Employer Learning and Statistical Discrimination

Joseph G. Aitonji

Department of Economics

and Institute for Policy Research, Northwestern University

and

NBER

Charles R Plerret

Bureau of Labor Statistics

November 1997

This project was funded by the U.S. Department of Labor, Bureau of Labor Statistics

under small purchase contract 41USC252C3 (Order No. B9J34633) and supported by the

Institute for Policy Research Northwestern University, the NationaJ Science Foundation.

The authors gratefully acknowledge the tremendous assistance provided by Nachmn

Sicherman with the NLSY data. Opinions stated in thk document do not necessarily

represent official position or policy of the U.S. Department of Labor.
Employer Learning and Statistical Discrimination

Abstract

We provide a test for statistical discrimination or “rational” stereotyping in environments in which agents

learn over time. Our application is to the labor market. If profit maximizing tirrns have limited

information about the generrd productivity of new workers, they may choose to use easily observable

characteristics such as years of education to “statistically discriminate” among workers. As fm acquire

more information about a worker, pay will become more dependent on actual productivity and less

dependent on easily observable charactensti& or credentials that predict productivity. Consider a wage

equation that contains both the interaction between experience and a hard to observe variable that is

positively related to productivity and the interaction between experience and a variable that fbns can

easily observe, such as years of education. We show that the wage coefficient on the unobservable

productivity variable should rise with time in the labor market and the wage coefficient on education

should fall. We investigate this proposition using panel data on education, the AFQT test, father’s

education, and wagea for young men and their siblings fkomNLSY. We also examine the empirical

implications of statistical discrimination on the basis of race. Our results support the hypothesis of

statistical discrimination, although they are inconsistent with the hypothesis that firms fully utilize the

information in race. Our analysis has wide implications for the analysis of the deterrninan ts of wage

growth and productivity and the analysis of statistical discrimination in the labor market and elsewhere.

JEL Classification: D83, J31

Joseph G. Altonji Charles Pierret

Department of Economics Bureau of Labor Statistics

Northwestern University 2 Massachusetts Ave. NE Suite 4945

Evanston, IL 60208 Washington, D.C. 20212

(847) 492-8218 (202) 606-7519

altonji@nwu.edu pierret_c@bls.gov

and NBER
1. Introduction

People go through life making an endless stream of judgments on the basis of limited information

about matters as diverse as the safety of a street, the quality of a car, the suitability of a potential spouse,

and the skill and integrity of a politician. When hiring, employers must assess the value of potential

workers with only the information contained in resumes, recommendations, and personal interviews. What

do employers know about the productivity of young workers, and how quickly do they learn? Given lack

of information about actual productivity, do employers “statistically discriminate” among young workers

on the basis of easily observable vaiables such as education, race, and other clues to a worker’s labor force

preparation. Mauy issues in labor economics hinge on the answers, including the empirical relevance of the

signaling model of education (Weiss (1995), statistical theories of discrimination (Aigner and Cain (1977),

Lundberg and Startz (1983)), snd the interpretation of earnings dynamics. The desirabili~ of changes in

the laws governing hiring procedures, evahration of employees, layoff and fixing costs, and the provision of

references for”former employees also hinge on the answers. Although labor economists typicrdly asmrne

wages are strongly influenced by employer beliefs about worker productivity, there is little empirical

research on how much employers know about their workers, or about how this information changes with

time in the labor market.’

h this paper we explore the implications of a hypothesis that we refer to as Statistical

Discrimination with Employer Learning, or SD-EL. Our working hypothesis is that tirrns have only

limited information about the quality of workers in the early stages of their careers. They distinguish

among workers on the basis of easily observable variables that are correlated with productivity such as

years of education or degree, the quality of the school the person attended, race, and gender. (To avoid

misunderstanding we wish to stress that part of the relationship between wages and race and gender may

reflect biased inferences on the part of employers or other forms of discrimination that have nothing to do

with productivity or information.) Firms weigh this information with other information about outside

activities, work experience to date, references, the job interview, and perhaps formal testing by the firm.

Each period, the fm observes noisy indicators of the worker% performance. Over time, these make the

information observed at the start redundant. Wages become more closely tied to actual productivity and

less strongly dependent upon the information that was readily available at the beginning of a worker’s

There is a largeempiricalandtheoreticaliteratureonlabormarketsearchandontheeffectsoflearningaboutthequalityof

thejobmatchonwagesandmobility.SeeDevineandKiefer (1991) for a comprehensivesurvey.

to observe background variables that influence productivity.3 While our basic theoretical framework and

most of the empirical analysis assumes that all employers have the same information about workers, we

provide a preliminary discussion of the implications of models in which the current employer has an

information advantage.

In Section 2 we present our basic theoretical framework in a setting in which information is public,

and then informally discuss the case in which it is private. We also consider the effect that associations

betweens, z, and job training would have on the analysis. In Section 3 we discuss the ITLSY data used in

the study. In Section 4 and 5 we present onr.pults for education and race. In section 6 we present results

in which we control for job training. In section 7 we discuss the case in which employer information is

private and provide some evidence on how hard to observe variables are related to the probability of a

layoff and the wage losses associated with layoffs. In section 8 we point out that interpreting our

estimates of the time profile of the effeet of AFQT on wages as the result of employer learning implies that

high ability workers would have a substantial financial incentive to take the AFQT to differentiate

themselves horn those who are less able in this dimension. The fact that we do not generally observe this

raises additional research questiona. In section 9 we close the paper with a discussion of some of the

implications of our analysis for a rnrinber of standmd topics in labor economics and a research agenda.

2. Implications of Statistical Discrimination and Employer Learning for Wages.

2.1 A Model of Employer Learning and Wages

k this section we show how the wage coefficients on characteristics that employem can observe

directly and on characteristics they cannot observe directly will change with experience if employers

statistically discriminate and become better informed about workers over time.

3We are using the term “statistical discrimination” as synonymous witi tbe use of the term “rational expectations” iu the

economics literature. We roes+ that in the absence of iidf infonnstioq f- distinguish between individuals with different

characteristics based on statistical regularities. In other words, we mesn that f- fomi stereo&pes that sre rational in the

sense that they are consistent with reality. Many papers that use the term statistical discrimination analyze race or gendm

differentials that arise because fm have trouble processtig the information they receive about the perfommnce of minority

group members. This difficulty may lead to negative outcomes for minorities because it lowers theti incentives to make

unobsemable investments that raise productivity. It afso may lead to negative outcomes if the productivity of a job mstch

depends on the tit between the worker and the job. Some papers afso considsr whether f- that starI with incorrect beliefs

about the relationship between personal characteristics and producdvity (inaccurate stereowes) would correct thq and, in

models with worker investment, whether the priors held by f- may be self fufffling. See Aigner and Cain (1977), Lundberg

and Startz (19S3), Lang (19Sd), and Coate and Loury (1993) and Oetduger (1996). h Oetdnger’s model productivity is match

specific and productivity signals are noisier for blacks than whites. As a result the sorting process across job changes is less

efficient for blacks, and a race gap develops over time.

3
Our model is very similar to Farber and Gibbons (1996). Let y,, be the log of labor market

productivity of worker i with ti years of experience. y, is determined by

(1) y,,=rs, + H(Q + alq, + @+qi

where Siis years of schooling, Ziis a vector of correlates of productivity that are not observed directly by

employers but are available to the econometrician, and H(tJ is the experience profile of productivity. The

variabIe qi consists of other determinants of productivity and is not directly observed by the employers or

the econometician. The elements of q might be a test score, the income of an older sibling, father’s

education, or indicators of childhood environment such as books in the home or ownership of a library

card. We normalize Ziso that all the elements of the conformable coefficient vector A are positive.

Without loss of generality we scale rliso that it has a unit coefficient in the productivity equation.

In addition to Si,the employer observes a vector ~ of other information about the worker that is

relevant to productivity. The elements of ~ are related to productivity by the coefficient Vectorr%, For

now we assume that the experience profile of productivity does not depend on Si,<, q, or rlP k section 2.2

we discuss the sensitivity of our analysis to this assumption. In most of the analysis we suppress the i

subscript. All variables are expressed as deviationa from population means. Although we use years of

schooling and race as our examples ofs, our analysis applies to any variable that emplo yers can easily

observe.

We assume that the conditional expectations of E(zls,q) and E(rl]s,q) are linear in q ands, so

(2) z= E(zls,q) +v=ylq+yzs+v

(3) rl=E(rlls,q) +e=~s+e,

where the vector v and the scalar e have mean Oand are uncorrelated with q ands by definition of an

expectation.’ The links tim s to z and q may be partially due to a causal effect of s.’ Equations (1), (2)

and (3) imply that Av + e is the error in the employer% belief about the log of productivity of the worker at

4The exclusion of q from tbe conditional mean of q is innocuous, since we are simply deftig q and the coefficient vector u,

on q in (1) so that tie mean of q does not depend on q.

5 For example, below we use tbe Armed Forces Qualification Test (AFQT) as z and years of education ass, and NeaI and

Jobmon (1996) present evidence that yesrs of education have a sizable positive effect on AFQT.

4
the time the worker enters the labor market. The sum Av+e is nncorrelated withs and q. We make the

additional assumption that Av +e is independent of q ands.

Each period that a worker is in the labor market, fws observe a noisy signal of the productivity of

the worker,

where y is y, - H(t) and e, reflects transitory variation in the performance of worker i and the effects of

variation in the firm environment that are hard for the firm to control for in evaluating the worker. (We

continue to suppress the i subscripts.) The term et is assumed to be independent of the other variables k“

the model. We are also implicitly assuming that the component of et that reflects temporal variation in

productivity t?om sources specific to worker i is serially uncorrelated, because otherwise tirrns would have

an incentive to base compensation in t+l on what they know about the worker specific component of C,.e

However, e, maybe serially correlated aa a result of the other factors.

Since the employers know q ands, observing&is equivalent to observing

(5) ~= Av + e -I-e, = <,-E(y]s,q)

The vector D,={dl,~,...,dJ summarizes the worker’s performance history. Let PIbe the difference

between Av+e and E(Av+elDJ. By definition V,is uncorrelated with D,, q ands but in addition we assume

p, is distributed independently of D,, q ands.

We also assume for now that q,s, and the worker’s performance history (summarized by the vector

D,={d,,&..~} are known to all employers, aa in Farber and Gibbons. (We discuss the private information

case in Section 7.) As a result of competition among firms, the worker receives a wage W, equal to the

expected value of productivity Y, (Y, = exp(y~) times the multiplicative error component exp(c,~that

reflects measurement error and firm specific t%tors that are outside the model and are unrelated tos, z, and

q. The wage model is

(6) W,= E(Y,/s,q,D,)e’l

Using (l)> (2), (3) and (6) leads to

6The fro’s knowledge of a serially correlated productiviw component would imply serially correlated hansito~ variation in

the wage error of the type found by Farber and Gibbons (1996), but would not have much effect on our analysis.

5
(7) W,= E(Y,ls,q, Dt) eq’= e~’~’) e(=[+AY’)@(a+AY’)’ e“*tie[Dc)E(e~l) e;!

Taking logs and collecting terms leads to

(8) w,= (r+ Ay2 + rt,)s + H*(t) + (Ay, + ril)q + E(Av+e lDt) + ~,

where w,= log(W) and H*(t) = H(t) + log(li?(e~)). We will suppress the g,term in the equations that

follow.

In the context of the debate over signaling models of education Riley (1979) and others have noted

that unless the relationship between schooliig and actual productivity changes, the coefficient ons will not

change. This is true regardless of ~s is related to productivity. Farber and Gibbona also make this

point by showing in a similar model that the expected value of the coefficient of an OLS regression of w,

ons does not depend on t. They estimate an equation of the form

(8a) w,= b,,s + H(t) + ct,q + E(Av + elDJ

with q treated as an error component. They find that b,t does not depend much on t.

Farber and Gibbons also make a second point, which is that if one adds the component z“of(Av + e)

that is uncorrelated with the employer’s initial informations and q to the wage equation and estimates

(8b) w,= b,,s + b,~’+ H(t) + rt,q + E(Av + elD),

the coefficients ons do not depend on t. This follows ahnost immediately from the first resul~ because

adding a second variable to a regression model has no effect on the expected value of the first if the two are

uncorrelated. They provide evidence from NLSY that b,cis relatively constant and btieis increasing in t.

hr this paper, we establish a related set of results that permit one to examine the issue of statistical

discrimination. We begin with the case in which z ands are scalars and then consider the more general

cases. Among those who are working the means of q,s, and z may depend on t although this will influence

estimates of H-(t). However, we assume throughout that among those who are working the covariances

among q,s, and z do not depend on t. Under these assumptions the variances and covariancea involving q,

s, and z and the regression coefficients @~,and @~Zdefined in (10) below do not vary with t.’

7 Estimates of the experience protile H“(t) will be affected if the means ofs, q, and z depend on t but this has no bearing on our

analysis.

6
Case 1: z is a scalar.

The analysis is cleanest when z ands are scalars. Least squares regression will identify the

parameters of the expectation of w, ons, z, and experience profile H“(t).sLet b,, and ba be the coefficients

ons and z in the conditional expectation function when t=o.. .T, with

(9) E(w, \s.z.t)= b~,s+ b~ + H“(t) .

When the individual starts work (t is O)this equation is

(9a) E(wO[s.z.0)= b,,s + bfiz + H“(O)

To simpli~ the algebra but without any additional assumptions we re-interprets, z, and q as components

ofs, z, and q that are orthogonal to H“. Then the wage process (7), the fact that E(Av+elDO)is O(since

there is no work history when t=O), and some straightforward rdgebra involving the least squares regression

omitted bias formula implies that

(*O) ~]=~+A~,+a;]+[@J

where 0,, and @~Zare the coefficients of the auxiliary regression of (al + Ayl)q ons and z.. The

parameters {b,,,b.}’ are the sum of the {b,,, bfl}’ and the coefficients of the regression of E(Av+e[DJ ons

and z. That is,

[1[- (lOa) b“ = b“

b,, b,o.

I

[

Var(z) 1[ –Cov(s,z) o

+—

Ivar(s,z)l” _cov(s,z) W(S) COY(V,E(Av +4 Dt)1

where lVar(s,z)[is the determinant of Var(s,z) and we use the facts that COV(S,E(Av+elDJ)=O and

cov(z,E(Av+elDJ)=cov(v,E(Av+elD)). This may be rewritten as

’11) tl=tl+-[-c;~ ‘cO::;]”’”[Avar(v)+cov(v;]

or

(12a) b,, = b,O+ 0,0,

8 Technically, it identifies the coefficients of the least squares linear projection of w, ons, z, and W(t) if E(Av+elDJ is not

linear in the functions ofs, z, aid t we introduce in our regression models. We ignore ti distinction.

7
(12b) b.= ba + E@Z

where 0, and Q, are the coefficients of the regression of Av+e ons and z and

(3,= cov(E(Av+e]D), z)/cov(Av+e, z)= cov(E(Av+elDJ,v)/cov(Av+e, v)

is a parameter that is specific to the experience level t. Note that fl~O, and 6~@Care the coefficients of the

regression of E(Av+elDJ ons and z and that tltsummarizes how much the firm knows about Av + e at time

t. It is easy to show (see Appendix 1) that 0, = - 0=0, where 0= is the coefficient of the regression of z

ons. (This is the baais of proposition 3 below.)

To determine the behavior of O,@,and @,@Zover time, note firat that !0, <0 and QZ>0 if cov (v,

Av+e) >0 and COV(S,Z) >0. The latter condition is true whens is schooling and the scalar z is AFQT,

father’s education, or the wage rate of an older sibling. The condition cov(v,Av+e) >0 simply states that

the unobserved (by the firm) productivity subcomponent v and composite unobserved productivity term

Av+e have a positive covarisnce. This seems plausible to us for the z variables we consider.

The change over time in b,, and bais determined by&. Intuitively, f),is bounded between Oand 1.

It is Oin period O,because in this period employers lmow nothing about Av + e, so E(Av+elDO)=O.The

coefficient is 1 if E(Av+e\DJ is Av+e, since in this case the employer has learned what Av+e is and thus

knows productivity y. It is also intuitive that e,is nondecressing in t because the additional information

that arrives as the worker’s career progresses permits a tighter estimate of Av+e.’

The regularity conditions on thee, process that are required for the time average of e, to converge

ahnost surely to Oas t becomes large constitute sufficient conditions for et to converge to 1 as t becomes

large. (See Theorem 3.47 in White (1984) for a very general set of conditions.) These conditions knit the

degree of independence among the E,and also restrict the variances. The intuition for this is that fbture

values of 61must be sufficiently independent of the earlier e’s to average out, and must not be so variable

that the fiture Qvalues have no new information about Av+e.’O

gTo establish &is note that since D,.1ia a subset of the information in D“

[Cov(v, E(Av+e]DJ - E(Av+elD,.,))]/Cov(v, Av+e) = &- %, z 0.

IOTo ~s~blkh the result note tit in each period, f- observe ~ =Av + e + <. fn general, the fO~ of E(Av+elDJ~lf depend

on the pattern of serial correlation and the relative variances ofs,.. ,er However, the fm can always choose to use E(Av+elbJ,

where b, ia the drne average ~ (Av + e +“sk)/ t, as an unbiased but p.dips inefficient estimator given D,. If as t goes to

1

intinity D converges abnost surely to Av+e, then Cov(~Av+e\D. v)/Cov(Av+e,v) converges to 1 as t goes to irdinity. Since

8
A simple example maybe helpful. If e, is iid with variance Oez,then e, has the familiar form

(13) @, =

var(Av + e)

fort =1, 2...; 60= O

var(Av + e) + c: /t

In this case, 0, is strictly increasing in t because the independence among the e, means that each 6, has

some new information about f3r 0, is Owhen t is Oand converges to I aa t goes to infinity.

There are two conclusions, which we summarize in Proposition 1 and 2:

Proposition I: Under the assumptions of the above model, the regression coej?cient bzt is nondecreo.ring

in t. The regression coefficient bst is noniiscreasing in t.1‘

Proposition 2: Ifj’irms have complete information about the productivity of new workers, then &st/d =

&zt/a = o.

These results underlie our empirical analysis below. Using AFQT and father’s education as z

variables, we examine the experience profile of b,~and bw The intuition for the decline in b~ is that as

employers learn the productivity of workers, s will get leas of the credit for an association with

productivi~ that arises becauses is correlated with z provided that z is included in the wage equation with

a time dependent coefficient and can claim the credit.lz We also are able to estimate the time profile of 6,

up to scale. Under the assumption that employers learn about v and e at the same rate, this enables us to

estimate the time profile of employer learning about productivity up to scale. In AP (1996) we examine

the implications of our estimates for pure signaling models of the return to education.

The model also implies a third resul~ which we state in proposition 3.

Proposition 3: Under the assumptions of the above model, &~t/~ = - Ozs &zt/6L

Since 0= is simply the regression coefficient of z ons and can be estimated, the coefficient restriction in

Proposition 3 may provide leverage in differentiating between the learninglstatistical discrimination model

and alternative explanations for the behavior of b,t and b..

E(Av+e/DJ is more eflicient than E(Av+e(D)[, E(Av+elDJ must also converge ahnost surely to Av+e, which establishes that

Cov(E(Av+elD), v) / Cov(Av+e, v) converges to 1. We cmrclude that El,converges almost surely to 1 as t becomes large.

1I me ~oeficien~ on ~ri~favorable z ch~cteristic, suchas criminal involvement or alcohol use, wilf become more negative

to the extent that tirese reflect permanent traits. Assumings is negatively comelated with the unfavorable z, b. will rise with t.

As noted earlier, we have normalized z so that A >0.

II It ~~t be ~fic~=Iy ~tere5fig to see if tie I’diPlOMSeffect” declines with t while the coefficientsonbard@obserw

productivity characteristics that correlate with getting a diploma rise. (See Fr.%zis(1993) for a recent snalysis of whether there is

a diploma effect.)

9
Additional Empirical Implications

As noted in footiote 4, the literature on statistical discrimination as well as the literature on labor

market networks has emphasized differences across groups in the amount of information that is available to

firms (or the mapping between a given.set of data and what the firm actually knows) may differ across

groups. Our model implies that tAese differences will lead to group differences in wage dynamics. To see

this, suppose that there are two ~oups, 1 and 2. For group 2 the firm’sinitial information set is larger than

for group one. Consequently, Var(Av + e ]group 2) < Vsr(Av + e I~oup 1) and COV(AV+ e, v Igroup 2) <

COV(AV+ e, v Igroup 1). From equation (1O’)or (11), it follows that bmand bti vary less overtime for

group 2 than group 1. In the extreme case, when firms are fully informed ahout group 2, COV(AV+ e, v I

group 2) is Oand b- and b. are constant. In future work, it would be interesting to use this implication as a

way of testing the hypothesis that the quality of information that employers have differs across labor force

groups. Theories that stress differences in the ability of employers to evaluate the pdormsnce of

membem of different groups imply different amounts of noise (from the point of view of the employer) in

the signals ~ and different paths of 9.

In standard labor data sets based on household interviews information on yi is not available.

However, it is interesting for at least two reasons to discuss the cross equation restrictions between the

equation relating yi tos and z that are implied by the model. Firs4 data could be gathered from both firms

and workers. Second, information on yi or indicators of y,may be available for use in other applications of

our methods to study statistical discrimination. For example, in the study of mortgage lending, panel data

on households might provide data on both credit records (related to y,), success in loan applications (the

counteqmrt to wit), and hard to observe background variables (such as the income and wealth of relatives).

Suppose that one has a measure Yi,-that is equal to yi plus noise & Assume that ~, is independent of all

other variables in the model. Then the model implies that

(13a) Yi,’= (bW+ Q,)s, + (bW+ @~zi+ error

where the error term is orthogonal tos and z. Note that the coefficients are time invariant. This eqnation

and (9) are heavily overidentified. By estimating the equations jointly one can identi~ @tsepsrately born

0, and 0,. The availability of a productivity indicator would be particularly usefid when one relaxes the

assumption that the effect ofs-ruid z on y is time invariant.

10
Case 2: z Is a vector

We now consider the case in which z is a vector z’= {zl.~,...,~..~. In this case,

,14) [;]=p~,+:;]+[:]

where [o~,, @W]’is the 1 x (K+l ) vector of coefficients ilom the auxiliary regression of (Ul + Ayl)q on

Sand Z.

In the vector case ~,. b~ are

(Is) [:I=[:l+vmz)-I[covi,E

where vsr(s,z) is a K+ 1 x K+l matrix, COV(Z,E(Av+elDJ) is a K element vector and we have used the

fact that COV(S,E(Av+elD))=O.

Let G, be the kh row of the K x K matrix G = [var(s)var(z) -cov(z,s)cov(z, s)’~’

where VW(S)is the variance of the scalars, vsr(z) is the variance of the vector z, and COV(Z,S)is the

vector of covariances betweens and the elements of z. In appendix 1 we show that b,, and b&,can be

expressed as

(16) b,, = b,,- ~(COWk;)G, .@~ .[coV(z,Av+e)])

k=]

(17) bat = bZ,,+var(s) G,.@~.[cov(z,Av +e)]

where G~ = cov(E(Av+e\DJ, ~/cov(Av+e, ~. Let 0,,, be the coefficient of the regression of ~ on

s, k=l,.. .,K. Equations using (16) and(17) lead to Proposition 4, which is the vector analog to

Proposition 3.

Proposition 4: When zis a vector and the assumptions of the above model hold,

~bst = ..- K

at

-p,,, ~.

11
Proposition 2 generalizes to the vector case. Proposition 1 does not. With multiple z variables,

one cannot in general sign ab,&3tand ~Z,t /~ even if all the elements of A are positive, each element

of COV(Z,Av + e) is positive, and ~,,, is positive and @~is increasing in t for all k. However, horn

Proposition 4, it follows immediately that if ib,,, / Zt s Oand b,,, >0 for all ~ used in the analysis

then db@ is <0. We can verify the conditions for a particulars and set of z variables.”

If the @~ are the same for each of the ~ ad equal to the common value 0,, then the time paths

of b~,and the elements of b. will all be proportional to Ot:

‘“a)M=E:I+’:[-:3

The oh will be the same for all k if the following two conditions on the conditioml distribution fof

D, and the conditional mean of z~hold:

Corrtition 1. ~(D,, Iz,,Av + e) = f(DJAv + e) for all k;

Condition 2. E(z, }Av+ e) = @~R(Av+ e) where $~is a scalar that is specific to k and R is some

fiurctionBasically, these conditions imply that the distribution of the signal D, is driven by e + Av and

that the signal D, is not more informative about particular elements of v than others.14 The condition

M I~itia~ywe ~ae sqrised thatthe conditionsthat A >0, COV(Z,Av + e) >0, and @&is increasing in t for aUk dOnot

guarantee that b. is positive even if ox> 0Ti6rafl k. The intuition is as follows- The OLS estimator of ba is equivalent to

regressing the wage in period t on the residuals ~t from the regression of % ons. ~k is the sum of v~plus the component of the

ktb element of y,q that is orthogonal tos. The components y,q that are orthogonal tos are unrelated to v~and e but are likely

to be correlated across ZK Consequently, using OLS to esdniate ba is analogous to applying OLS in a situation in which

se~eral of the regressors are measured with error, and the measurement errors are correlated. (The Tkmaybe thought of as

noisy measures of v~) It is possible in such a situation for the probability limit of the OLS estimator to take on the wrong sign.

14TO estibfishtie conditions, note fit that

COV((E(AV+elD~, z,)) = { { (zKE(Av +elDt). g(Dt,Zk\AVk). h(v)

AV+.Z,D,

= *~c~~E(Av+elD,) g(D,lAv) @lAv)h(Av)

= ~{=WZ,lAV)E(E(Av+elD,)lAv) h(Av)

and that

COV(AV+e,z~) = .~+CE(z~lAv+e) (Av+e) h(Av+e). It is easy to verifi from these equations that Cov(E(Av + elDt,

z~/Cov(zJAv + e) is the same for all ~ if (E(zJAv +e) =@kY(Av+ e)

12
will hold if, for example, &is generated by (5) and e and the elements of v are normally distributed.

The conditions rule out the possibility that the range of a particular element of v, say Vtiis either

-100,000,0, or 100,000. In this case, a very small or very large vrdue of D, would be very informative

about Vw

These conditions are quite strong. For example, if the firm obtains indicators about

subcomponents of v and e as well as y, then it is likely to learn about some components of productivity

faster than others. In this case, equation (16) and (17) continue to hold, but the time path of the

education slope is a weighted average of the @Lthat determine the time paths of the individual ~.

The paths of the individual ~ will reflect differences across ~ in the rate at which firms learn about tie

productivi~ components that they are correlated with. Tlris is an important result, because it states

that differences in the effects of particular variables on wage growth may reflect differences in the rate

at which firms learn about the variables. This provides an alternative or a complement to the stsmdsrd

view that the differential effects on growth rates reflect differences in the relationship between the

variables and other sources of wage growth such as on-the-job training.

Case 3:s and z are both vectors.

Finally, we consider the case in which boths and z are vectors. In this case we reinterpret all of the

of the related variables and parameters in the model, such as b,O,bti, v, etc as vectors or matrices. The

vectors of coefficients b,Oand b@ons and z in the base year satisfy (14) where the vectors @@and ~~= are

the coefficients in the regression of q ons and z. The vectors b,, and b. are given by

[1[1 (17b) } = y + AIcov(v, E(Av + elD,)] where

zt .0

[

~ = – W@)-’ Cov(s,z)pr(z) – Cov(z,s) w(s)-’ Cov(s,z)]

[Var(z)-cov(z,s) var(s)-’ Cov(s,z)]

13
Since -var(s]’cov(s,z) k the matrix of coefficients from the reaession of z ons we obtain the vector

version of proposition 4:

b,, -b,, = Om(bti –bzO),

where 0= is redefined to be the matrix of coefficients of the regression of the vector z on the vectors.

When conditions 1 and 2 are satisfied and the signal D, is not more informative about particular elements

of v than others then (17b) reduces to (17a) with both bx and bti as vectors.

Statistical Discrimination on the Basis of Race

Firms observe race. If race ia correlated with productivity and firms violate the law and use

race as information, then race has the properties of ans variable. To seethe empirical implications of

thk, partitions into two variables,s] and S2,wheres, is an indicator variable for membership in a

particular racial group and Ootherwise, ands, is schooling.’s In this case, the model implies almost

immediately that the coefficient ons, does not vary over time if the interaction between z and t is

excluded horn the model. If th!s interaction is included (17a) implies that the time paths of b,,t and b~t

are

b,,,=b,,O- @#,,

b,,,=bs20- @=,9c

where @Z,,and @=2are the coefficients ons, and ~ in the regression of z on SIand Sz. Assuming ~.,

is negative, as it is whens, indicates that the person is black and z is AFQT, father’s education, or the

wage of an older sibling, then the wage coefficient on S1will rise over time.

In contrast, if tirms obey the law and do not use race as information, then in the econometric

model, race has the properties of a z variable. In the case in which race is the only z variable and ones

variable, such as education, is included in the analysis, then the coefficient on z in equation (11)

corresponds to the coefficient on race. The model implies that if (i) race is negatively related to

productivity (A< O),@l)firms do not statistically discriminate on baaia of race, and (iii) firms learn

over time, then the race differential will widen as experience accumulates. The intuition is that with

1sfie ~lement of r ~o=espondimg to tie race fidi~tOr s, ~ & pmd~tiyi~ eqwl&n (1) is 0 unless consruner or emplo yee

tastes for discrimination reduce profitability of employing members of the nrinori~ group, as in Becker (1971). (Even if r is O

race nray be negatively related to productivity if it is correlated with elemenb of z, q, or q that affect productivity.)

Presumably, f- that violate the law and discrirninite ih respome tti their own prejudice or tbe prejudice of consumers or

other employees might also be willing to use race as information. Employers who harbor prejudice against certain groups IMY

14
learning firms are acquiring additional information about performance that may legitimately be used to

differentiate among workers. If race is negatively related to productivity, then the new information

will lead to a decline in wages. J-feducation is negatively related to race, then the coefficient on

education should fall over time.

What happens if firms do not discriminate on the basis of race and one adds a second z variable

with a time varying coefficient to a model that contains race and ans variable? Let z, denote race and

+ denote the additional variable, and let b,,, denote the coefficient on race when experience is t and ~

is included in the model and let b,,,’ denote the corresponding coefficient when ~ is excluded.

Assume that @~, = @~ =@, where @~ is defined below (17) above. In Appendix 3 we show that

c%,,,/d - %,,,” I a = -r%, I a .[QZ20Z,Z1]

where 0=2 is the coefficient on Z2in the reg”kssion of Av + e ons, z, and Z2and @zZ=, is the coefficient

on ZIin the regression of ~ on z, ands. When zl indicates whether the person is black and z is APQT,

father’s education, or the wage of an older sibling, 02,1 is negative. If these variables are positively

related to productivity, with 0,, >0 then C%=,(/ Z1– ZbZl,*/ Z7>0. We conclude that if firms do not

statistically discriminate on the basis of race and race is negatively related to productivity, then (1) the

race gap will widen with experience and (2) adding a favorable z variable to the model will reduce the

race difference ii the experience profile. We wish to stress that other factors that influence race

differences in experience profiles as well as other fonps of discrimination will rdso influence the wage

results.

2.2 Incorporating On-the-Job Training Into the Model:

The analysis so far assumes that the effects of z ands on the log of productivity do not depend

on t. Human capital accumulation is included in the model through the H(t) firnction but is assumed to

be “neutral” in the sense that it does not influence the time paths of the effects ofs and Z.’$ In the more

general case, the time paths of z ands depend on other factors as well as learning. In this section we

first consider the effect that such dependence would have on OLS estimates of the interactions between

be especially urdikely to form beliefs about tbe productivity of those groups that are rational in tbe statistical sense used in this

paper.

“ One may easily modify the theoretical framework to aflow for this form of human capital accumulation. For example, the

H(t) function may reflect learning by doing h alfjobs that is obsermble to fm, or worker fuced bwestrnents in human

capital that are observable to fm.

15
t and z ands. Then we discuss estimation of a more realistic model that includes both human capital

accumulation and learning/statistical discrimination. As we shall see, there is no clean way to sort out

the relative roles of these two mechanisms without data on productivi~.

Suppose thats is complementary with le-g by doing or enhances the productivity of

investments in general skills. We return to the case of scalacz. Then the productivity equation (net of

training costs) might take the form

(18) y,=rs+rlst +H(t)+ct,q+Az+q.

Assuming that the training activity is observed (firms know (18)) and workers pay for the

general training, the wage equation (9) becomes

(19) w,= (b,, + rlt) s + b= + H(t) + rtlq + E(Av + e\D)

Most discussions of human capital and most of the empirical evidence on employer provided

training suggest that education makes workers more trainable and that educated workers receive more

training. In this case r, will be greater than 0.’7 Probit models of the probability that a worker

receives training in a given year show strong positive effects of schooling, and APQT as well as

smaller but positive, statistically significant effect of father’s education. (See below.)

What are the implications of this for our investigation of the hypothesis that the reliance of

employers on easily observable variables to estimate productivity declines over the career? In

estimating the model we identifi the sum b,t +r,st rather than b,f. If r, is greater than O,then the

estimated relationship between b,, + r,st and t will be biased against the hypothesis that employers

learn about productivity. As it turns out, we find a strong negative relationship between b,, + r,st and t,

which is only consistent with a training interpretation if education reduces learning by doing, the

productivity of training investments, ador the quantity of training investments.

There is also the possibility that the productivity of employer provided training and/or learning

by doing depends on z andor q. This case is harder to analyze because employers do not observe z

and q directly and are learning more about them as time goes on. As a start, we consider the extreme

IT~tig~ ~Iop_ d~end on tie expected productivity of the worker if the costs or returns to Gaining dep~d Onv~ables ~ch

ss z ors. Altonji and Spletzer (1992) fmd a relationship between test scores and measures of training using the NLS72 data se~

and many studies fmd a Iii between schooling and training measures. See for example, Bartel and Sichenuan (1992) and

Lynch (1992).

16
case in which firms are fully informed about z, so that e! is 1 and bti in (9) is a constant in the absence

of training.

Suppose that the productivity equation is

(20) y,=rs+r,st+ r2zt+H(t)+ ctlq+Az+rl, r2>0

If firm’s knowledge ofs and q is fully informative about z, then the presence of r, in the productivi~

equation should lead the effect of z on the wage to rise with experience even if bmdoes not depend on

time (6,=1). However, the presence of rzz t in the productivity equation seems unlikely to lead to a

negative estimate Ofab,~at.

It is important to point out, however, that if the effect of z on y rises with t then introducing the

interaction between z and t into the wage equation could lower the estimate of the change over time in

the wage response tos. Let B,, be the expectation of the OLS estimator of the effect ofs on the wage

in period t. Then B,, is bm+ rlt + 0= r2t, where 0= is the coefficient of the regression of z ons. When

one adds z4 to the regression, B,, becomes b,O+ r, t. Bn, the expectation of the OLS estimator of the

effect of z in period L becomes ba + r~t. If O=s Oand rz>0, then @=rz >0. The_ in the

coefficient ons when z t is added is -cD=rzt. Consequently, in the scalar case the simple training

model with full information about z implies that [dB,@t] declines by - @zs [dB#3t] when z t is added

to the wage equation.

In the pure employer Iearninglstatistical discrimination model dB#t is equal to db,~ dt snd,

according to proposition 3, the learning model also implies that dB,@t declines by -#@bti= -O=dt

when z t is added to the wage equation. However, models differ in their implications for the level of

dB,@t after zTis added. A pure human capital model with perfect information implies dB,,/dt ~ O

unless, in contrast to the available evidence, s has a negative partial effect on the quantity or return to

on-the-job training (rl < O).

Con@ollig for Training.

In the absence of data on productivity, sorting out the relative importance of employer learning

and non neutral (with respect to z ands) on-the-job training may require that one build a model of the

quantity of training as a function ofs and z and use a proxy baaed on the training model to control for

the effects of nonneutral general human capital accumulation in the wage equation. This raises a

number of difficulties that we explore in the next few paragraphs.

17
We reiurn to the case of scalar z. Assume that the productivity equation (net of training costs)

takes the form

(21) y,= rs +Y(~Ti,) - C(T,J +H(t) + cqq + q

where XTiz= Z,=,,,iTiZ,Y(.) is an increasing fiction that summarizes the effect of accumulated

training on productivity, and C(TiJ is the cost in terms of tbe log of productivity of Titunits of training

in period t, and the fimction H(t) has been redefied to accommodate the inclusion of training,

Assume that Ticis determined by employer beliefs about productivity given D“ q,s, and L as well as by

Do q,s, and experience. Then

(22) T,, = ND,,% S, t) = r(s,z,t) + rrt

where r(s,z,t) is E(h(Dt, q,s, t)ls,z,t) and ~ is an error term that is related to q and Dt but is assumed

independent ofs, z, and t. Following through on a series of substitutions that parallels those leading

to (8), and assuming that the worker pays for and receives the returns to the general training yields the

wage equation

(23) w,= (r+ y,+ a2)s + V(Z Tiz) - C(T,J + H*(t) + A(Y1+ rt,)q + E(Av+e lDt) + G,

Suppose that up to an irrelevant constant Y(Z,.., Tit)) = y, %., TF ~d C(TiJ = C, Tit.

Then the regression fimction relating w, tos, z, ~ Tic,and Titin period t maybe written as

(24) w,= (r+ a,~s + (v,+AJ2 Tit + (~t-c,)Ti, + a,,z + H*(t) + em

where al,, ~t, ~,, and a~tare the coefficients of the linear least squm~ ProjWtion of A(~[ + %)q +

E(Av+e IDJ ontos, ~ Ti~, Tit, and z, and the error term e- is uorelated to the variables in the model

by definition of a,, ~ti ~. and a,,. The time path of a,, and a,, will be influenced by changes overtime

in the correlations ofs, z, and A(Y1+ rq)q with ~ Tiz and Titas well as changes overtime in the

correlations of z, ~ Tit, and Titwith E(Av+e lDt). (The coefficients of the experience profile H*(t)

wi~lbe influenced as well.)

Two implications follow from (23) snd (24). First, even if training depends ordy on

information that is known to the firm at the start, the relationship between q and Tit and ZTi~may

18
change with c leading to changes overtime in the coefllcient ons even if there is no learning. The

second point follows from the fact that training depends on D, and so will be correlated with it. The

least squares estimates of the coefficients on the training variables will reflect both the direct effect of

training and a relationship between the time path of Titand E(Av+e IDJ. .4s a result, the effect of

adding the training variables to the model on b,, and ba is complicated in a mixed human

capita~employer learning model. In particular, one might ezpect the addition of fimctions of Titand

ZTiTto the model to change and quite possibly reduce the rate of increase of bm for two reasons. First,

the training variables change over time and are positively correlated with z. Second, they will abaorb

part of the trend in E(Av+e IDJ, and it is changes in this term that induce the variation with t in b,, and

bm Furthermore, the introduction of the training terms alters the partial correlation between z ands,

which changes the effect on the path of b,, of introducing z with a time varying coefficient.

Unfortunately, we have do not have a way to isolate the effects of training from the effects of

statistical discrimination with learning if, as seems plausible, the quantity of training is influenced by

the employer beliefs about productivity. Consider the null hypothesis that (1) learning is important, (2)

variation withs and z in the rate of skill accumulation is not, and (3) variation in our measure of

training is driven by worker performance (which leads to promotion into jobs that offer training)

rather than by exogenous differences in the level of human capital investment. Even under this

hypothesis one would expect the introduction of the training measures to lead to a reduction in the

growth over time in the coefficient on z and a reduction in the impact of z on the time path of the

coefficient ons. With an indicator of yit,that problem is aily solved, but we lack such sn indicator.

Despite the absence of a clear structural interpretation of the results we think it is important in

this initial study to see how irr~oducing measures of training altera b,, and b.. Consequently, below

we report estimates of (24). There are two additional problems in using the training data. First, the

measure T’,,of Ti,is ahnost certain to contain measurement error. Swond, the quali~ of the training

data prior to 1988 is too poor to be used, which means that the data needed to form the measure XTi. is

missing for persons who letl school prior to that year. We do not have a solution for the first problem

but deal with the latter problem by estimating a flexible model relating T“i,tos, z, and t using data ffom

1988-1993 and using the model to impute values in the earlier Years.lsWe estimate variants of (24)

“ Spletzer and Lowenstein (1996) provide means of dealing with measurement error in the training data but these are beyond

the scope of our study.

19
below. Our preferred specification is a wage growth model based on the firat difference of (24). The

growth specification has the advantage of only requiring data on Ti, and Tit.,. Perhaps more

importantly, this specification also eliminates bias ffom unobserved person specific effects that are

known to firms and are correlated with both training and wages.

3. Data

The empirical analysis is baaed on the 1992 release of NLSY. The NLSY is a panel study of

men and women who were aged 14-22 in 19~8. Sample members have been surveyed annually since

1979. (In 1994 the NLSY moved to a bhnrmsl survey schedule.). me NLSY is an attractive data set

for the study of employer learning and statistical discrimination. First, the sample sizes are large.

Second, sample members are observed at or near the start of their work careers and are followed for

several years. Third, the NLSY contains detailed employment histories, including reasons forjob

changes. Fourth, it contains a rich set of personal characteristics that maybe related to productivity

and may be hard for employers to observe, including father and mother’s education and occupation,

drug and alcohol use, criminal activity, AFQT, aspirations and motivatio~ and performance in school.

Furthermore, the data set contains a large number of siblings. The earnings of older siblings as well

as parents maybe used as indicators of characteristics of younger sibliigs that affect productivi~ but

are hard for employers to obseme. Finally, it contains measures of training, which we need to

investigate the possibility that variation with experience in the effects of schooling and our measures

of hard to observe personal characteristics are due to a relationship between these variablea and the

quantity of training received.

We restrict the analysis to men who are white or black who have completed 8 or more years of

education. We exclude labor market observationa prior to the first time that a person leaves school and

accumulate experience tim that point. When we analyze wage changes, we fin-her restrict the sampIe

to persons who do not change education between successive years. Actual experience is the number of

weeks in which the person worked more than 30 hours divided by 50. Potential experience is defined

as age minus years of schooling minus 6. To reduce the influence of outliers, father’s education

(F_ED) is set to 4 if father’s education is reported to be less than 4. AFQT is standardized by age.”

19 me age of fie ~qle ~embers at ~e time & AFQT was adrninktered vari$s somewhat in fhe my s~Ple. ~s

induces some variation in schooliig levels at the time the AFQT is taken. To calculate standardized AFQT, we adjust the raw

20
The means, standard deviations, minimum and maximums of the variables used in analysis are

provided in Table Al in the Appendix, along with the variable definitions. The mean of actual

experience is 4.9. The mean of potentird experience is 7.3, and the mean of education is 12.7. All

statistics in the paper are unweightcd. Blacks are over sampled in the NLSY and contribute 28.8

percent of our observations. Table A2 reports correlation coefficients and simple regression

coefficients that summarize the relationships among the key variables used in the analysis.

4. Results for Education

InTable 1-3 we report estimates of our basic wage level specification. In table 1 we use

potential experience as the experience measure and use OLS to estimate the model. The equations also

control for a cubic in experience, a quadratic time trend, residence in so urban area, and dummy

variables for whether father’s education is missing and whether AFQT is missing. We add interactions

between the dummy variables for missing data and experience when interactions between father’s

education and experience and AFQT and experience are added to the model. These variables are not

reported in the tables. Standard errors are White/Huber standard errors computed accounting for the

fact that there are multiple observations for each worker.

In column 4 we present an equation that includess, Black and sxt. This corresponds to (7a)

with b,, restricted to b,, = b,. + b,lxt. The coefficient on sxt/10 is -.0077 (.0062), suggesting that the

effect of education on wages declines slightly with experience. In cohmm 5 we add AFQT and F_ED,

where F_ED is years of father’s education. As had been well documented, AFQT has a powerfol

association with earnings even after controlling for education. A shift in AFQT from one standard

deviation below the mean to one standard deviation above is associated with an increase in the log

wage of. 157. The coefficient on Education declines to .080 and b,, becomes more negative.

In column 6 we add linear interactions between t and two different z variables, AFQT and

F_ED, to the equation. The resulting equation corresponds to (9) with the restriction that b,, = b,O+

b,,xt and b.= ba + bzlxt, except that we introduce two z variables rather than 1. The estimates imply

AFQT score by sub~acting the mean score for each age and dividing by the standard deviation for that age. For individuals

with siblings in the ssmple, the coefficients oftbe regression of the unadjusted test score of the oldsr sibling on the test score of

the younger sibling and the regression of the test score of tbe younger sibliig on the the score of the older sibling are very

similar aftm one also controls for age, suggesting that the information in the testis not very sensitive to age over the range in

the sample.

21
that the effect of AFQT on the wage increases greatly with experience t. b~m,, which is the

coefficient on AFQTxt/10, is .0820 (.0125). b~~,, w~ch is I%vWAFQT,rises tiom only .0179 whm

experience is Oto .0999 when experience is 10. The results imply that when experience is 10 and

education is held constant, persons with AFQT scores one standzrd deviation above the mean have a

log wage that is .200 larger than persons with AFQT scores one standard deviation below the mean,

whi!e the difference is only .036 when experience is O. The effect of father’s education also increases

with experience. The main effect is actually slightly negative (but not significant). However, the

interaction term is positive, though not statistically significant.

Our results for AFQT and F_ED are consistent with Farber and Gibbon’s results in which they

use the components of AFQT and an indicator for whether the family had a library card when the

person is 14 that are orthogonal to the wage on the first job and education. The key result in the table

is that the coefficient on sxt/10 declines sharply (to -.0351 (.0069)) when AFQTxt and F_EDxt are

added. The implied effect of an extra year of education for a person with 10 years of experience is

only .0633. Strikingly, the coefficient ons rises to .0984 which is ahnost exactly what we obtain when

we exclude all terms involving F_ED and AFQT iiom the model (columns 1 and 4).

These results provide support for the hypothesis that employers have limited information about

the productivity of labor force entrants and statistically discriminate on the baais of education. Early

‘wagesare baaed on expected productivity conditional on easily observable variables such as education.

As experience accumulates, wages become more strongly related to variables that are likely to be

correlated with productivity but hard for the employer to observe directly. When we condition the

experience profile of earnings on both easy to observe variables, such as education, and hard to

observe variables, such as AFQT and father’s education, we find the partial et%ct of the easy to

observe variables declines substantially with experience. While one might argue that the positive

coefficients on AFQTxt and F_EDW are due to an association between these variables and tmining

intensity, it is hard to reconcile this view with the negative coefficient on sxt. While measurement

error in schooling may enhance the effect of F_ED and AFQT and may partially explain the decline in

s behveen columns 1 and 3, it does not provide a simple explanation for the behavior of the interaction

terms with experience.

In Table 2 we present OLS results using actual experience in place of potential experience as

the experience measure t. The main difference between this table and table I is that the return to

22
education is lower and the sxt interaction is positive and fairly large in the equations that exclude

AFQTxt and F_EDxt. ,However, the coefficient on SX~10declines from .0200 in column 5 to -.0056

when the interaction terms are added in column 6 of Table 2. This decline is similar to the decline that

we obtain in column 3.

The results in Table 2 are difficult to interpret, because the intensity of work experience maybe

conveying information”fo employers about worker quality. It is an outcome measure itselfl The

implications of emplo yer learning for the wage equation are changed if one conditions on information

that becomes available to employers as the wgker’s career unfolds and may reflect the productivi~ of

the worker. Conditioning on actual work experience raises some of the issues that would arise if we

conditioned on wages in t- 1 or on training received. On the other hand, the results based on potential

experience are likely to be biased by the fact that potentird experience mismeasures actual. For this

reason, in Table 3 we report the results of re-estimating the models by instrumental variables (IV),

treating all terms involving actual experience as endogenons with corresponding terms involving

potential experience as the instruments. The results in cohnnna 5 and 6 of Table 3 are basically

consistent with those in Table 1. The coefficient on AFQT is .0177 (.0096) and the coefficient on

AFQT4/10 is.1 148 (.0164). These estimates imply that conditional on years of schooling, AFQT has

only a small effect on ti”tial wages, but when t is 10a two standard deviation shift in AFQT is

associated with a wage differential of .247. The coefficient on sU1 Odeclines tiom -.0181 when the

interactions are excluded in column 5 to -.0561 in column 6.

Controlling for Secular change in the Retito Education

In column 9 of Tablesl, 2, and 3 we add the interaction betweens and calendar time to the

model containing father’s education and AFQT. 20 In the case of potential experience in Table 1, the

education slope is reduced by .02 per year, and the interaction between education and experience/1 O

drops to -.051, but otherwise the results change little. In column 10 we add the interactions between

calendar time ands, F_ED, and AFQT to the model containing the interactions between t and all three

variables. In column 10 the interactions between F_ED and AFQT and calendar time have positive

mMurphy and Welch (1992), Katr and Murphy (1992), Taber (199d) and Cbay and Lee (1997) are among a large number of

recent study of changes in the sfnrcture of wages in tbe U.S.. Since calendar time is positively correlated with experience t in a

panel data set, the Ieamingkatistical discrimination model implies that estimates of secular changes in the return to education

and .4FQT will be biased in opposite directions if one fails to add tie interaction between these variables and t to the model.

23
coefficients, indicating that the effects of these variables rose during the 1980s. Adding the time

interactions reduces the size of the experience interactions with F_ED and AFQT, but the qualitative

pattern of the results does not change.

Controlling for Occupation

One objection to the theoretical framework underlying the estimates in TabIes 1-3 is that it

assumes that the flow of information to employers is independent of the type of job the worker begins

in. This is contrary to the idea that some jobs are “dead end” jobs. Perhaps education (and high

AFQT) enables a worker to gain access to jobs in which tirms have the ability to observe whether the

worker has higher level skills that are strongly related to productivity. As a simple check on this

possibility, we present a series of equations in Table 4 that control for the 2-digit occupation of the

first job. The results are very similar to what we obtain when occupation is excluded?’.

The Effects of the Wage oi?a Sibling

In Table 5, we use the wages of siblings with 5 to 8 years of experience as a hard to observe

backgonnd characteristic. The coefficient on sxt/1 Ois -.0097 (.0089) in column 4, which includes the

log of the wage of the oldest sibling. The learning model does not provide an explanation for the

negative interaction term, nor does the conventional view of how education is related to on-the-job

training. However, when we add the interaction between the sibling wage and t in cohrrnn 5, the

coefficient on the education interaction falls to -.0146, and the coefficient on the interaction between

the sibling wage and t/1Ois .086 (.0327).22The effect of the sibling wage rises horn. 127 upon labor

force entry to .213 atler 10 years of eiperiencc---a very large increase. The point estimate of the

interaction between education and experience result is essentially unchanged when we allow the effect

of sibling wage. In Table 5, columns 5 and 6, we show that these results are robust to allowing the

effects of education and the sibling wage to depend on calendar time. Our interpretation of these

results begins with the premise that the labor market productivi~ of siblings are comelated. As a

“ .&I interesting project for fiture research woufd be to use information from the Dictionary of Occupations Titles on skill

requiremen~ of occupations and trace how easy to observe and hard to observe productivity chamcteristics are related to

changes over a career in the skill requirements of the job a worker holds. It would also be intemstiug to examine how the

slopes are influenced by the skill requirements of the initial occupation held by the individual.

n The corresponding point estima”bs are -.022 and .080 when we alfow the effects of education and the sl%lingwage to depend

on calendar time.

24
worker acquires experience this comelation is reflected in the performance record D, and in wage rates.

The sibling wage is correlated with education, &d so the effect of education on the wage declines with

experience because firms are estimating productivity with a bigger information set than at the time of

labor force entry.n

The Experience Profile of the Effects of AFQT and Education on Wages

In this section we take a more detailed look at how the effects of AFQT ands vary with

experience by estimating models of the form

Wt= f(z,~b) + h(s,~b, ) + H(t) + ~it

where b, and b, are now vectors of parameters. Table 6 is baaed on models in which f(z,~b~ and

h(s,tb,) are quartic polynomials in t. In the top panel, the experience measure is potential expenencq

in the bottom panel we use actual experience instrumented by potential experience. All of the models

in the tables contain the other control variables discussed above. They also include F_ED and

F_EDXt.

The columns report dw@AFQT, #w@FQT, dt dw@s, and &w@dt at various experience

levels. The first column of the table shows that 6w@4FQT increases steadily born .0197 when t is O

to .121 when t is 12. (We only go out to t=12 because sample information becomes thin at higher

values.) The specification that we use in most of the paper, in which f(z,~b~ and h(s,t;b,) are linear in

t (column 6 in tables 1-3), suggests an increase in dw@4FQT horn .0179 to .116 as t goes ftom Oto

12.

As noted earlier, employer learning implies that .3w@4FQT is nondecreasing in t ( i.e.,

d2w@4.FQT,dt zO), with a strict inequality likely if some new information arrives each period on y. If

the noise in observations of y, are iid, then the rate of increase &w@AFQT,dt should decline with t, as

z FarberandGibbons(1996)use men and women, include Hispanics, and restrict their sample to persons who have worked at

least three consecutive yews since attending school. Using this sample the coefficients on AFQTxt and the effect on sxt of

adding AFQTx t are siiilar to those reported above. We also obtain qualitatively similar results when we folfow Farber and

Gibbons and use the level of wages rather than the log. We experimented with an indicator for whether any person in the

respondent’s household had a library card at the time the respondent was 14, a variable which Farber and Gibbons also used.

We confii Farber and Gibbons’ finding that the coefficient on the residual from a regression of this variable on the initial real

wage, education, part-time status, rar interaction between education and part-tie status, race, sex, age, and csfendar year

increases with experience, as well as their finding that the results for library card and AFQT are weakened substantially when

these variables are interacted with calendar rime. However, when we use the library card variable itseIf the effect of the library

25
shown in expression (12c) for et above. The rate of increase must decline eventually because the

amount of additional information in observationa of labor market pertorrnance is declining. @, is

bounded at 1.) However, it is possible that the first two or thee observations on a worker are

particularly noisy because of factors that we have left out of the model. For example job specific or

occupation specific match quality may be more variable for new workers than more experienced ones.

In column 2 we report &w@4.FQT,~ for various experience levels, The values increase from

.0025 when t is Oto .0104 when t is 5, remains at about this level until t is 8 (the maximum is .0108 at

t = 6.5) and then decline to .0048 when t is 12. These results are reasonably consistent with a decline

in the amount of new information with experience tier an initial period of noisy observations.24

In panel B we replace potential experience with actual experience, and treat actual experience

as endogenoua. The 99th percentile value for this variable is only 13.33, so there not much sample

information on t beyond this point. In column 1 we see that the effect of AFQT increases with

experience. The rate of increase &w@AFQT,i3t rises at first thm .0092 when t = Oto .0138 when

t=5, but declines to -.0012 when t = 12. However, the standard errors on these derivatives are quite

large. These results are also loosely consistent with the proposition that the rate at which new

information about initial productivity arrives declines with experience, but the estimates are not

sufficiently precise to say much about this. As the NLSY sample ages, it will be interesting to revisit

the issue.

In the model with potential experience, the return to education increases slightly be~een *O to

t=3, and then declines sharply. In the model with actual experience, the decline is constant throughout

from .0881 at no experience to .0299 at 12 years of experience.

Testing the restrictions on the experience profiles of the effects ofs and z on the wage.

It is interesting to see how well the experience profiles of the education snd AFQT coefficients

satis~ the restrictions in propositions 3 and 4. One complication in performing these tests is the place of

cardvariable falls rather ths.a rises with experience. We thaak Henry Farber for assisting us ia reconsrrucdng the Fsrber aad

Gibbons ssrnple.

MWe used two other non-liiear specifications. The f.rst used spliae fimctions with breakpoints at =2, t==, &7,snd &IO. In

the second we restricted f(z,~b~ so that %@4FQT & = Owhea t is 2S and h(s,tb~ so that &w@s & = Owhen t is 25. The

idea is that rhe iafonnation about productivity that is contained ia AFQT is fidly revealed by the time t is 25. Both of these

specifications yielded results similar to the reported model in whkh &w@4FQT L%& flat or increasing and then definitively

&creasing after about 7 years.

26
race within our model --- should we treat race ans variable or a z variable? The answer to this question

hingea on the extent to which employers violate the law and use race as an indicator of productivity. We

discuss this at length in section 5 below. For now we will sidestep the issue by running separate tests on

the white and black samples. Conaider fist a specification in whichs and z are both scalars, education

and AFQT score, respectively. Proposition 3 says that the product of -cov(s,z)hr(s) --- the negative of

the coefficient of the regression of z ons -- times the coefficient on the interaction between AFQT and

experience (zm) should equal the coefficient on the interaction between education and experience (sxt). In

the white sample, the product is -.00162 and the coefficient on sxt is -.00232. A Wrdd teat does not reject

the proposition. In the black sample the corresponding numbers are -.00196 and -.00498 and the

proposition is rejected?s

We might also want to test whether the entire profile of the interactions betweens and t and

between z and t are in accordance with proposition 3. Gne way to do this is to estimate the model in

which the interactions are specified as fourth-order polynomials and jointly test whether the

coefficients on the four polynomial interactions are related by the coefficient of the regression of z on

s. This seems a bit restrictive in that we only expect the relationship to holdover the range of

observed data and polynomials that have very different coefficients can be fairly similar over a short

range. However, we performed these tests on models”in which the interactions of AFQT and

education with experience are modeled as fourth order polynomials. Once again, we fail to reject the

proposition for whites but reject for blacks.

We also tested proposition 4, the vector analog of proposition 3, on models which include both

AFQT and father’s education. We also considered as z variables the dummy variables indicating

whether these quantities were known. This test amounts to at-test of whether sum of the products of

-cov(s,z)/var(s) and the coefficient on zxt for each z variable is equal to the coefficient on sxt. For

whites, the sum of the products equals -.00193, the coefficient on sxt is -.00254, and the proposition is

not rejected. For blacks, we obtain -.00166 and -.00456 and reject the proposition.

Wage Growth Equations

hr Table 7 we estimate (9) in first diffmence form. We restrict b. to be b$o+ b,, t and b. to be

ba + b,, t. The usual reason for working in fist differences is to eliminate correlation between the
regressors and a fixed error component. This motivation is not compelling in the present ease.

However, it is possible that the first difference specification maybe less sensitive to errors in

identi&ing when individuals start their careers.

Columns 1-4 report OLS estimates with potential experience. The coefficient on the sxAt will

pick up the effects of secular changes in the return to education as well as the changes with experience

in the return to education. The upward secular trend in the return to schooling may partially explain

the fact that the sXAthas a positive coefficient in the basic model in column 1 while it is negative for

the corresponding level specification in Table 1, column 4?S (A secular trend in the return to education

or AFQT matters less when estimating the equations in levels because much of the variation in

experience is across persons of different ages). Also, the estimates are much less precise when we

estimate in first difference form. However, the key results are qualitatively similar to the level

specifications. In particular, the coefficient on s/1Odeclines &om .0148 (.0094) in column 1 to -.0092

(.01 10) when we add the AFQT and F_ED interaction terms in column 2. The size of the decline in

this coefficient is very similar to the drop in the coefficient on sxt when we add AFQTxt and F_EDxt

to the level specifications. (See columns 5 and 6 of Table 1). The AFQT interaction term is positive

with a t value of 3.4. The F_ED _@eraction is also positive and similar in magnitude to the result

obtained in levels, but it is not statistically significant.

Columns 5-8 reports IV estimates of wage growth equations using actual experience as the

experience measure. The coefficient on AFQTxAt/10 is .0905 (.0197), which compares to the value of

.1148 in Table 3, column 5. The coefficient on sxAtf10 declines tlom .0295 (.0079) to -.0030 (.0100)

when AFQTxAt/1 Oand F_EDxAtfl Oare added.

5. Do Employers Statistically Discriminate on the Basis of Race?

llms far we have focused the discussion on employers’ use of education as an indicator of labor

market productivity. In this section we examine the role of race. By almost any meaaure, young black

men are disadvantaged relative @whites in the U.S.. on average, black males have Poorer, less

educated parents, are more likely to grow up in a single parent household, live in more troubled

neighborhoods, attend schools with fewer resources, and have fewer opportunities for teenage

~ See Murphy and Welch (1991) and many subsequent studies. Mumane et al (1995) provide evidence of an increase in tbe

retunr to aptitude and achievement, as measured by tests.

2s
employment than white males. Many of these factors are correlated with educational attainment and

labor market success. They are likely to lead to a blacldwhite differential in the average skills of

young workers. Discrimination in various forms may tirrther hinder the development of human capital

in black children, and add to a gap in skills that is due to the race difference in socioeconomic

background. The gap in some indicators of skill are very large. In our sample, the mean percentile

score on the AFQT for the black sample is 23.78 while the mean for whites is 53.27. Neal and

Johnson (1996) and a number of earlier papers have shown that in the NLSY sample of men a

substantial part of the race gap in wages is associated with the race gap in AFQT.

If pre-msrket discrimination is an imporkmt factor in a gap between the average skills of black

and white workers, then it seems likely that various forms of current labor market discrimination

contribute to race differences in wages that are unrelated to skill. However, it is nevertheless

interesting to examine the possibility that a correlation between race and skill might lead a rational,

profit maximizing employer to use race as a cheap source of information about skills and statistically

discriminate on the basis of race. Sirch statistical discrimination rdong racial lines can have very

negative social consequences ilnd is against the law. However, such discrimination would be difficult

to detect.

A statistically discriminating firm might use race, along with education and other information

to predict the productivity of new workers. With time, the productivity of the worker would become

apparent and compensation would be based on the larger information available rather than the limited

information available at the time of hire. Consequently, if statistical discrimination on the basis of

race is imp-ortant, then adding interactions between t and z variables such as AFQT and father’s

education to the wage equations should lead to a positive (or less negative) coefficient on blackxt and

should lead to an increase in the race intercept. As noted in section 2, if firms use race as information

then it behaves as ans variable in the model and the logic is the same as in our analysis of the effect of

education. On the other hand, if firms do not use or only partially use race as tiormation, then a race

indicator behaves as a z variable. As discussed in Section 2, in this case the race gap should widen

29
with experience if race is negatively related to productivity, and adding a second z variable that is

negatively related to race will reduce the race gap in experience slopes.z’

The race differential in our basic specification in column 1 of Table 1 is -.1801. This drops to

-.0969 when AFQT, F_ED, and educationxt are added to the equation (column 5). When BlackXt/10 is

added in column 6, it enters with a coefficient of-.1456 (.0216). This coefficient is consistent with the

hypothesis of no or very linited statistical discrimination on the baais of race and inconsistent with the

hypothesis that firms make fill use of race as intbrniation. The coefficient on Black is insignificantly

different from O,although the models do not-provide a clear pre~ction about the sign of this variable,

since race may be correlated with information in q that can legally be used. The fict that coefficient on

Blackxti10 rises to -.0816 when F_EDxt and AFQTxt are added to the equation (column 8) is not

informative about whether or not firms make full use of race as information. 2s

We obtain similar results using rdternative experience measures in Tables 2 and 3. In Table 4,

columns 7 and 8 we obtain similar results after controlling for initial 2-digit occupation. We obtain

similar results using growth equations in Table 7, which should be robust to the presence of an economy

wide time trend affecting the return to education, race, and AFQT. However, in the level equations we

find that the results for race are sensitive to treatment of economy wide time trends. When we use

potential experience as the measure of t the coefficient on BIackxt declines only slightly ( from -.0146 to -

.0144) when we adding time trend interactions involving race and AFQT to the wage level equation

corresponding to Table 1, column 7, but the race-experience interaction no longer drops when AFQT and

experience is added- (Not reported.)

We wish to stress that the simple model of statistical discrimirration cannot explain the negative

coefficient on Blackxt unless firms do not make full use of race as information. The accumulation of

additional information during a career that can legally be used to differentiate among workers is fully

consistent with our results. However, there are several other explanations of the race differences in the

‘7The learning model in section 2 implies that differences across groups in the association betweens and tbe z varisble will

lead to group differences in tie bmsndb=coeflicients. Wehsvenot explored this empirically. An obstacle to doing so is that

the results might be sensitive to the linearity assumptions that we have nrade.

“ Japanese and Chinese Americsns scoreligher on aptitude and achievement tests thsn whites. Our snalysis predicts that if

f- statistically discriminate on the basis of race and ethnic background ken the addition of AFQT and AFQT*t to an

equation containing a durnrny and experience interaction term for these groups d! lead to an increase in the dummy variable

and a reduction in the experience intemcfion. Sample sizes do not petit sn analysis of these groups. While one could

differentiate smong whites based on ethnicity (see Borjas (1992), it is not clear tit these ethnic differences are obsemable to

30
experience slope in the literature that maybe at work here. It is also important to point out that the results

for Black and Blackxt alone (i.e., ignoring the behavior coefficients of the coefficients on education and

educationxt) are potentially consistent with a story in which firms are filly inform~ AFQT is positively

associated with on-the-job training, and the race difference in AFQT is partially responsible fbr a race

differential in wage growth. Adding AFQTXt would reduce a negative bias in Blackxt associated with

differential training levels. The increase in Blackxt when AFQTxt is added to the model would lead to a

fall in the coefficient on Black. As we report below, we obtain qualitatively similar results when we add

controls for employer training, but these controls reduce the magnitude of the coefficient on Blackxt and

the effect of adding AFQTxt on the coefficient on Blackxt.

Another potential test of whether race is used to statistically discriminate or not is to see

whether proposition 4 holds either when race is treated as sos variable or when it is treated as a z

variable. To do this, we use the model in column 8 of table 1. With race treated as ans variable, we

regress the z variables (AFQT, father’s education, and the dummies for not knowing these quantities)

on the twos variables. We sum the product of these coefficients and the coefficients on the zxt

interactions in the main re~ession and compare them to the coefficients on the sxt interactions. We

can then conduct a joint teat of whether these two quantities are equal. For the education interaction

the sum of the products equals -.00183 while the model coefficient is -.00301. For the race interaction,

the two terms have opposite signw the sum is .00644 while the model coefficient is -.00816. Not

surprisingly, the proposition is soundly rejected.

When we treat race as a z variable, we begin our test by regressing the 5 z variables on

education, ours variable. Here, we have only one restriction to teat. The sum of the products equals

-.00215 while the model coefficient eqnrds -.00301. The proposition can be rejected at conventional

levels of significance (the P-value is .027) but with corrected standard errors this will probably not be

the case. This is a further indication that employers are not treating race ss information, or at least not

fully.

6. Models with Training

In Table 8 we report estimates of equation (24) along with models that exclude the training

variables. Jn these models we have excluded father’s education. In the basic model in column 1 the

employers. Our methods could be used to investigate statistical discrimination on the basis of attending prestigious cojlcges m

31
coefficient on sxt/1 Ois -.0102. In column 2 we add T, and 21Ti,to the equation. The variable T,has

the expected negative sign of-.1044 (..0179), while IIT:t haa a coefficient of .1864 (.01 14). The

coefficient on sxt/1 Ofalls to -.0346. The coefficient on AFQT falls horn .0828 to .0582 while the

coefficient on education rises slightly. The substantial negative experience slope on education might

be consistent with a human capital story in which knowledge obtained in school depreciates overtime

unless one receives training. In column (3) AFQTxt/10 enters with a coefficient of .0502 (.0125), and

the coefficient on and sxt/1 Odrops from -.0358 to -.00427. These changes are consistent with

employer learningktatistical discrimination. If we reverse the order in which the variables are added

by adding AFQTXt before the tr~g measures, the marginal effect of the training measures on

educatiorwt is much smaller. We have also estimated separate models for blacks and for whites and

obtain a similar pattern.

In Columns 4-6 we investigate the effect of introducing the training measure on the race gap in

wage slopes. The coefficient on blackWIO declines flom -.1467 to -.1048 when we add the training

measures. Adding AFQTxt/10 leads to a further decline to -.0777.

To reduce the difficulties associated with the lack of data on training in the early years of the

study and individual heterogeneity that is correlated with both training and wages, we turn to a tirat

difference version of (24). In the first difference version the current and lagged vahres of T, enter.

These results are in Table 9. The coefficient on educationWIO declines from .0126 (.0094) to .0073

when the training measures are added. The coefficient on Black rises from -.0995 (.0351) to -.0923

(.0353). However, the coefficient on T, is positive while the coefficient on T,., is negative. These

signs are inconsistent with a simple human capital model but are consistent with an EL-SD model in

which training opportunities are given to more productive workers aod learning about productivity

occurs over time. Adding the training variables to a mo&l that contains AFQT and F_ED haa little

impact on the coefficients on these variables. (Compare columns 2 and 4.) Imprecision in the training

measures may partially explain this fact, but does not provide an explanation for the sign pattern in the

training coefficients. The coefficients on sxt and Blackw decline in absolute value when AFQT and

F_ED are added, as is predicted by the EL-SD. Overall, the wage change results are quite consistent

with an important role for EL-SD

particular college majors.

32
We view the evidence as consistent with a role for both human capitaI and EL-SD, but cannot

make a precise statement about the relative contribution of these factors because, as discussed above,

training wiIl be influenced by new information about employee performance and the quaIity of the

training data is suspect.

7. Information Transmission Across Firms:

The formal model that we have used to interpret the results assumes that employers have the

same information about workera. The resulta.suggest that tiormation about productivity does

eventually get reflected in wages. However, they do not identi~ whether these adjustments occur

primarily in the current firm, presumably in response to outside pressure from competitors who have

information about the worker, or through moves to other empIoyers with associated wage increases for

workers who do not move.zg In this section we briefly examine the issue of information transmission

across firms.

A number of theoretical papera discuss whether tiormation about productivi~ will be

reflected in promotion paths and wage increases within tirrns, as well as the strategies firms might use

to try to hide information about good workera (e.g. Greenwald (1986), Waldrnan (1984), Lazear

(1986), Gibbons and Katz (1991))?0 Unfortunately, the theory is ambiguous about whether a MS

private information concerriing the worker will be reflected in wages offered by that firm to incumbent

workers and about the mechanism that induces the firm to adjust wages. hr some private information

models in which only wages and perhaps position witbin the firm are observable to outaide firms, the

employer’s information is not reflected in wages until the worker gets an outaide offer. In Waklrnarr

(1984) it is reflected in wages ailer the fm reassigns the worker to a position in which output is more

29Although we do not Imow of systematic evidence on this, casual empiricism suggests that changes in the legal system have

led some f-to adopt the explicit policy of not providing references for former employees. Also, increased ffig costs and

concern about litigation may have made employers more reluctant to discharge workers for poor performance. Stad.stical

disc-ation may become a more seriow”problem if information flows are restricted. This may lead f- to relate

compensation to performance more explicitly, with more turnover being a “voluntay” response to below average wage

increases. On the other hant diffmence in wages across groups maybe attenuated because f- may be reluctant to open up

large wage differentials between pemonr with similar education, seniority, and experience. It is posdde that the balance

between these two considerations has changed over time.

20None of WS litemmre ~on~idera&e fiPlications of the possibility that employers and co-workers ac~e ~Pu~tiOns fOrhOw

positive they are in promotig the careers of individuals or that the incentives of co-workers and even supervisors to keep

favorable information about a colleague private or in concealing unfavorable information fmm aasoc.iatesoutside the fm nmy

be quite different from those of the employer. These factors would undermine the case hat f- would want to and be able to

keep inside informati&r inside the fm

33
sensitive to ability. In Gibbons and Katz it is reflected in wagea if the firm chooses not to lay off the

worker. The firm lays off low productivity workera, who are hired by other firma at lower wages.

Outside firms infer that the remaining workera are of higher quaMy, which forces the employer to raise

wages of those who stay with the firm. Both models have the implication that hard to observe

variables like AFQT, F_ED, and the wage of an older sibling should be positively related to wage

growth if one does not condition on whether a person was laid off or not. This is what we found

above.

Gibbons aod Katz (1991) provide empirical support for the hypothesis that layoffs should be

negatively related to wage growth. But there area number of other reasons why layoffs should be

negatively related to wage growth (labor market condltiona, lost seniority, for example). To obtain

more focused tests, we interact personal characteristics that are hard for employers to observe directly

with indicators for layoffs and discharges. The coefficients on these variables should differ tlom the

coefficients on characteristics that affect productivi~ and are easy for employers to observe, such as

years of schooling if (1) layoff: occur for multiple reasons, some of which have nothing to do with the

worker, (2) the probability that a layoff reflects low worker specific productivity relative to the wage is

related to z variables, and (3) outaide employers have information about the nature of the layoff or

obtain information (through references, for example) ahout productivity.

This suggests an cquationof the form

If knowledge acquired by firms is reflected in wages, then ~, should be nonzero, and ~, and ~, should

be near zero. If knowledge acquired by firms is not reflected in wages, then ~, should be small and ~,

and ~~should be nonzero. Given sample size limitations we have estimated a simplified version of the

above equation on the sample of layoffs only, with z[Layof~ ]t excluded:

w, - W,.l= (PO+ 13,)+ z ~S+ other controls.

Our evidence on whether hard to observe variables such are positively associated with layoff losses is

weak at best. In fact, we find that losses are larger for persona with high AFQT. We have not controlled

for labor market conditions, and among the sample of layoffs they maybe correlated with AFQT.”

Mwe kv=tigated~he~er thefm,>it WagelossesrisewithAFQT is driven by a positivecorrelationbe~een ~QT md

employmentinawhiteCO1lSI, nonunionjob,wherelayoffsareleastIiiely tobe influencedby seniori~rules. Gibbonsand

34
k Table 10 we report estimates of the effect of AFQT and F_ED on employer initiated

separations. These include layoffs, firinga, and plant closings. Our results were not very sensitive to

distinguishing among these three types of job loss. We tind that AFQT has a weak negative effeet on

the probability of losing one’s job, even tier conditioning on seniority in the firm. However, when

senion-ty is controlled for a swing of two standard deviations in AFQT changes this probability by .02,

which is only 1/5 of the mean layoff rate of. 1. We obtain similar results when the seniority control is

dropped.

Our results suggest that only a small part of the rise with t in the effect of AFQT on wages

operates through an association between AFQT and layoffs and the wage losses experienced by those

who are laid off.

Lazear (1986] presents a model in which both the current firm and outside firms observe

indicators of the productivity of the worker. His model predicts that workers with favorable

productivity traits that are hard to observe directly will be more likely to receive outside offers smd

more likely to quit than workers whose hard to observe characteristics make them less productive. In

results not reported we find that F_ED is positively related to the quit rate conditional on education

and experience and tenure. AFQT does not have a significant effect. Neither AFQT nor F_ED is

significantly related to wage growth among those who quit. (Not reported).

These results tentatively suggest that information flows in the labor market are sufficient to

force a firm to differentiate among workers as the fiq-nobtains better information about their

productivity. A careful investigation will require a separate paper..

8. The Potential for Testing Services to Certi& Skill

Ourestimates provide information about the rate at which employers learn about worker

quality. In Altonji and Pierret (1996) we use our empirical estimates to explore the implications of the

rate at which employers learn about worker quality for the empirical relevance of the educational

screening hypothesis. We show that even if employers learn relatively slowly about the productivity

of new workers, the portion of the return to education that could reflect signaling of ability is quite

limited. While education may be too expensive to serve as a means for able workers to certi~

Katr note that layoffs are likely to be a particularly negative signal for white collar workers snd restrict their analysis to hem.

However, splitting the leads to an even more negative coefficient for white collar workers than for blue collar workers,

35
themselves to employers, perhaps other mechanisms could perform this fiction, at least for some

determinants of productivity. Here we point out that interpreting our estimates of the time profile of

the effect of AFQT on wages as the result of employer learning implies that high ability workers

would have a substantial financial incentive to take the AFQT to differentiate themselves from those

who are less able in this dimension.

Suppose that a third party were to administer the AFQT and certi~ the results to outside

employers, in much the same way that the Educational Testing Service administers the SAT exams.

Using our estimates of the learning profile and assuming that firms know all of the information contained

in AFQT by the time experience is 15, we have computed how much a person who believes that he is 1

standard deviation above the mean for the AFQT would pay to take the test at the time he enters the

workforce.32 The OLS estimates using potential experience underlying Table 6, panel A, column 3)

imply that if tin-is become fully informed shout productivity by the time experience is 15 end the interest

rate is. 1, then the person would be willing to pay .559 of the first year’a salary for the test.33 The

corresponding value when we use potential experience as an instrument for actwd experience (panel B,

column 3) is .330.

These calculations raise the issue of why such a testing service has not emerged if information

is initially imperfect. One tisw~” is.that firms are not aware that the AFQT captures characteristics

that have a strong association with productivity. It is only recently, with the availability of the NLSY,

that labor economists have become aware of this. Another is that it would be difficult for a testing

firm to become established at a national level. A third is that, given race differences in the distribution

of AFQT scores, firms who make use of AFQT information in hiring for a specific job would have the

burden of establishing that they are relevant to productivity in that job or run the risk of violating

discrimination laws. This would be true even if individuals provided firms with the test results.

However, we do not find these answers to be tidly satisfactory.34 Analyses baaed on variables such as

32 If ~worker ad not kIICWtis ability, he could take a practice test on his own. Presumably, this would not raise the total cost

of the test very much.

33 ff~l~ we ~e ~SS~g tiat CJIIIy1 worker ties the test and ignoring the fact that the composition of the pool of workers

who choose to take the test in equilibrium would influence return for a particular type of worker.

34 N~t~ ~lSOtit fi & absence of su iIIstjtuti,xI such ss the Educational Testing Service, a fm might provide the test. Some

f- perform their own tesdng.. However, if the results were svailable to the employees or other fm know that a particular

fm tests its employees, then the fm would not be able to capture the fuUretrmr to testing.

36
the wage rates of siblings or i%ther’seducation may be less vuhrerable to this objection. In any even~

we should also point out that our estimates of the AFQT-experience profile are sensitive to treatment

of time trends and training, so that financial return to being certified as high AFQT is probably

substantially less than the above nombers imply.

9. Conchrsion

This paper explores the implication of the premise that firms use the information they have

available to them to form judgments or about the productivity of workers and then revise these beliefs as

additional information becomes available. This a premise that seems natural to us and receives some

strong empirical support in Farber and Gibbons (1996). If profit maxirruz“ ing firms have limited

information about the general productivity of new workers, then they may use easily observable

characteristics such as years of education or race to statistically discriminate among workera. We show

that as firms acquire more information about a worker, pay may become more dependent on productivity

and less dependent on easily observable characteristics or credentials. This basic idea is quite general and

provides a way to test for statistical discrimination in the labor market and elsewhere in situations in which

agents learn, such as credit markets.

We investigate it empirically by estimating a wage equation that contains interactions between

experience and hard to observe characteristics such as AFQT and father’s education along with the

interaction between experience and a variable that firms can easily observe, such as years of education.

We assume that all three variables are related to productivity. We find the wage effect of the

unobservable productivity variables rise with time in the labor market and the wage effect of education

falls. These results match the predictions of our model of statistical discrimination with learning.

We use a similar methodology to investigate whether employers statistically discriminate on

the basis of race. If our model is taken literally, the small race differentials for new workers and the

spread in the race gap with experience is most consistent with the view that race is negatively

correlated with productivity and the productivity gap becomes reflected in wages as fms acquire

additional information that can legally be used to differentiate among workers. We wish to stress

however, that other factors are probably as or more important in differences between whites and blacks

in wage profiles, and race differences in human capital accumulation accounts for at least part of our

37
findings. Also, our empirical results for race are sensitive to treatment of economy wide changes in

the effects of race, AFQT, and education. Future research should also address the large race gap and

education gap in employment rates, particularly for young workera. In situations in which there are

alternatives to the conventional labor market and employees in the alternative sector do not acquire

work histories that have value or are informative to firms in the conventional sector, then statistical

discrimination of the type described above may reduce participation rates of the disadvantaged group

in the conventional labor market.

It is worth emphasizing that the analysis in the paper suggests alternative interpretations of

empirical models of wages and other outcomes that involve experience interactions. It will be usefid

tore-examine the results of other studies that included interactions between experience and easy to

observe vtisbles such as schooling, race, gender, and experience in equations that also contain

interactions between experience and harder to observe background measures. We have not been

successful in sorting out the relative importance of differences among workera in training on one hand

and statistical discrimination with learning on the other for our results. This is an important area for

fiture research.

h important and reasonably strsightfomvsrd extension of the analysis is to other easily

observable and hard to observable background characteristics. For example, do firms statistically

discriminate on the baais of the neighborhood one is ffom or on the baais of the reputation of the high

school, college, or graduate school one attends? A study of whether new immigrants are j@@ by the

average skills of their counbyrnen in the U.S. would be a natural step in the research by Borjss (1992)

and others documenting differences hong immigrants in labor market success. These issues are

researchable using the approach developed in this paper. Finally, it would be nsefid to apply the

methods of the paper to other labor market outcomes in addition to wages.

38
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41
Appendix 1

From equation (11) we have ~, = – COV(S,Z)*

Avar(v) +CQV(V, e) ad

\var(s,z)l

@z= – Var(s)*

Avar(v) +COV(V, e) We know that ~= =

Cov(s,z)

]var(s,z)l —. This gives us the desired rcszdt:

var(s)

Q, = -@=Qz

Appendix 2: Derivation of Equation (16) and (17).

Consider equation ( 15). Rewriting var(s,z)-’ as a partitioned matix leads to

[ 1

Var(s) Cov(s,z) ‘1

Var(s,z )-[ =

Cov(z,s) Var(z)

where var(s,z) is the (K+ 1)x(K+ 1) varirmce matrix.

Using the partitioned inverse formula and ignoring tie first column (since it will be multiplied by O),

we have:

‘“a)‘[:l=”[::l+P:(N*’cOv

where G = [var(s) “var(z)– COV(Z, s) *cov(s,z)]-’

Now, consider the diagonal matrix K which has elements of COV(Z,Av+e) along the diagonal. K’ is

also diagonal. Thus (15a) may be rewritten as:

‘“b)‘kl=El+rc0::3*K*K’*[c0v(z7E(v+e’DJ’~

Manipulating this further gives us:

‘“c) ‘tl=E1’[c;:;::l*@’*’c’v(:Av+e”

42
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1 I I 1 1 I

I 1 I I I I
Table 6: The Effects of Standardized AFQT, and Schooling on Wages Over Time

Derivatives at Selected Experience Levels

Dependent Variable Log Wage

A) Potential Experience.

Years of awt w J.%’ *

~

Experience MFQT WFQT,Ot as as,at

o 0.0197 0.0025 0.0786 0.0053

(0.0235) (0.0139) (0.0092) (0.0040)

1 0.0235 0.0049 0.0830 0.0034

(0.0275) - (0.0144) (0.0101) (0.0040)

3 0.0370 0.0084 0.0865 0.0002

(0.0347) (0.0155) (0.0116) (0.0042)

5

I

0.0560 I0.0104 I0.0843 I-0.0023

(0.0415) (0.0166) (0.0131) (0.0043) I

8 0.0881 0.0104 0.0731 -0.0048

(0.0512) (0.0181) (0.0152) (0.0046)

12 0.1206 0.004.8 0.0513 -0.0056.

(0.0640) (0.0201) (0.0179) (0.0048)

B) Actual Experience Irr.strurnentEdwith Potential Experience.

Years of aw, aw; q ~

Experience WFQT ‘“ MFQT,cl as aa,at

o 0.0183 0.0092 : 0.0881 -0.0024

(0.0205) (0.0231) (0.0105) (0.0086)

1 0.0278 0.0099 0.0843 -0.0051

(0.0316) (0.0251) (0.0137) (0.0089)

3 0.0496 0.0120 0.0711 -0.0074

(0.0496) (0.0288) (0.0190) (o.oo9q

5 0.0755 0.0138 0.0566 -0.0068

(0.0658) (0.0323) (0.0236) (0.0102)

8 0.1172 0.0131 0.0406 -0.0037

(0.0893) (0.0373) (0.0300) (0.0112)

12 0.1475 -0.0012 0.0299 -0.0032

(0.1206) (0.0436) (0.0381) (0.0123)

Theequationsthesamevariablesastheequationincolumn(6)oftable1excepttheinteractionbetween

educationandexperienceandbetweenAFQTandexperienceinvolvefourth-orderpolynomialsinexperience.In

panelB,theimmrrnentalvariablesarethecorrespondingtermsinvolvingpotendalexperienceandtheother

variablesintbemodel.

49

—

—

@j

—

—
.—
Table 10: Tbe Effects of Potential Experience, Standardized AFQT, Father’s Education, and Schooling on tie

Probability of Employer-fnitiated Separation

Linear probabili~ Models

Dependent Variable Employer-Initiated Separation.

OLS estimates (standard errors)

Model: (1) (2)

(a) Potential Experience 110 -0.0302 -0.1646

(0.0194) (0.0540)

(b) Potential Experience -0.0143 0.0148

Squared / 100 (0.0113) (0.0129)

(c) Tenure -0.0141 -0.0146

(0.0006) (0.0006)

(d) Education -0.0153 -0.0206

(0.0012) (0.0027)

(e) Black 0.0272 0.0265

(0.0057) (0.0057)

(t-) Standardized -0.0108 -0.0251

AFQT (0.0029) (0.0061)

(g) Father’s 0.0303 0.0991

Education / 100 (0.0701) (0.1532)

(h) Education * 0.0083

Experience / 10 (0.0033)

(i) AFQT * 0.0188

Experience / 10 (0.0065)

(j) Father’s Ed* -0.0910

Experience /1000 (0.1738)

NotcTAn Employer-Lnidated Separation includes separations because of layoffs, frings, and plant closings. Alf equations

control for urban residence, and-dummy variables to control for whether Father’s edu;ation k-missing and whethm-AFQT

is miming, and interactiorm between these dummy variables and experience when Experience interactions are included.

Standard errors are White/Huber standsrd errors computed accounting for the fact that there are mrdtiple observations for

each worker. The sample size is 27443 observations from 4034 individual.

53
Table Al: Descriptive Statistics

Variable Mean Standard Minimum Maximum

Deviation

Red Hourly Wage 8.370 4.766 2.01 96.46

Log of Real Hourly Wage 2.005 0.474 0.7 4.5-?

(w)

Potential Experience (t) 7.349 3.665 0 21

Actual Experience (t) 4.925 3.424 0 18.26

Education (s) 12.699 2.136 8 18

Black dummy (Black) 0.290 0.454 0 1

Dummy for not bowing 0.038 0.191 0 1

AFQT Score

Standardized AFQT Score -0.133 1.022 -2.780 1.922

(AFQT)

Dummy for not bowing 0.119 0.324 0 1

Father’s Education

Father’s Education (F_ED) 11.709 3.112 4 20

Dummy for Urban Dweller 0.781 0.413 0 1

Year 86.623 81.558 79 92

Training (TO 0.096 0.200 0 1

Cumulative Training (Z T7) 0.462 0.549 0 5.592

54

Sample size = 27,704 observations except for the training measures where it is 25,115 observations.
Table AZ: Relationships ‘Among Wages, Schooling, AFQT, and Parental Education Sinmle Remession

t--

Right Hand

Side Vmiable

Highest

Grade

Father’s

Education

Standardized

AFQT

F

Weeks of

Company

Training

Layoff

I

I

r

Actual

Experience

Potential

Experience

‘Coeftici~nts (~andard error~”and[Correlation coefficient] ‘ -

Dependent Variable I

og Wage

0.0785

(0.0014)

[0.3615]

0.0298

(0.0010)

[0.2092]

0.1565

(0.0031)

[0.3567]

0.0045

(0.0007)

[0.0429]

-0.1659

(0.0104)

[-0.1094]

-0.2145

(0.0076)

[-0.1909]

0.0444

(0.0010)

[0.2893]

0.0174

(0.0010)

[0.1044]

Highest Father’s

Grade Education

0.6197

(0.0098)

[0.4029]

0.2592

(0.0041)

[0.4029]

1.2245 1.4280

(0.0119) (0.0204)

[0.5829] [0.4362]

0.0214 0.0268

(0.0029) (o.oo4@

[0.0514] [0.0392]

+

-0.E921 -0.6558

(0.0468) (0.0728)

[-0.1259] [-0.0542]

-0.3232 0.0814

(0.0348) (0.0539)

[-0.0589] [0.01 12]

-0.0374 -0.0350

(0.0047) (0.0072]

[-0.0329] [-0.0331]

--1- -0.1899 -0.1561

(0.0042) (0.0065

[-0.2923] [-0.1538

I

Xandsrd. Weeksof

-t

AFQT company

Training

0.2747 0.1189

(O.0027) (0.0163)

[0.5829] [0.0514]

T

0.1341 0.0621

(0.0019) (0.0106)

[0.43621 [0.0392]

T

0.3072

(0.0345)

[0.0645]

T

0,0124

(0.0014)

[0.0645]

-0.3904 -0.2702

(0,0222) (0.1 112)

[-0.1 174] [-0.0130]

-0.0683 -0.2321

(0.0165) (0.0821)

[-o.030q [-0.0190]

-0.0106 -0.0436

(0.0022) (0.0110]

[-0.0142] [-O.02E2]

r

-0.0718 -0.0647

(0.0020) (0.0103

[-0. 2329] [-0.0453

Layofi Quit Actual Potential

Experience Expa”ence

-0.0193 -0.0128 -0.0823 -0.4831

(0.0010) (0.0014) (0.0103) (0.0106)

[-0.1259] [-0.0589] [-0.0329] [-0,2923]

-0.0059 0.0014 -0,0323 -0.1660

(0.0007) (0.0009) (0.0067) (0.0071)

[-0.05421 [0.0112] [-0.0331] [-0,1538]

-0.0377 -0.0121 -0.1036 -0.8138

(0.0021) (0.0029) (0.0218) (0.0227)

[-0.1 174] [-o.030q [-0.0142] [-0.2329]

-0.0011 -0.0017 -0.0173 -0,0297

(0.0004) (0.0006) (0.0044) (0.0047)

[-0.0130] [-0,0190] [-0.0282] [-0.0453]

-0.2707 -1.1766 -0.3223

(0.0092) (0.0696) (0.0753)

[-0.2080] [-0.1391] [-0.0629]

-0.1478 -1.2747 -0.8834

(0.0050) (0.0510) (0.0553)

[-0.2080] [-0.1658] [-0.1070]

-0.0116 -0.0230 0.8605

(0.0007) (0.0009) (0.0045)

[-0.1391] [-0.1658] [0.7953]

-0.0027 -0.0138 0.7452

(0.0006) (0.0009) (0.0039)

[-0.0629] [-0.1070] [0.7953]

7

“#

55
National Longitudinal Surveys (NIX)

Discussion Paper Series

m

92-01

92-02

92-03

92-04

92-05

92-06

92-07

92-08

&

Michael R Pergamit

Norman M. Bradbum

Mmdrr R. Fmnkel

Reginald P. Baker

Michael R. Perganrit

Saul Schwat.z

Robeti Hutcherrs

George Jakubson

A. Colin Cameron

R. Mark Grim

Thomas MaCurdy

Henry S. Farber

Frank L. Mott

Paula Baker

Audrey LigJrt

ManueIita Ureta

Lisa M. Lynch

92-09 Evangelos M. Falaris

H. Elizabeth Peters

92-10 Anne HIO

June E. O’Neil]

92-1 I Arleen Leibowitz

Jacob Alex K1erman

Liida Waite

92-12 Lee A. Lillard

Joseph G. Akonji

Thomas A. Dunn

_Thle

How the Federal Government Uses Data from

the National Longitudinal Surveys

A Compwision of Computer-Assisted Personal

Interviews (CAPI) with Paper-and Pencil Interviews (PAPI) in the National Longitudinal Survey

of Youth

Dynamic Models of the Joint Determination of

Labor Supply and Family Structure

The effects of Unemployment Compensation

on the Unemployment of Youth

Evaluating Competing Theories of Worker

Mobility

Evaluation of the 1989 Ckild-care Supplement

in the National Longitudinal Survey of Youth

Gender Differences in the Quit Behavior of

Young Workers

The Jmpact of Private Sector Training on Race

and Gender Wage Differential and the Career

Patterns of Young Workers

Responses of Female Labor Supply and FertiIity

to the Demographic Cycle

A Study of Intercohort Change in Women’s

Work Patterns and Earnings

Womenrs Employment During Pregnancy

and Following Birth

Work Experience, Job Tenure, Job Separation,

and Wage Growth

Family Background and Labor Market Outcomes
92-14 George J. Borjas

Stephen G. Bmnars

Stephen J. Trejo

SeW-Selection and f.nti Mig@inn in tie

r.llited states

Jnrnes J. Hecknmn

Stephen V. Cameron

Peter Z. Schochet

The Determinants and Consequences of Public

Sector and Private SectorTra”tig

92-15

93.16

94-17

94-18

94-19

95-20

95-21

95-22

95-23

95-24

R. Mark Gritz

Thomas MaCurdy

Pmticipation in Low-Wage Labor Markets by

Young Merr

Alnn L. Gustnmrr

Thomas L. Steinmeier

Retirement in a Fumily Context A Structural Model

for Husbands and Wives

Audrey Light Transitions !iom School to Work A Survey of

Research Using the National Longitudinal Surveys

Christopher J. Ruhm High School Employment: Consumption or

Investment

Mark Lowenstein

James Spletzer

Iufnrmal Trainiig A Review of Existing Data nnd

Some New Evidence

Jacob Alex Klenrmu Charactetiziig Leave for Maternity Modeling the

NLSY Dnta

Jacob Alex Klerrnnn

Arleen Leibowitz

Employment Continui@ Among New Mothers

Stephen G. Brormrs

Cnrol Moore

fncentive Pay, Information, nmdEarnings: Evidence

from the National Longitudinal Survey of Youtb

The Evolving Structures of Female Work Activities:

Evidence from the National Longitudinal Surveys of

Mature Women Survey, 1967-1989

Donald O. Parsons

95-25

95-26

95-27

95-28

Donald O“.Parsons Poverty Dynamics Among Mature Womem Evidence

from the National Longitudinal Suweys, 1967-1989

Technological Change and the Skill Acquisition of

Yomrg Workers

Amr Bmtel

Nachmu Sichemmrr

Audrey Light High School Employnrent

Laura Branden

R. Mark Gritz

Michael R. Pergamit

The Effect of interview Length on Attrition in the

National Longitudinal Survey of Youth

96-29 Thomas Drum

Douglas Holtz-Eakin

Capital Market Consmaints, Parental Wealth nnd the

Transition toself%rnployment among Men and

Women

—
96-30 Jeff Grogger

Nick Ronan

96-?1 Jonathau Veum

96-32 MichaeI R. Pergamit

96.33 Eric P. Slade

97-34 Bernard Dugoni

Lisa Lee

Roger Toumageau

97-25 Joseph G. Altonji

Chudes K Pierret

97-36 Joseph G. Akonji

Charles R. Pierret

The Intergenerational Effects of Fatherlessness on

Educatioael Attaiient and Entry-ievel Wages

Trainiig Wages, end the Human Capital Model

Asse~iug School to Work Transitions in the United

States

An Analysis of the Consequences of Employer

Lincked Health Insurance Coverage in U.S.

Report on the NLSY Round 16 Recall Experiment

Employer Learning and the SignalingValue of

Education

Employer Learning and Statistical Discrimination

..47,