) categorization. Boston categorizes all CPS occupation codes as either primary or secondary sector on the basis of training. The primary-sector occupations include professionals, technical workers, clerical workers, managers, officials, and proprietors. The secondary-sector occupations include workers reporting occupations such as laborer, retail sales, or food service. [13] For white workers, 3011 of 5985 observations (50%) fall into the primary-sector classification, while 848 of 2653 observations (32%) of black workers are considered primary-sector workers.

Table 4 contains parameter estimates for these subsamples. Table 5 and the remaining graphs of Figure 1 contain the predicted wage growth due to tenure and experience for these groupings. Surprisingly, there appears to be little or no difference in the returns to tenure or experience in the primary-sector samples, and t-tests based on the numbers in Table 5 fail to reject the hypothesis of equal returns to tenure and experience at two-, four-, six-, and eight-year horizons. Black workers with primary-sector occupations appear to enjoy the same wage growth as white workers in the same group.

The final column of Figure 1 contains the wage profiles for secondary-sector workers. For both groups, cumulative wage growth due to general experience is lower than that in primary-sector occupations. In fact, as can also be seen in Table 5, black workers receive almost no return to general experience in secondary-sector occupations, earning only 1.8% wage growth with eight years of experience compared to a 16.2% received by secondary-sector white workers.

Given this difference in returns to experience, one might also expect a similar result for returns to tenure for the secondary-sector occupations. However, the results for black workers stand in stark contrast. Black workers in secondary-sector occupations receive higher returns to tenure than those in primary-sector occupations (37.6% vs. 28.7% with eight years of tenure) and in fact earn higher returns to tenure than white workers of either occupational category. [14] Of the four groupings by race and occupation, black workers in secondary-sector occupations stand out. They earn far lower returns to general experience and higher returns to tenure than all other workers do. Because 68% of black workers fall into this category, they also drive the results for the full sample. In the context of the theoretical model, these results suggest that employers undervalue black workers in secondary-sector occupations. We will return to this and other explanations for this result later.

Another interesting grouping is on the basis of AFQT score. Altonji and Pierret (1997) find that the correlation between AFQT and wages grows over time and attribute this to the fact that employers are learning about ability over time. This finding reinforces the idea that AFQT may serve as a measure of unobserved ability and suggests that returns to tenure may differ with AFQT score. For example, one possibility is that high-AFQT black workers might benefit from more learning and thus possess much higher returns to tenure. To investigate this possibility, we group all workers into two categories, those scoring above the 20th percentile on the AFQT (high AFQT) and those scoring in the 20th percentile or below (low AFQT). The majority of white workers fit into the high-AFQT category (79% of observations), while the majority of black workers fit into the low-AFQT category (71% of observations).

Tables 6 and 7 present results for the AFQT subgroups by race, and Figure 2 contains graphs of the predicted wage growth with tenure and experience. [15] These results contain no evidence of greater learning among black high-AFQT workers and closely mirror the occupation results. For high-AFQT workers, the profiles are virtually identical for black and white workers, but low-AFQT white workers earn lower returns to experience and tenure, while low-AFQT black workers earn very small returns to general experience but very large returns to tenure on the job. [16]

In our samples, 71% of black workers and 61% of white workers with low AFQT hold secondary-sector jobs. Thus, there is an overlap between the occupational and test score groupings, though the groups are not identical. However, low-AFQT workers likely share other attributes as well. Neal and Johnson (1996) find that family background and secondary school attributes explain a good portion of the variation in AFQT scores. Workers who fall in these groups also may live in poorer geographic areas and perhaps share common cultural attributes. While our results should not be considered as identifying a single defining attribute, one group, whether defined on the basis of occupation or test score, stands out. Secondary-sector black workers or black workers with low AFQT scores earn almost no returns to general experience but very high returns to tenure on the job.

There are many potential explanations for the results. For example, Lazear's (1979) contract theory asserts that employers may choose steeper earnings profiles to reduce worker shirking. If employers perceive the risk of shirking to be larger among black workers, they may choose a contract with lower initial wages but higher returns to tenure. Likewise, differences in training and affirmative action legislation could generate differences in the earnings profiles of black and white workers. While our model can explain results for the full sample, employers must identify only a subset of black workers as less productive than other workers for the theory presented in section 2 to explain the results in subsamples. If that model does provide all or part of the explanation, the critical question is, How fast do employers learn? The reduced forms cannot answer this question, so we now turn to the problem of estimating the structural parameters of the model.

5. Estimating the Parameters of the Structural Model

The general model summarized in section 2 describes how initial perceptions of employers affect wages of employees. In this section, we estimate the parameters of the structural model, allowing the perceptions to differ across races. The estimation requires translating the model of individual wage growth to averages across groups and also requires several simplifying assumptions. However, this exercise serves to illustrate the model outlined in section 2 and allows an assessment of whether the model can generate the same patterns found in section 4.

The key feature of that structural model is Equation 9, which summarizes the employer's assessment of employee ability after observing T periods of output. The model allows for the possibility that employee's ability varies across groups. Let [micro] denote the mean value of [alpha] ln A in a particular group. The employer's assessment of [alpha] ln A based on output is ln [y.sub.t] - [beta] ln [X.sub.t] -- [gamma] ln [J.sub.t] and furthermore E[ln [y.sub.t] -- [beta] ln [X.sub.t] - [gamma] ln [J.sub.t]] = [micro] because [epsilon] has mean zero. Substituting the expected value into Equation 9 and normalizing the variance of output to one reduces Equation 9 to

E[[[micro].sub.t]] = T[[[sigma].sup.2].sub.prior][micro]/T[[[sigma].sup.2].sub.prior] + 1 + [[micro].sub.prior]/T[[[sigma].sup.2].sub.prior] + 1. (12)

Notice that Equation 12 is quite intuitive. The first term contains true ability [micro], which reflects the observations of output weighted by T[[[sigma].sup.2].sub.prior]/(T[[[sigma].sup.2].sub.prior] + 1). The second term contains the prior mean, weighted by 1/(T[[[sigma].sup.2].sub.prior] + 1). As the number of observations of employee output grows, the employer places more weight on the level of ability implied by output (which on average is [micro]) and less weight on the prior assessment. As previously stated, larger values of [[[sigma].sup.2].sub.prior] imply that the employer has less confidence in the initial assessment of ability. Not surprisingly, Equation 12 implies that larger [[[sigma].sub.2].sup.prior] cause the employer's assessment of ability to converge to true ability much faster. Finally, notice that if the employer's prior assessment is accurate ([[micro].sub.prior] = [micro]), we expect perceived ability to equal actual in every period.

With our assumption of a perfectly competitive labor market, Equation 2 supplies wages of each employee. Taking the expected value of this equation generates expected wages:

E[ln [w.sub.T] = E[[alpha] ln A + [beta] ln [X.sub.T] + [gamma] ln [J.sub.T]] = E[[micro].sub.T] + [beta] ln [X.sub.T] + [gamma] ln [J.sub.T]

= T[[[sigma].sup.2].sub.prior][micro] / T[[[sigma].sup.2].sub.priorA] + 1 + [[micro].sub.prior]/T[[[sigma].sup.2].sub.prior] + [beta] ln [X.sub.T] + [gamma] ln [J.sub.T]

= [J.sub.T][[[sigma].sup.2].sub.prior][mirco] / [J.sub.T][[[sigma].sup.2].sub.prior] + 1 + [[micro].sub.prior] / [J.sub.T][[[sigma].sup.2].sub.prior] + 1 + [beta] ln [X.sub.T] + [gamma] ln [J.sub.T]. (13)

Notice that in the final step, we assume that the employee's tenure supplies the number of observations of output and substitute [J.sub.T] for T.

Let the subscripts 0 and 1 denote the model parameters for white workers and black workers, respectively. Because we are interested in whether black workers are undervalued, we assume that prior assessments are accurate for white workers, or [[micro].sub.prior] = [mirco] for this group. This implies no learning on average for white workers, and under this assumption wages of white workers are simply

E[ln [w.sub.t0] = [[micro].sub.0] + [[beta].sub.0]ln [X.sub.t0] + [[gamma].sub.0]ln [J.sub.t0]. (14)

Black workers may benefit from learning, and thus wages are still determined by Equation 13:

E[ln [w.sub.tl] = [J.sub.tl][[[sigma].sup.2].sub.prior,l][[micro].sub.l] / [J.sub.tl][[[sigma].sup.2].sub.prior.l] + 1 + [[micro].sub.prior.l] / [J.sub.tl] [[[sigma].sup.2].sub.prior.l] + 1 + [[beta].sub.t] ln [X.sub.tl] + [[gamma].sub.t]ln [J.sub.tl]. (15)

Letting the subscript i refer to specific individuals, [D.sub.i] denotes a dummy variable set equal to one for black workers, and combining Equations 14 and 15 yields

E[ln [w.sub.ti]] = [[micro].sub.0] + [D.sub.i]([J.sub.t1][[[sigma].sup.2].sub.prior,1]([[micro].sub.1] - [[micro].sub.0])/[J.sub.t1][[[sigma].sup.2].sub.prior,1] + 1 + [[micro].sub.prior,1] - [[micro].sub.0]/[J.sub.t1][[[sigma].sup.2].sub.prior,1] + 1) + [[beta].sub.1] ln [X.sub.t1] + [[gamma].sub.1] In [J.sub.t1] + [D.sub.i]([[beta].sub.t] - [[beta].sub.0]) ln [X.sub.ti] + [D.sub.i]([[gamma].sub.1] - [[gamma].sub.0] ln [J.sub.ti]. (16)

In principle, Equation 16 could be estimated using nonlinear least squares. However, the likelihood function for this problem proved quite flat. Intuitively, this occurs because it is difficult to separate learning from the group-specific returns to tenure. Thus, we add two simplifying assumptions to estimate the model.

First, we assume that the difference in returns to tenure across groups equals the difference in returns to experience, or [[beta].sub.1] - [[beta].sub.0] = [[gamma].sub.1] - [[gamma].sub.0] = [delta]. This assumes that any gap in returns to experience would also appear in returns to tenure in the absence of any learning. This helps to identify the model because any difference in the tenure and experience profiles is attributed to learning.

Second, we choose values for [[micro].sub.1] - [[micro].sub.0] and estimate the other parameters conditional on this assumed difference in true ability. Intuitively, it is difficult to determine whether the initial wage gap should be attributed to a gap in true or perceived ability, and thus parameter estimates in a model with both parameters are imprecise. The statistical model conditional on an assumed value for the gap in true ability eliminates this problem and leads to precise estimates for the other parameters.

Table 8 contains parameter estimates for the structural model. Column 1 results are based on assuming no difference in true ability, while columns 2, 3, and 4 assume that wages of black workers trail those of white workers by 3%, 6%, and 9%, respectively, because of premarket factors. The results in column 1 indicate that employers initially perceive black workers as 39% less productive, while those in columns 2, 3, and 4 suggest that initial perceptions place black workers at roughly 17% to 18% less productive. The parameter [[[sigma].sup.2].sub.prior] measures the strength of the employer's beliefs in the initial assessments, with higher values implying less faith in the prior and faster learning. The results for [beta] and [gamma] suggest substantial wage growth with tenure and experience, and the estimates of [delta] indicate lower wage growth with both for black workers.

Over time, employers should update their assessments of black workers. The first panel of Table 9 contains the employer's average perception of ability for black workers after observing zero through eight years of output. The second panel of Table 9 contains total wage growth due to employer learning. This portion of Table 9 shows 8% to 25% cumulative wage growth attributable to learning predicted by the model for black workers.

Focus on the results on column 3, which assume that black workers' true ability trails that of white workers by 6%. The results in the first row of Table 9 indicate that employers initially perceive black workers as 17.7% less productive than white workers. Because results assume that black workers are indeed 6% less productive, this implies that employers initially undervalue black workers by 11%. After one year of tenure, the perceived difference in ability falls to 12.7%, and wages of black workers rise by 5% because of learning. After eight years of tenure on the job, the perceived ability gap is 7.7%, and black workers have received 10% cumulative wage growth with tenure due to employer learning. The results in column 4 assume a larger true gap and thus generate faster learning, while columns 1 and 2 assume smaller differences in true ability.

Figure 3 presents the cumulative wage growth attributable to tenure and experience for both groups for assumptions of 0%, 3%, and 6% difference in true ability. For white workers, the graphs are simply based on estimates of [beta] and [gamma]. For black workers, the cumulative growth in log wage due to experience is ([beta] + [delta])In X. The cumulative growth in wages due to tenure for black workers includes the gap [delta] and the rise in wages with tenure due to learning.

In all three panels of Figure 3, black workers earn much lower returns to general experience than white workers, just as in the earlier results reveal. However, the returns to tenure also include the learning component that boosts wage growth for black workers. Assuming no gap in true ability, the results imply much larger returns to tenure for black workers than white workers, and the magnitudes greatly exceed those found in section 4. However, the results based on an assumed productivity gap of 3% or 6% lead to more similar returns for both groups. In both cases, the model seems to explain the observed patterns of wage growth quite well.

Before leaving this discussion, several caveats are worth noting. First, we make no assumption regarding the source of any productivity difference. Using the language of Neal and Johnson (1996), this could stem from any number of premarket factors or even reflect discrimination that does not diminish with learning. In addition, the assumption that deficits in returns to tenure and experience would be similar in the absence of learning plays a crucial role in the estimation. Although the assumption seems reasonable, further research into the source of the low returns to general experience among black workers is needed to provide additional support for this assumption.

6. Discussion

This paper examines the possibility that employers' assessments systematically undervalue workers from some groups. The model outlined in section 2 examines the returns to general experience and to tenure when worker output is observed with some error. The employer begins with an initial assessment of worker ability conditional on the worker's group, which may differ from actual ability. When undervalued workers perform better than anticipated, they are rewarded with higher wage growth if they continue on their current job because the employer can directly observe their productivity. Conversely, undervalued workers do not benefit from learning if they change jobs and accumulate general experience without tenure. Thus, undervalued workers should earn higher returns to tenure on the job than they can earn from general experience.

Our empirical work examines patterns of wage growth of young black and white males in the NLSY. The results show that black males earn much lower returns to general experience than white workers, but they earn similar if not higher returns to tenure. Interestingly, this result is concentrated among black workers who have low AFQT scores and/or who work in secondary-sector occupations. Although in this subsample black workers earn almost no returns to general experience, they earn higher returns to tenure on the job than high-AFQT black workers with high-skill occupations as well as all white workers. In the context of our model, the high returns to tenure reflect employers learning that their initial assessment undervalued black workers. Estimates of the structural parameters of the model suggest that if black workers trail white workers by 9% in true productivity, employers initially perceive an 18% productivity deficit. These results also predict that black workers continuing on the same job for eight year s will receive 9% additional wage growth because of employer learning.

This paper also raises several interesting questions. For example, several extensions of the model might provide interesting insights. First, the assumption that no information is transmitted from an old employer to new employers might be relaxed. Second, the model could be extended to allow multiple employers with different priors. Such a model could allow workers to search over employers for those with more favorable opinions of their own group.

With regard to the empirical work, future research should focus on finding the source of very low returns to general experience among low-AFQT and secondary-sector black workers. As a starting point, such research might focus on what attributes are shared by these groups. Geographic location, family background, secondary school attributes, and more detailed breakdowns of occupation are among potential explanations for the result. Until further evidence emerges, inaccurate initial assessments of ability among young black workers offers one plausible explanation for the observed patterns of wage growth.

(*.) SLU Box 813, Southeastern Louisiana University, Hammond, LA 70402, USA; E-mail dlewis2@slu.edu.

(+.) Department of Economics, Louisiana State University, Baton Rouge, LA 70806-4001, USA; E-mail mdterre@unixl.sncc.lsu.edu; corresponding author.

We would like to thank David Allen, Bernt Bratsberg, Jeff Moore, and two anonymous referees for helpful comments.

Received July 1998; accepted March 2000.

(1.) For example, see Smith (1990); Cross (1991); Turner, Fix, and Struyk (1991); and Blanchflower, Levine, and Zimmerman (1998).

(2.) Understanding the source of employer perceptions about the group ability is an important but difficult issue. The empirical findings of O'Neill (1990); Donohue and Heckman (1991); Juhn, Murphy, and Pierce (1991); Grogger (1996); and Gottschalk (1997) suggest that the wage differential between blacks and whites diminished between the mid-1960s and 1970s, but empirical evidence recording progress since has been nil. In fact, Darity, Guilkey, and Winfrey (1996); Rodgers and Spriggs (1996); and Gottschalk (1997) attribute approximately 12% to 15% lower wages for black men due to discrimination in the labor force. These empirical results do not appear consistent with a narrowing wage gap due to updating perceptions of group ability on this basis and warn that many factors may influence employer priors on group ability.

(3.) In this general model, the only assumption required is that these parameters exist for each individual. Thus, any assumption is possible about the source of priors. However, the later empirical work focuses on the possibility that prior parameters differ across black and white workers.

(4.) Note that the new worker begins with no tenure on the job, so [J.sub.0] = 0.

(5.) Farmer and Terrell's (1996) model uses a general human capital variable (H) in the production function. In the Farmer and Terrell model, human capital can be purchased directly through education and is not accumulated simply through labor market experience. Thus, Farmer and Terrell's human capital variable best captures education, while this paper focuses on the human capital accumulated with work experience only. It is also useful to note that results of Farmer and Terrell (1996) were driven by an interaction of employee purchases of human capital and employer learning. In this model, because employees are not allowed to purchase human capital, employer learning drives the model.

(6.) See Berger (1980, 92-6) for details and examples of conjugating normal priors.

(7.) Note that because the employee accumulates one period of tenure each period, we can also replace [J.sub.t] with t. Because they may have experience from other jobs, it remains as before in the equation.

(8.) An alternative version of the model would allow other employers to observe worker output with probability p. This allows one to relax the assumption that workers earn their expected marginal product, which is strong in this setting, where some information is firm specific. Because the more complex model yields identical qualitative predictions, this paper presents this simple, more intuitive model.

(9.) To allow for differences between high school graduation and enrollment dates, anyone reporting a high school graduation date within three months of the last date of enrollment is included in the sample. To further check the sample, we exclude anyone who reports enrolling in college in any other year.

(10.) To avoid reporting and coding errors in the data, the sample also excludes observations with wages greater than $300 per hour or less than $1.50. Results are not sensitive to these restrictions.

(11.) For those who graduated prior to 1979, the algorithm gives the individual credit for experience equal to the minimum of weeks after graduation and reported tenure in each year.

(12.) The t-test assumes independent samples and is computed using cumulative returns and standard errors in Table 3.

(13.) Tables 1 and 2 of Boston (1990, pp. 102-3) provide a full listing of the categories.

(14.) T-tests of the difference reject the hypothesis of equal returns to experience across workers for secondary occupations at all time horizons but fail to reject the hypothesis of equal returns to tenure at all time horizons (at the 5% significance level).

(15.) We also ran a model with a time trend and interactions between AFQT and time. The results from this model revealed similar patters and are available from the authors.

(16.) For four-, six-, and eight-year horizons, one-railed t-tests reject the hypothesis of equal returns in the low-AFQT samples in favor of lower returns to experience and higher returns to tenure for black workers.

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 Means
 White Workers Black Workers
 Standard Standard
 Mean Deviation Mean Deviation
Log hourly wage 1.878 0.438 1.667 0.420
Tenure 3.365 3.467 2.422 2.817
[Tenure.sup.2] 23.349 43.379 13.823 30.805
Experience 7.382 4.060 7.596 3.963
[Experience.sup.2] 70.975 64.784 73.408 63.680
Part time 0.060 0.237 0.097 0.296
Spouse present 0.480 0.500 0.244 0.429
Union 0.247 0.431 0.287 0.453
Northeast region 0.216 0.412 0.132 0.338
North-central region 0.398 0.489 0.136 0.343
West region 0.117 0.322 0.047 0.211
Health limits work 0.026 0.160 0.018 0.135
Hourly wage 7.216 3.676 5.892 5.238
AFQT 43.098 23.492 15.796 14.066

In the sample, there are 5985 observations for white workers and 2653 observations for black workers for all variables except AFQT. There are 2596 observations reporting AFQT for black workers and 5629 observations reporting AFQT for white workers.

 Wage Regressions
 Full Sample (Excludes AFQT)
Variable White Black
Intercept 1.405 1.330
 (0.019) (0.029)
Tenure 0.052 0.055
 (0.004) (0.007)
[Tenure.sup.2]/100 -0.232 -0.188
 (0.034) (0.066)
Experience 0.038 0.020
 (0.005) (0.008)
[Experience.sup.2]/100 -0.142 -0.106
 (0.031) (0.047)
Part time -0.214 -0.071
 (0.021) (0.025)
MSP 0.104 0.132
 (0.010) (0.018)
Union 0.278 0.221
 (0.011) (0.016)
DNE 0.018 0.161
 (0.014) (0.023)
DNC -0.021 -0.031
 (0.012) (0.022)
DWEST 0.144 0.222
 (0.017) (0.035)
Health -0.094 -0.031
 (0.030) (0.053)
SMSA 0.052 0.028
 (0.005) (0.007)
AFQT
 Full Sample (Includes AFQT)
Variable White Black
Intercept 1.295 1.278
 (0.020) (0.029)
Tenure 0.053 0.053
 (0.004) (0.007)
[Tenure.sup.2]/100 -0.252 -0.213
 (0.035) (0.065)
Experience 0.040 0.019
 (0.005) (0.008)
[Experience.sup.2]/100 -0.157 -0.098
 (0.032) (0.047)
Part time -0.194 -0.074
 (0.021) (0.025)
MSP 0.096 0.135
 (0.011) (0.018)
Union 0.281 0.204
 (0.011) (0.016)
DNE 0.005 0.137
 (0.014) (0.023)
DNC -0.030 -0.049
 (0.012) (0.022)
DWEST 0.106 0.159
 (0.017) (0.036)
Health -0.078 -0.010
 (0.030) (0.055)
SMSA 0.045 0.017
 (0.005) (0.007)
AFQT 0.003 0.005
 (0.000) (0.001)

Standard errors are in parentheses. There are 2653 observations for black workers and 5985 observations for white workers when AFQT scores are excluded. There are 2596 observations for black workers and 5629 observations for white workers when AFQT scores are included because of missing observations of AFQT.

 Cumulative Wage Growth Attributable to Tenure and Experience
 AFQT Excluded AFQT Included
 Cumulative Cumulative Cumulative
 Returns to Returns to Returns to
 Experience Tenure Experience
Years White Black White Black White Black
2 0.071 0.035 0.095 0.102 0.073 0.035
 (0.009) (0.013) (0.007) (0.012) (0.009) (0.013)
4 0.131 0.062 0.172 0.190 0.134 0.061
 (0.015) (0.023) (0.012) (0.020) (0.015) (0.023)
6 0.179 0.080 0.230 0.262 0.182 0.080
 (0.020) (0.029) (0.015) (0.023) (0.020) (0.029)
8 0.216 0.090 0.270 0.320 0.217 0.091
 (0.022) (0.032) (0.016) (0.025) (0.022) (0.032)
 Cumulative
 Returns to
 Tenure
Years White Black
2 0.096 0.098
 (0.007) (0.012)
4 0.171 0.178
 (0.012) (0.019)
6 0.227 0.242
 (0.015) (0.023)
8 0.262 0.288
 (0.016) (0.024)

This table presents the cumulative growth in log wages attributable to tenure and experience. Standard errors are in parentheses. The samples include 2653 observations for black workers and 5985 observations for white workers when AFQT scores are excluded from the model. Sample sizes are 2596 observations for black workers and 5629 observations for white workers when AFQT scores are included. The cumulative returns to experience are calculated as [b.sub.x][X.sub.t] + [b.sub.xx][[X.sup.2].sub.t], where [b.sub.x] and [b.sub.xx] are the regression coefficients for experience and experience squared. The standard error of the cumulative return is calculated using the usual formula for the variance of a linear combination of random variables, var([b.sub.x][X.sub.t] + [b.sub.xx][[X.sup.2].sub.t]) = [[X.sup.2].sub.t]var([b.sub.x]) + [[X.sup.4].sub.t]var([b.sub.xx]) + 2[[X.sup.3].sub.t]cov([b.sub.x], [b.sub.xx]). Similar calculations are used to compute the results for the cumulative returns to tenure.

 Regression Results Grouped by Occupation
 Primary-sector Secondary-sector
 Occupations Occupations
Variable White Black White Black
Intercept 1.425 1.312 1.400 1.348
 (0.028) (0.052) (0.026) (0.034)
Tenure 0.049 0.036 0.057 0.059
 (0.006) (0.012) (0.006) (0.009)
[Tenure.sup.2]/100 -0.198 -0.033 -0.321 -0.239
 (0.045) (0.115) (0.053) (0.079)
Experience 0.045 0.049 0.028 0.006
 (0.007) (0.014) (0.007) (0.009)
[Experience.sup.2]/100 -0.165 -0.248 -0.110 -0.043
 (0.046) (0.084) (0.042) (0.055)
Part time -0.189 -0.139 -0.195 -0.047
 (0.034) (0.046) (0.025) (0.029)
MSP 0.093 0.111 0.110 0.144
 (0.014) (0.030) (0.015) (0.022)
Union 0.269 0.250 0.312 0.217
 (0.016) (0.030) (0.015) (0.019)
DNE 0.026 0.140 0.021 0.158
 (0.019) (0.037) (0.020) (0.028)
DNC -0.010 -0.059 -0.015 -0.006
 (0.017) (0.040) (0.017) (0.026)
DWEST 0.162 0.212 0.141 0.229
 (0.023) (0.058) (0.024) (0.062)
Health -0.052 0.138 -0.121 -0.103
 (0.044) (0.100) (0.039) (0.062)
SMSA 0.050 0.032 0.035 0.023
 (0.007) (0.012) (0.007) (0.008)

Standard errors are in parentheses. Primary-sector occupations include professionals, technical workers, sales workers, managers, officials, and proprietors, while secondary-sector workers are defined as workers reporting laborer, service, or clerical worker as an occupation. The sample sizes for black workers are 848 observations for primary-sector occupations and 1805 for secondary-sector occupations. For white workers, the sample sizes are 3011 observations for primary-sector occupations and 2974 for secondary-sector occupations.

 Cumulative Learning Grouped by Occupation
 Primary Sector Secondary Sector
 Cumulative Cumulative Cumulative
 Returns to Returns to Returns to
 Experience Tenure Experience
Years White Black White Black White Black
2 0.088 0.093 0.087 0.070 0.051 0.010
 (0.013) (0.024) (0.010) (0.021) (0.012) (0.016)
4 0.163 0.166 0.159 0.137 0.092 0.016
 (0.023) (0.041) (0.017) (0.033) (0.020) (0.027)
6 0.215 0.220 0.215 0.201 0.125 0.018
 (0.029) (0.053) (0.021) (0.039) (0.026) (0.035)
8 0.273 0.273 0.255 0.262 0.150 0.018
 Cumulative
 Returns to
 Tenure
Years White Black
2 0.101 0.108
 (0.011) (0.015)
4 0.177 0.198
 (0.017) (0.024)
6 0.227 0.268
 (0.021) (0.028)
8 0.252 0.319

This table presents the cumulative growth in log wages attributable to tenure and experience. Standard errors are in parentheses. Primary-sector occupations include professionals, technical workers, sales workers, managers, officials, and proprietors, while the secondary-sector includes workers reporting laborer, service, or clerical worker as an occupation. The sample sizes for black workers are 848 observations for primary-sector occupations and 1805 for secondary-sector occupations. For white workers, the sample sizes are 3011 observations for primary-sector occupations and 2974 for secondary-sector occupations. The cumulative returns to experience are calculated as [b.sub.x][X.sub.t] + [b.sub.xx][[X.sup.2].sub.t], where [b.sub.x] and [b.sub.xx] are the regression coefficients for experience and experience squared. The standard error of the cumulative return is calculated using the usual formula for the variance of a linear combination of random variables, var([b.sub.x][X.sub.t] + [b.sub.xx][[X.sup.2].sub.t]) = [[X.sup.2].sub.t]var([b.sub.x]) + [[X.sup.4].sub.1]var([b.sub.xx]) + 2[[X.sup.3].sub.t]cov([b.sub.x], [b.sub.xx]). Similar calculations are used to compute the results for the cumulative returns to tenure.

 Regression Results Grouped by AFQT Score
 Low AFQT Scores High AFQT Scores
Variable White Black White Black
Intercept 1.114 1.321 1.344 1.166
 (0.045) (0.035) (0.025) (0.065)
Tenure 0.041 0.060 0.058 0.043
 (0.010) (0.009) (0.005) (0.013)
[Tenure.sup.2]/l00 -0.239 -0.291 -0.271 -0.133
 (0.082) (0.086) (0.038) (0.110)
Experience 0.024 0.005 0.047 0.051
 (0.010) (0.009) (0.006) (0.014)
[Experience.sup.2]/100 -0.063 -0.033 -0.198 -0.247
 (0.070) (0.054) (0.036) (0.091)
Part time -0.169 -0.0867 -0.170 -0.025
 (0.037) (0.029) (0.026) (0.047)
MSP 0.113 0.134 0.087 0.113
 (0.023) (0.021) (0.012) (0.034)
Union 0.302 0.148 0.268 0.299
 (0.025) (0.020) (0.012) (0.030)
DNE -0.047 0.091 0.025 0.201
 (0.030) (0.028) (0.016) (0.037)
DNC -0.106 -0.048 -0.014 -0.042
 (0.027) (0.026) (0.013) (0.042)
DWEST 0.044 0.149 0.114 0.147
 (0.045) (0.045) (0.018) (0.061)
Health -0.047 -0.138 -0.040 0.257
 (0.053) (0.065) (0.036) (0.102)
SMSA 0.090 0.020 0.039 -0.003
 (0.012) (0.008) (0.006) (0.014)
AFQT 0.022 0.009 0.001 0.004
 (0.002) (0.002) (0.003) (0.001)

Standard errors are in parentheses. An AFQT score that is in the 20th percentile or lower is considered a low AFQT score, while a score above the 20th percentile is considered a high AFQT score. Our full sample includes 2596 observations for black workers and 5629 observations for white workers. The low-AFQT subsample contains 1840 observations for black workers and 1207 for white workers, and the high-AFQT subsample includes 756 observations for black workers and 4422 observations for white workers.

 Cumulative Learning Grouped by
 the Level of AFQT Score
 Low AFQT High AFQT
 Cumulative Cumulative Cumulative Cumulative
 Returns to Returns to Returns to Returns to
 Experience Tenure Experience Tenure
Years White Black White Black White Black White
2 0.045 0.009 0.071 0.108 0.086 0.093 0.105
 (0.018) (0.015) (0.016) (0.015) (0.010) (0.025) (0.008)
4 0.085 0.015 0.124 0.193 0.156 0.165 0.187
 (0.026) (0.027) (0.027) (0.023) (0.018) (0.044) (0.014)
6 0.120 0.019 0.157 0.254 0.210 0.218 0.249
 (0.040) 0.034) (0.033) (0.027) (0.022) (0.056) (0.017)
8 0.150 0.020 0.171 0.292 0.249 0.252 0.288
 (0.043) (0.037) (0.036) (0.030) (0.025) (0.061) (0.018)
Years Black
2 0.080
 (0.022)
4 0.150
 (0.036)
6 0.209
 (0.044)
8 0.258
 (0.046)

This table presents the cumulative growth in log wages attributable to tenure and experience. Standard errors are in parentheses. An AFQT score that is in the 20th percentile or lower is considered a low AFQT score, while a score above the 20th percentile is considered a high AFQT score. The full sample includes 2596 observations for black workers and 5629 observations for white workers. The low-AFQT subsample contains 1840 observations for black workers and 1207 for white workers, and the high-AFQT subsample includes 756 observations for black workers and 4422 observations for white workers. The cumulative returns to experience are calculated as [b.sub.x][X.sub.t] + [b.sub.xx][[X.sup.2].sub.t], where [b.sub.x] and [b.sub.xx] are the regression coefficients on the variables experience and experience squared. The standard error of the cumulative return is calculated using the usual formula for the variance of a linear combination of random variables, var([b.sub.x][X.sub.t] + [b.sub.xx][[X.sup.2].sub.t]) = [[X.sup.2].sub.t]var([b.sub.x]) + [[X.sup.4].sub.t]var([b.sub.xx]) + 2[[X.sup.3].sub.t]cov([b.sub.x], [b.sub.xx]). Similar calculations are used to compute the results for the cumulative returns to tenure.

 Parameter Estimates for the Structural Model
Parameter 1 2 3 4
[[micro].sub.1] - [[micro].sub.0] 0 -0.03 -0.06 -0.09
[[micro].sub.prior,1] - [[micro].sub.prior,0] -0.389 -0.174 -0.177 -0.177
 (.028) (.028) (.032) (.032)
[[sigma].sub.prior]32 0.217 0.476 0.759 0.759
 (.176) (.475) (.820) (.219)
[beta] 0.118 0.117 0.116 0.116
 (.007) (.007) (.007) (.007)
[gamma] 0.088 0.088 0.088 0.088
 (.004) (.004) (.004) (.004)
[delta] -0.035 -0.038 -0.035 -0.035
 (.010) (.008) (.006) (.006)
All estimates are conditional on the assumed
value for [[micro].sub.1] - [[micro].sub.0].
Asymptotic standard errors are given in
parentheses or all estimated parameters.
 The Evolution of Employer Priors over Time
 Parameter 1
 [[micro].sub.1] - [[micro].sub.0] 0
 Years of Tenure [[micro].sub.prior,1] -
 0 -0.389
 1 -0.320
 2 -0.271
 3 -0.236
 4 -0.208
 5 -0.187
 6 -0.169
 7 -0.154
 8 -0.142
Cumulative Wage Growth Due to Learning
 1 0.069
 2 0.118
 3 0.153
 4 0.181
 5 0.202
 6 0.220
 7 0.235
 8 0.247
 Parameter 2 3 4
 [[micro].sub.1] - [[micro].sub.0] -0.03 -0.06 -0.09
 Years of Tenure [[micro].sub.prior,0]
 0 -0.174 -0.177 -0.177
 1 -0.128 -0.127 -0.123
 2 -0.104 -0.106 -0.110
 3 -0.089 -0.096 -0.104
 4 -0.080 -0.089 -0.101
 5 -0.073 -0.084 -0.099
 6 -0.067 -0.081 -0.098
 7 -0.063 -0.079 -0.097
 8 -0.060 -0.077 -0.096
Cumulative Wage Growth Due to Learning
 1 0.046 0.051 0.055
 2 0.070 0.071 0.067
 3 0.085 0.081 0.073
 4 0.095 0.088 0.076
 5 0.101 0.093 0.078
 6 0.107 0.096 0.079
 7 0.111 0.099 0.080
 8 0.114 0.101 0.081