BLS WORKING PAPERS 

 

U.S. Department of Labor 

U.S. Bureau of Labor Statistics 

Office of Employment and Unemployment Statistics 

Wage Compression and the Division of Returns to Productivity Growth: 

Evidence from EOPP 

Harley Frazis, U.S. Bureau of Labor Statistics 

Mark A. Loewenstein, U.S. Bureau of Labor Statistics 

Working Paper 398

August 2006

All views expressed in this paper are those of the authors and do not necessarily reflect the views or policies of the 

U.S. Bureau of Labor Statistics. 
Wage Compression and the Division of Returns to Productivity Growth: 

Evidence from EOPP 

Harley Frazis Mark A. Loewenstein 

Bureau of Labor Statistics Bureau of Labor Statistics 

2 Massachusetts Ave. NE 2 Massachusetts Ave. NE 

Suite 4945 Suite 4130 

Washington D.C. 20212 Washington D.C. 20212 

Frazis_H@BLS.GOV Loewenstein_M@BLS.GOV

August 2006 

Any views expressed in this paper are the authorsí and do not necessarily reflect those of the 

Bureau of Labor Statistics. 
I. Introduction 

The relationship between wages and productivity is fundamental to labor economics. In 

this paper, we examine this relationship using subjective measures of worker productivity from 

the Employment Opportunity Pilot Project (EOPP) data. We seek to answer the following 

questions. To what extent are differences in productivity between workers on the same job 

reflected in their relative wages? To what extent is productivity growth reflected in wage growth? 

To what extent can data on wage and productivity growth, and the relative wages and 

productivity of workers on the same job, identify the division of returns to human capital and the 

extent to which wages are compressed relative to productivity? 

We follow Bishop's (1987) paper in examining the relationship between wages and 

productivity in the EOPP data. Bishop (1987) finds that direct measures of productivity reported 

by the employer have quite weak effects on wages and notes that indirect indicators of 

productivity such as relevant experience have stronger effects. We extend Bishop's research by 

using these indicators as instruments for the noisy measures of productivity. 

In the simplest static model of a competitive labor market, the relationship between 

productivity and wages is straightforward: wages equal marginal product. In dynamic models, 

such as Becker (1962), this equality need not always hold. In Beckerís model, workers bear the 

full cost and return to acquiring general human capital, so general human capital acquisition does 

not affect the equality of wages and productivity. In contrast, the costs and returns to acquiring 

skills specific to the employer are shared between the employer and the worker, so that wages 

are above marginal productivity before training and below productivity after training. More 

recent models and empirical work1

 suggest that employers share the costs and returns to general 

 

1

For examples, see Acemoglu and Pischke (1998,1999), Loewenstein and Spletzer (1998), Chang and Wang (1996), 

Autor (2001), Balmaceda (2005), Bishop (1991), Harhoff and Kane (1997), and Booth and Bryan (2002). 
 2

as well as specific human capital. Even if worker realize the full return and bear the full cost of 

training, market frictions such as search costs (Acemoglu and Pischke (1999) and Zoega and 

Booth (2005) may cause wages to diverge from productivity. In addition, as suggested by 

Akerlof and Yellen (1990) and others, social norms may constrain wages from fully reflecting 

productivity differentials. We refer to the phenomenon of differences in wages less than fully 

reflecting differences in productivity, for reasons other than the sharing of the costs of human 

capital acquisition, as "wage compression". 

As detailed below, the EOPP data contain measures of a recently hired workerís 

productivity at various points in time. Labor economists typically abstract away from the fact 

that wages are not adjusted continuously. However, our data show that productivity typically 

grows quite rapidly at the start of a job. Since wages are not adjusted continuously, starting 

wages very likely reflect not just the low productivity at the very start of the job but also the 

much greater productivity typically attained within a few weeks. We develop a method that 

allows us to take this into account in estimating the relationship between starting wages and 

productivity. 

Our data allow us to estimate how productivity growth affects wage growth in the first 

two years in a job, and how differences in starting productivity between workers affect starting 

wages. We show that under reasonable assumptions, if one regresses differences in starting 

wages for workers in the same job on differences in starting productivity and differences in 

productivity growth, the coefficient on starting productivity identifies the extent to which starting 

wages are compressed. The coefficient on differences in productivity growth in the same 

regression identifies the extent to which employers share the cost of general human capital 

acquisition. 
 3

Our results show a dramatic amount of wage compression. Our point estimate from our 

benchmark specification is that only 32 percent of differences in starting productivity are 

reflected in differences in starting wages, even after accounting for differences in productivity 

growth. The hypothesis that starting wages equal starting productivity after taking into account 

human capital acquisition is decisively rejected. Our results also indicate that productivity 

growth translates into substantially lower wage growth: productivity growth of 10 percent results 

in wage growth of only 2.6 percent. This reflects employer sharing of the costs and returns to 

human capital acquisitions and/or increased wage compression over time. Unfortunately, we do 

not obtain a precise estimate of the amount of employer sharing of human capital investment per 

se. 

The great extent of wage compression poses a challenge to theories of wage 

determination. Existing theories of wage compression seem unlikely to explain the magnitude of 

compression that we find. This is especially true in view of the fact that our wage compression 

coefficient is to a great extent identified by differences in relevant experience. That employers 

would pay experienced workers their marginal products seems intuitive and is the basis of 

Becker's (1962) prediction that employers do not share the costs to general human capital. In our 

final section we briefly develop a model that generates wage compression via equity norms that 

prevent employers from paying experienced workers hired from the outside more than workers 

with the same skills trained at the firm. The ìequity normî not only leads to wage compression, 

but also amplifies any initial tendency toward employer sharing of the return to general human 

capital acquisition, as the wage compression and sharing effects reinforce each other. 
 4

II. Identifying the Relationship Between Wages and Productivity Using the EOPP Data 

EOPP is one of the few surveys that we are aware of that has information on the 

productivity of individual workers.2 The EOPP items on the productivity of the last worker hired 

and the typical worker at various points in time and the availability of instruments such as a 

workerís relevant experience elsewhere and job complexity make the data an ideal source for 

analyzing the relationship between productivity and wages. The EOPP data have been analyzed 

fairly extensively, but the relationship between wages and productivity has been under-explored. 

We use the data to estimate the rate at which productivity growth during the first two years of 

employment translates into wage growth and the extent to which productivity differences among 

workers who are hired for the same position are reflected in differences in starting wages. 

Description of the EOPP Data 

The EOPP data come from a 1982 survey sponsored by the National Institute of 

Education and the National Center for Research in Vocational Education. Employers are asked a 

series of questions about the wages, experience, productivity, and training activities of the last 

worker hired and the typical worker in the same position.3

 Descriptive statistics can be found in 

Table 1. 

For our purposes, the key EOPP data are the information on wages and productivity. 

Employers in the survey are asked about the starting wage paid to the last worker hired and the 

average hourly wage paid to workers who have had two yearsí experience in the position. In 

addition, employers in the EOPP survey are asked about the productivity of the last worker hired 

 

2

 The Small Business Administration survey, which is modeled after EOPP, also has information on worker 

productivity; see Barron, Black, and Berger (1999). There are a few company data sets with information on 

productivity. Using performance ratings at a major corporation, Medoff and Abraham (1981) find that that withingrade-level seniority ñ earnings differentials cannot be explained by performance differentials. Analyzing the 

personnel records of a large company, Bartel (1995) finds that training is positively related to both wage growth and 

performance. 

3

 For more information about the survey and the training questions, see Barron, Black, and Loewenstein (1989). 
 5

and the typical worker in the position during the first two weeks of employment and from the 

ìthird week to the twelfth week at work.î Employers in the survey also provide an estimate of 

the productivity of the ìtypical worker who has been in this job for two years.î In forming their 

productivity estimates, employers are told to rate workers on a ìproductivity scale of zero to one 

hundred, where one hundred equals the maximum productivity any of your employees can attain 

and zero is absolutely no productivity.î4 

As mentioned in the introduction, our key extension of Bishop's (1987) research on 

wages and productivity using these data is to correct for measurement error in productivity by 

using IV. For IV to produce consistent estimates, measurement error in log productivity must be 

uncorrelated with true log productivity. One possible objection to our procedure is that the 

employers answering the EOPP productivity question may tend to exaggerate productivity 

differences between workers (and also exaggerate productivity growth). Suppose that an 

employerís productivity estimate is given by 

ln p = + ln p * +e α 0 α1 , 

where p* is true productivity and e is a mean-zero error uncorrelated with ln p*. If α1 > 1 (that is, 

if reported productivity differences are greater in magnitude than actual productivity differences), 

then measurement error will be positively correlated with ln p* and IV estimation of the effect of 

log productivity on wages will underestimate the coefficient on log productivity.5

 

Examining the data, we find that the average coefficient of variation for productivity for 

jobs where we have observations for two workers, using observations where the worker has been 

on the job for more than 0.8 years, is 0.20 (this is the case for both productivity during the first 

 

4

 Employers also provide information on the productivity and starting wage of the previously most recently hired 

worker in the same position as the last worker hired, but this information is unfortunately missing in the majority of 

observations. 

5

 Bollinger and Chandra (2005), writing about general models of measurement error, note that "[t]o our knowledge, 

no study has ever found [α1] > 1." 
 6

two weeks and productivity from the third to the twelfth week; other tenure cutoffs give similar 

results). This is almost identical to the average found in a review of studies examining variation 

in output for which physical measures existed (Schmidt and Hunter 1983), so there is no 

evidence that our productivity measure exaggerates differences between workers. 

We estimate log productivity growth over the first two years as the difference between 

the typical workerís log productivity after two years and the most recent hire's log productivity 

after two weeks. As can be seen in Table 1, average productivity growth over the first two years 

is very high: productivity after two years is on average eighty percent higher than productivity at 

the start of the job. 

We can decompose productivity growth over the two year period into productivity 

growth occurring at the very start of the employment relationship and productivity growth 

occurring after the twelfth week. Specifically, we estimate log productivity growth over the first 

three months as the difference between log productivity from the third to the twelfth week and 

log productivity during the first two weeks (given the way the question is worded, this may be an 

underestimate); productivity growth from the twelfth week on is estimated as the difference 

between log productivity after two years and log productivity from the third to twelfth week. As 

reported in Table 1, productivity during the third to twelfth week is on average 51 percent higher 

than productivity during the first two weeks while productivity after two years is 29 percent 

higher than during the third to twelfth week. Apparently then, productivity does not grow evenly 

over the first two years, but is heavily concentrated toward the start of the job: at least two-thirds 

of the growth in productivity over the first two years occurs during the first three months. 

Besides the information on productivity and wages, EOPP also contains many additional 

variables that are useful for our analysis. As alluded to above, EOPP provides fairly detailed 
 7

information on both formal and informal training. Employers indicate the number of hours 

during the first three months of employment that were spent providing formal training through 

ìself-paced learning programs or Ö by specially trained personnelî to not only the last worker 

hired, but also to the typical worker in the same position. With respect to informal training, 

employers provide information on the number of hours during the first three months of 

employment that management and line supervisors spent giving individualized training to the last 

worker hired and the typical worker in the same position. Employers also indicate the number of 

hours that co-workers who are not supervisors spent away from their normal work giving 

informal individualized training to the last worker hired and the typical worker. Finally, 

employers indicate the total number of hours during the first three months of employment that 

the average new employee in the position spends in training activities watching other people do 

the job rather than doing it himself. 

Two other items in the data are also relevant for our analysis. There is information on the 

most recently hired workerís relevant employment experience in jobs ìthat had some 

applicationî to the position for which he was hired. In addition, employers estimate the number 

of weeks it takes a new employee in the most recently filled position to become fully trained and 

qualified if he or she has the necessary school provided training but no experience in the job. As 

discussed by Barron, Black, and Berger (1999) and Frazis and Loewenstein (2005), the latter 

variable can be thought of as capturing job complexity. 

Framework for Empirical Analysis 

The EOPP data enable us to estimate two equations: a regression of differences in starting 

wages on differences in starting productivity for workers in the same job and a regression of 

wage growth on worker productivity growth. As described above, EOPP has information on 
 8

both formal and informal training. As reported in Loewenstein and Spletzer (1999), the 

employers in EOPP report that most of the skills the new employee learns on the job are useful 

elsewhere.6 Still, we allow for the possibility that some human capital is employer-specific. We 

assume that human capital acquisition has the multiplicative structure ln H = ln G + ln S, where 

G and S are the workerís stocks of general and specific human capital, respectively, and H is 

equal to productivity. 

Workers will typically have different amounts of general human capital when they start a 

job, while by definition all workers will have zero firm-specific capital when they are hired. One 

would therefore expect that within a job differences between workers in human capital 

acquisition will be dominated by differences in general training, even for jobs where there are 

large amounts of specific training. Indeed, in the case where all workers in a job are brought to 

the same level of general and specific human capital by the end of a training period, there will be 

no differences in specific human capital acquisition between workers in the same job. To 

simplify the discussion below, we assume that specific human capital acquisition does not vary 

among workers in the same job. We view this assumption as quite reasonable, particularly in 

light of the fact that there is some question whether much human capital acquisition is specific to 

start with. 

Consider a two period model. Workersí starting wages depend upon their starting 

productivity and upon their human capital acquisition: 

(1) 1 1 1 1 1 1 1 lnw = α + β ln H + γ g g + γ s s + u , 

where H1 is the workerís stock of general human capital at the start of the match, g ≡ ln G2 ñ ln 

G1 and s ≡ ln S2 are general and specific human capital acquisition during the first period, and u1

 

6

 Seventy-two percent of employers indicate that nearly all or most of the skills learned are general; eight percent 

indicate that none of the skills are general. Similarly, workers in the NLSY indicate that most of the skills acquired 

in training are useful at other employers. 
 9

is a mean zero residual. In interpreting (1), note that the coefficient β1 denotes the extent of 

wage compression. If β1 = 1, differences in productivity are completely reflected in differences 

in wages once human capital cost sharing is accounted for. If β1 < 1, differences in wages are 

compressed relative to differences in productivity. The coefficients γ1g and γ1s are nonnegative 

and reflect the degree to which the employer shares the cost of human capital acquisition. Cost 

sharing by the employer means that worker is paid a starting wage higher than he otherwise 

would receive.7 If the worker bears the full cost to general human capital acquisition, then γ1g = 

0. 

Similarly, wages in period 2 are given by 

(2) 2 2 2 2 2 2 2 lnw = α + β ln H + γ g g + γ s s + u . 

As with equation (1), the coefficient β2 reflects wage compression. The coefficients γ2g

and γ2s are nonpositive and reflect the employer sharing the return to general and specific human 

capital accumulation, respectively: if the employer shares the return to human capital 

accumulation, then the worker is paid a wage below what he would otherwise receive.8 

Estimating (1) and (2) would require measures of productivity in dollar terms and 

decompositions of measured productivity growth into specific and general components, neither 

of which is present in the EOPP data. Measurement error is also a concern. In light of these 

considerations, we use a set of instruments to estimate two differenced equations: a wage growth 

 

7

 If workers become more productive simply because of learning by doing, then human capital acquisition does not 

entail an explicit cost. However, as made clear in the model laid out in Section IV, if employers realize part of the 

return to the higher productivity in period 2, a zero profit equilibrium condition implies that workers will be paid a 

first period wage that exceeds their starting marginal product, so that γ1g and γ1s are positive. 8

 Note that the specification in (2) is no less general than the specification 

2 2 2 2

'

2 2 2 2 2 lnw = α + β ln G + β ln S + γ g g + γ ' s s + u : the two specifications are equivalent if β2+γ2S = βí2+ 

γí2S. Since s = lnS2, the sum βí2 + γí2S is identified, but not the parameters ' β 2 and γí2S. 
 10

equation that is obtained by subtracting (1) from (2) and a first differenced starting wage 

equation obtained by differencing (1) between two different workers in the same job.9

 Differencing the starting wage equation (1) for two workers, A and B, in the same job: 

(3) ln ln (ln ln ) ( ) 1 1 1 1 1 1

A B

g

A B A B w − w = β H − H + γ g − g

 ( ) ( ) 1 1 1

A B A B

s + γ s − s + u − u . 

Consider a regression of A B w1 w1 ln − ln on predicted differences in the two workersí human 

capital: 

(4) w w b H c h u A B A B A B − = + + − à − à ln ln 1 1 1 1

where ((ln ln ) | ) àH E H1 H1 Z A B A B ≡ − − , 

 ((ln ln ) (ln ln ) | ) àh E H2 H1 H2 H1 Z A B A A B B ≡ − − − − 

 ) E((g g ) (s s ) | Z A B A B = − + − , 

u is a residual, and Z is a set of instruments. Under our assumption that 0 ( − ) = A B s s for all 

jobs, (( ) | ) àh E g g Z A B A B = − − and the consistency of 2SLS implies that 1 1 p limb = β and 

g p c = γ 1 lim .

10 In Becker's (1962) classic model of human capital acquisition, there is no wage 

 

9

 Due to idiosyncrasies of the data which we discuss below, it is not possible to difference second period wages 

between two workers in the same job. 

10 These results depend on our assumption that workers in the same job acquire the same amount of specific human 

capital. More generally, project A B H − à on gà E(g g ) | Z) A B A B ≡ − − and sà E(s s ) | Z) A B A B ≡ − − : 

H d d g d s v A B A B A B = + + + − − − à à à 0 1 2 . Then one can show that 

( ) ( ( à ) (à ) ( ( à , à )) ) ( )

( )( ( à ) (à ) ( ( à , à )) ) lim ( ) 2 2

1 2

2

1 2

1 d d Var g Var s Cov g s Var v

d d Var g Var s Cov g s

p b A B A B A B A B

A B A B A B A B

g s − − +

− − = + − − − − −

− − − −

β γ γ . 

Also, g s p limc = ωγ + (1− ω)γ 1 , where the weight ω is determined by the relative covariances of predicted 

general and specific human capital with A B H − à and A B h

à − : 

2 )) à , à ) ( ( à ) ( à (

) à , à , à ) ( à ) ( à ) ( à , à (

A B A B A B A B

A B A B A B A B A B A B A B

Var H Var h Cov H h

Var H Cov g h Cov H g Cov H h

− − − −

− − − − − − −

−

− ω =
 11

compression and workers bear the full cost and return to general human capital acquisition 

occurring on the job, so that b1 = 1 and c1 = 0. 

Now subtract (1) from (2) to obtain an equation for wage growth between the first and 

second period: 

 (5) 2 1 2 1 2 1 1 lnw − lnw = (α − α ) + (β − β )ln H 

 +( ) ( ) ( ) 1 2 1 1 2 1 u2 u1 g s β + γ g − γ g + β + γ s − γ s + − . 

Consider a regression of 2 1 lnw − lnw on human capital acquisition h

à : 

(6) ( ) à ln ln 2 1 2 2 2 1 w − w = b + c h + u − u , 

where (ln ln | ) à

h ≡ E H2 − H1 Z . One can show that 

(7) lim (1 )( ) ( ) ( ) 2 1 2 1 2 1 ω2 β 2 β1 p c = β + −ωs γ g − γ g +ωs γ s − γ s + − , 

where the weight )à ) ( à ωs ≡ Cov(sà, h Var h is the contribution of (predicted) specific human capital 

to the overall variance of (predicted) human capital growth and )à ) ( à , à ( 2 2 ω ≡ Cov H h Var h .

11 

Note that ωs and ω2 and therefore c2 will depend on the choice of instruments.12 This reflects the 

fact that the effect of productivity growth on wage growth varies depending on the relative 

 

11 Analogously to above, (ln | ) àH2 = E H2 Z . We have : 

)à (

, à) à , à) ( ) ( à ,ln ) ( ) ( à ( ) (

)à (

,ln ln ) à ( lim

2 1 2 1 2 1 1 2 1

1

2 1

2

Var h

Cov h H Cov h g Cov h s

Var h

Cov h w w

p c

g g s s β − β + β + γ − γ + β + γ − γ = β +

− =

(where we add and subtract β1 ln H2 from (5) and note that ) 0) à ( , Cov u2 − u1 h = . The text 

expression follows by noting that ). à , à) ( à , à) ( à Cov(h g + Cov h s = Var h

12 For example, letting gà = κ0g + κ1gZ, sà = κ0s + κ1sZ , and noting that 

à à ( ) ( ) , à ∆h = g + s = κ0g + κ0s + κ1g + κ1s Z one can easily see that ωg will be determined by the relative 

magnitudes of κ1g and κ1s: instruments having a stronger relationship with general human capital relative to specific 

capital will weight the general human capital coefficient more heavily. 
 12

contributions of general and specific human capital to productivity growth.13 Under the Becker 

model, with β1 = β2 = 1 and 0, γ g 2 = γ g1 = the coefficient c2 will converge to 1 + ωs(γs2 - γs1), so 

the deviation of c2 from 1 will depend on the extent to which the employer shares the return to 

specific capital and (predicted) specific capital's overall contribution to the variance of 

(predicted) human capital growth. A low value of c2 can be taken as evidence against the Becker 

model if it implies an implausibly high contribution of specific capital to overall productivity 

growth. Note that c2 can differ from 1 for two possible reasons: (a) because the employer shares 

the returns to human capital acquisition, either through wage compression or through direct 

sharing of costs and return (as picked up in the first three terms of (7)) and (b) because the extent 

of wage compression changes over time. 

III. Empirical Results

The wage equations that we estimate are dictated by the workers for whom we have wage 

and productivity information. In section II we provided interpretations for wage growth 

regressions and for regressions of differences in starting wages on differences in productivity for 

workers in the same job. Ideally, we would estimate a wage growth equation for the last worker 

hired or the typical worker, and we would estimate a separate equation for the difference 

between the starting wage of the last worker hired and the typical worker. However, we know 

the typical workerís wage after two years, but not at the start of the job. And while we know the 

starting wage paid to the last worker hired, we do not have useful information on the wage this 

worker received subsequently.14 Consequently, we estimate a pseudo-wage-growth equation, in 

 

13 Angrist and Imbens (1996), Angrist, Imbens and Rubin (1995), and other papers in the literature on local average 

treatment effects analyze the properties of IV when the effect of the regressor of interest varies across the population, 

and similarly find that the limit of the IV estimator will depend on the choice of instruments. 

14 Employers are asked about the wage received by the last worker hired at the time of the interview, but this 

workerís tenure is typically quite short. For example, the last worker hired has been on the job less than one year in 
 13

which the dependent variable is ln( ) ln( ) w104 w0

typ − , where typ w104 denotes the typical workerís wage 

after 104 weeks and w0 denotes the starting wage paid to the last worker hired. 

Letting typ w0 denote the typical workerís log starting wage, one can write 

(8) ln( ) ln( ) (ln( ) ln( )) (ln( ) ln( )) w104 w0 w104 w0 w0 w0

typ typ typ typ − = − + −

The first term on the right hand side of (8) is simply the growth rate in the wage of the typical 

worker during the first two years of employment. The growth rate in the typical workerís wage 

depends on the growth in this workerís productivity, or 

(6í) 104 0 2 2 2 2 ln(w ) − ln(w ) = c h + l X + ε typ typ typ , 

where ln( ) ln( ) 104 0

typ typ typ h ≡ H − H denotes the difference in logarithms between the typical 

workerís productivity after two years and when he is initially hired, and ε2 is an error term with 

mean 0. The X2 term denotes a vector of variables, described below, that influence wage growth 

independently of productivity, possibly due to contracting considerations. The second term on 

the right hand side of (8), the difference between the log starting wage of the typical worker and 

of the last worker hired, depends on these workersí marginal products at the time of hire, or 

 (4í) 0 0 1 1 1 1 1 ln(w ) − ln(w ) = b ∆H + c ∆h + l X + ε typ , 

where ln( ) ln( ) H H0 H0

typ ∆ ≡ − is the difference between the log starting productivity of the 

typical worker and the last worker hired, (ln( ) ln( )) (ln( ) ln( )) H104 H0 H104 H0 h typ typ ∆ ≡ − − − is the 

difference between the productivity growth rate of the typical worker and of the last worker, X1 

denotes variables other than productivity that affect starting wage differences, and ε1 is a mean 

zero error term 

Substituting (6í) and (4í) into (8) yields 

 over 50 percent of the sample observations. We will subsequently use this information to estimate the length of time 

until the first wage adjustment. 
 14

(9) w w c h b H c h typ typ ln( 104 ) − ln( 0 ) = 2 + 1∆ + 1∆ . 1 1 2 2 1 2 + l X + l X + ε + ε

OLS Estimation

For comparison purposes, we begin by estimating an OLS version of (9).15 We do not 

have a direct report on the productivity of the last worker after two years and therefore are not 

able to include the variable ∆h to obtain an estimate of c1. (We include predicted values of ∆h in 

our subsequent analysis.) The control vector X2 includes a constant, union indicator, the log of 

the number of employees at the firm, and tenure.16 Ideally, X1 would contain differences in 

characteristics between the typical worker in the job and the last worker hired. However, the 

survey does not contain information on the characteristics of the typical worker. These 

characteristics are accordingly imputed by using predicted values from regressions of the 

characteristics of the last worker hired on the X2 variables plus a vector Ztyp of characteristics of 

the typical worker or the job that affect productivity but do not otherwise affect wages.17 Each 

variable in X1 is calculated as the difference between the actual characteristic of the last worker 

hired and the imputed value. The vector X1 includes the following variables: age, age squared, 

dummies for years of schooling of 16 or more and greater than 12 but less than 16, and dummies 

for prior vocational training, female, part-time (less than thirty-five hours a week), and 

temporary/seasonal job. 

As reported in the top panel of Table 2, the estimated coefficient on productivity growth 

is only 0.035, which, although statistically significant from zero, is very small by any standard. 

The estimated coefficient on the difference in log productivity, reported in the first column of 

 

15 Productivity at time 0 equals 0 for a few of the observations. We therefore add a small number (.1) to time 0 

productivity and time two year productivity before taking logs. Our results are not sensitive to the choice of number; 

the results are also not affected if one simply drops the observations where time 0 productivity is zero. 

16 Employers are (implicitly) asked about the starting wage paid to the most recently hired worker at the time he was 

hired. Since wages increase over time, greater tenure is associated with a lower starting wage and higher wage 

growth. 

17 The vector Ztyp is described below. 
 15

Table 2, is only 0.023. This is similar to the coefficient on initial productivity of 0.055 found by 

Bishop (1987) using a sub-sample with observations of two workers in the same job. 

The implicit hypothesis in using productivity at the very start of the job as our starting 

productivity measure is that at any instant workers are paid on the basis of their marginal product 

at that point in time. This is something of a straw man because wages are not adjusted 

continuously over time, but instead are fixed for discrete intervals. Indeed, as discussed above, 

the descriptive statistics reported in Table 1 indicate that productivity growth is particularly high 

at the very beginning of employment. It seems likely that expected productivity beyond the first 

two weeks is folded into the starting wage. 

The second column of Table 2 reports estimates using average productivity over the first 

three months on the job as our starting productivity measure, which we calculate as a weighted 

average of the productivity during the first two weeks and the productivity from the third week to 

the twelfth week: 0,12 0,2 3,12 H = (1/ 6)H + (5 / 6)H , where Ht,t' is average productivity between 

weeks t and tí. The coefficient on productivity growth increases to 0.073, still quite small, while 

that on the difference in starting productivity is unchanged. 

Instrumental Variables Analysis

We now turn to instrumental variable (IV) estimation. IV has two advantages here: it 

corrects for measurement error in productivity, a likely reason for the small estimated 

coefficients using OLS, and it gives us a measure for predicted ∆h. to allow estimation of (9). 

As noted by Bishop (1987), the EOPP productivity estimates likely contain considerable 

measurement error. Prima facie evidence for this is provided by the fact that the productivity 

reports are predominantly round numbers. For example, about 95% of the 1,502 observations for 

the productivity of the last worker hired in the first two weeks are divisible by 5, and about 5% 
 16

of the observations are exactly 50. Measurement error typically implies that OLS estimates are 

biased downward. However, one might well argue that the standard result does not apply to the 

present case because the wage offered by an employer should depend directly on the employerís 

imperfect estimate of worker productivity, and not on the workerís unobserved ìtrueî 

productivity. 

There are two possible explanations why the employerís wage offer might depend on 

something other than the employerís reported productivity estimate. First, the employer might 

recognize that his initial estimate of the workerís productivity, H, is fraught with error, and refine 

it by combining it with the average productivity of workers with similar characteristics to obtain 

an improved estimate, H

~ , on which pay is based. To the extent that the employer reports H

rather than H

~ to the EOPP survey, the estimated OLS effect of productivity on wages will be 

biased downward. 

The alternative explanation is ìFriedmanesqueî in nature: employers may simply be 

acting as if they are making wage offers based on their assessments of worker productivity. 

Rather than consciously forming productivity estimates, employers may be basing their wage 

offers on workersí observed characteristics, and presumably being driven to the optimal wage 

offers over time. In this scenario, employers only explicitly obtain an actual measure of worker 

productivity when they are asked to do so by the survey. Again, the estimated OLS effect of 

productivity on wages will be biased downward. 

We adopt a two stage least squares procedure. In the first stage, we estimate a 

productivity equation, which is then subsequently used to predict htyp, ∆H , and ∆h in (9). Our 

productivity equation estimates the path that productivity follows over time. Thus, besides 

eliminating the possible downward bias from measurement error, our IV analysis also enables us 
 17

to examine the effect of allowing the length of time until the first wage adjustment--hereafter 

referred to as "contract length"--to vary. For the time being, we continue to assume that the 

wage is initially set for a period of twelve weeks. 

Employers in the survey are asked about the productivity of the last worker hired at the 

time of the interview and the typical worker who has been in the position for two years. This 

allows us to estimate the following productivity equation 

(10) 104 1 2 1 1 1 1 1 ln( p / p ) = ψX + δX + χ Z + χZ + (ψ X + χ Z + χ Z')τ typ typ typ typ

typ

t

 typ typ t + ψ X + χ Z + χ Z τ + m + v 2 1 2 2 2 ( ') , 

where we adopt the spline specification τ1=min(ln(t+1),ln(12+1)) and τ2 = max(ln(t+1)-ln(12+1), 

0), tenure t is measured in weeks, and where we have normalized by dividing the last workerís 

productivity by the productivity of the typical worker after two years. The vector Ztyp includes 

the logarithm of the number of hours the typical new employee in the position spends watching 

other people do the job, the logarithm of the number of hours of formal training provided to the 

typical worker, the logarithm of the number of hours of informal training provided to the typical 

worker, and the logarithm of the number of weeks it takes a new employee in the most recently 

filled position to become fully qualified. The vector Z contains the log of the most recently hired

workerís formal training, the log of the most recently hired workerís informal training, and the 

log of the most recently hired workerís relevant experience; the vector Z' excludes the log of 

relevant experience from Z. The residual consists of m, which is a mean-zero person-specific 

fixed effect, and vt, which is iid measurement error. The error structure is important in allowing 

us to derive a closed-form expression for expected log productivity growth, as the fixed effect 
 18

factors out.18 This error structure implies that the variance of the regression error is invariant 

with respect to tenure, as is the covariance between residuals for the same worker at different 

tenures. Neither implication is rejected by the data.19 

From (10), the most recently hired workerís true productivity during the first twelve 

weeks is equal to 

(11) ∫ − ≡

12

0

0,12 12

( )

dt p vp t t

 ∫ ψ + χ + χ = + ψ + δ + χ + χ

12

0

1 1 1 1

104 1 2 12

exp( ')ln

exp( ) dt

X Z Z t

p m X X Z Z typ typ

typ typ

typ 

 = exp( ) ( , , ',12,0) p104 m J Ztyp Z Z typ , 

where

( )( 1)

exp( )(( 1) ( 1)) ( , , , , )

4 5 1 1 1 1 1 3

1 2 1 2 4 5

1 2 3 4 5

1 1 1 1 1 3

− + + +

+ + + + − + ≡

+ +

y y X y y

X X y y y y J y y y y y

typ

X y y

typ

typ

ψ χ χ

ψ δ χ χ ψ χ χ

. 

Note that the productivity of the typical worker during the first 12 weeks can be obtained by 

substituting the typical workerís training and experience for that of the last worker hired. 

Specifically, 

 (12) exp( ) ( , , ,12,0) '' '

0,12 104 typ typ typ

typ typ p = p m J Z Z Z , 

 

18 One can show that interacting imputed variables with the tenure spline leads to an error structure that is 

heteroscedastic with respect to tenure so that there is no closed form solution for predicted productivity growth 

(equation (13) below). This is why X2 and the log of relevant experience are not interacted with the tenure splines. 

The p value of the interaction of these variables with the tenure spline variables is .25. 

19 The variance of the regression error in starting productivity during the first two weeks is significantly larger than 

the variance of the regression error for all subsequent points in time, but the first two weeks constitute a sufficiently 

small fraction of the first period that the fixed-effect is still a good approximation. Regressing the squared residual 

on tenure and tenure squared beyond the first two weeks yields a p value of .59. Interacting the residual for starting 

productivity with the residual for productivity from the third to the twelfth week and regressing on tenure and tenure 

squared yields a p value of .39; interacting the residual for starting productivity with the residual for productivity 

after the twelfth week and regressing on tenure and tenure squared yields a p value of .93; interacting the residual for 

the residual for productivity from the third to the twelfth week with the residual for productivity after the twelfth 

week and regressing on tenure and tenure squared yields a p value of .83. 
 19

where ' Ztyp denotes the vector obtained when one replaces the elements of Zí with the 

corresponding elements of Ztyp and '' Ztyp denotes the vector obtained by replacing the elements of 

Z with the corresponding elements of Ztyp and the relevant experience of the typical worker. 

From (12), the predicted log productivity growth of the typical worker is given by 

(13) (ln( ) ln( )| , , , , ) ln( ( , , ,12,0)) '' '' '

typ

'

104 0,12 1 2 typ typ typ typ typ

typ typ E p − p X X Z Z Z = − J Z Z Z . 

One can similarly predict ln( ) ln( ) 0,12 0,12 p p typ − , the difference between the log productivity of the 

most recently hired worker and the typical worker during the first twelve weeks, and 

(ln( ) ln( )) (ln( ) ln( )) 104 0,12 104 0,12

typ typ t p − p − p − p , the difference in log productivity growth 

Selected coefficients in the estimated productivity equation can be found in Table 3.20 

The coefficients conform to oneís expectations. The greater the last hireís relevant experience in 

jobs having some application to his current position, the greater is the initial productivity of the 

last hire relative to the productivity of the typical worker who has been in the job two years. In 

contrast, the length of time it takes the typical worker with no experience to become fully trained 

and qualified, the number of hours the typical worker spends in training activities watching other 

people do the job, and the training the last worker hired receives all reduce the initial 

productivity of the last hire relative to the productivity of the typical worker who has been in the 

job two years. These variables also raise the rate at which the relative productivity of the last 

worker hired rises over time.21 The latter effect is much stronger during the first three months 

than subsequently. 

 

20 Note that we have up to three observations per worker--an observation from between 0 and 2 weeks, from 3 to 12 

weeks, and productivity at the time of the interview. 

21 Relevant experience and the length of time until qualified are ideal instruments in that they should only affect 

wages indirectly through their effect on productivity. However, aside from its effect on productivity, training may 

entail costs that also affect wages. We would expect this effect to be relatively small compared to the productivity 

effect. But in any case, given the positive correlation between training and productivity growth and the negative 
 20

Table 4 shows IV estimates of the wage equation. As indicated in the first row of Table 4, 

the IV estimate of b1 is equal to .32. While significantly different from zero, it is also 

substantially and significantly below one. Recall that the difference between one and this 

coefficient indicates the degree of wage compression for starting wages, so we have evidence of 

substantial wage compression. The estimate of c1 is only equal to .19. Recall that c1 indicates 

the degree of employer sharing of the costs of general human capital acquisition, so there is little 

evidence of sharing. However, this coefficient is imprecisely estimated, so one cannot rule out 

substantial sharing. The IV estimate of c2 is 0.22, indicating that wage growth is substantially 

less than productivity growth. 

The preceding sharing rule estimates assume that productivity over the first twelve weeks 

is folded into the starting wage. It is straightforward to modify the analysis to reflect alternative 

assumptions about contract length.22 Rows 2- 5 of Table 4 show estimates of the productivity 

coefficients for other values of τ. The b1 coefficient is quite stable, showing that the evidence for 

wage compression is not an artifact of a particular assumed contract length.. The c1 and c2 

coefficients are more volatile, with c1 decreasing (and even becoming negative) and c2 increasing 

with contract length. 

One obvious objection to the previous estimates is that contract lengths need not be 

constant across workers. Fortunately, one can estimate contract length from the data in the 

 correlation between training and starting productivity, this will cause one to overestimate both the effect of 

productivity growth on wage growth and the effect of starting productivity on starting wages. 

22 If wages are initially set for a period of length τ ≥ 12, then starting productivity over the initial contact period is 

given by 0, 0,12 ,12

12 ( 12) τ τ ττ

τ

p p p − = + , so that the predicted productivity growth of the typical worker is 

given by 

) ( , , , ,12)) 12 ) ( , , ,12,0) ( 12 ln( ) ln( ) ln(( '' ' '' '

104 0, τ

τ

τ

τ τ typ typ typ typ typ typ

typ typ p p J Z Z Z J Z Z Z − − = − + . 

Similarly, one can obtain expressions for the predicted difference between the log productivity of the most recently 

hired worker and the typical worker during the first τ weeks and for the predicted difference in log productivity 

growth. 
 21

survey since EOPP provides information on the last-hired workerís wage at the time of the 

interview. We assume that the probability that a worker with a specified amount of tenure, t, has 

already experienced a wage change is given by 

(14) ) Pr( ) ( wt w0 F t ≠ = ξ , 

where the function F(·) is the cumulative standard normal distribution and where the vector t ξ

includes the variables tenure, tenure squared, a dummy variable equal to 1 if tenure exceeds one 

year, predicted productivity growth after the initial twelve week period 

( (ln( ) ln( ) | , , , , )) ''

typ

' E p104 p0,12 X1 X 2 Ztyp Ztyp Z typ − ), and tenure interacted with predicted productivity 

growth. Productivity growth is included in the probit wage change equation because it seems 

likely that the faster productivity grows, the shorter will be the length of the period for which the 

wage is fixed.23 

All of the productivity variables in (9) are functions of the contract length τ. Integrating 

across possible contract lengths using the parameter estimates in (10) and (14), a workerís 

expected wage growth is given by 

(15) 

∫

∫

∫

∞

∞

∞

+ ∆ + +

+ −

− = −

0

1 1 1 2 2

0

1 0 0

0

104 0 2 104 0

( ) ( ) . à

( )) ( ) ) à ( )) ln( à ((ln(

( )) ( ) ) à ) ln( à (ln( ) ln( )) (ln(

c h f dt l X l X

b H H f dt

E w w c H H f dt

t t

t t t

typ

t t

typ typ typ

ξ ξ

ξ ξ ξ

ξ ξ

In practice, we assume that the initial wage is not set for a period longer than 104 weeks or 

shorter than 12 weeks and amass the probability weights in the tails at the truncation points.24 

 

23 Our estimation results are not sensitive to the choice of τ. 

24 The estimated probit parameters imply that on average the probability that the wage is initially set for a period of 

time that is less than or equal to 12 weeks is .41. Since the productivity growth coefficient is positively related to 
 22

The probit estimation results are reported in Table 5 and the resulting estimates of b1, c1, 

and c2 are reported in the last row of Table 4. The probit results indicate that at least in this data 

set, wages are initially set for a relatively short period of time: for the average worker, mean 

contract length is only 18 weeks.25 The wage change probit also provides support for the 

hypothesis that the probability of wage changes varies with expected productivity--a joint test 

rejects the hypothesis of no effect of the productivity coefficients at the 1 percent level. For 

employees with the mean level of productivity growth, the predicted probability of a wage 

change by 18 weeks is 50 percent, while for employees with productivity growth one standard 

deviation above the mean the corresponding probability is 55 percent. 

As reported in the last row of Table 4, the resulting estimate of b1 is .32 and the estimate 

of c2 is .26. Both estimates are significantly different from one. The estimate of c1 is only .17, 

but is very imprecise. Thus, the data provide strong evidence of wage compression, but do not 

allow us to say much about the degree of cost sharing in the form of a positive relationship 

between the starting wage and productivity growth. Interestingly, when productivity growth is 

zero, the estimated two year wage growth of the average worker in the average job is 6 percent. 

This may reflect the fact that the employerís productivity estimate does not incorporate all costs 

 tenure for low values of tenure, truncating the contract length distribution at 12 weeks raises the estimated 

coefficient on productivity growth. The estimated probability that the wage is initially set for a period in excess of 

two years is .13. The results in Table 4 imply that truncating the contract length distribution at 104 weeks has little 

effect on the estimated productivity growth coefficient. 

25 One possible objection to this analysis is that the data are from the early 1980s, at the end of a period of high 

inflation. Many of the raises for low values of tenure may have been cost-of-living adjustments unrelated to 

productivity. We tested for this by estimating a non-linear regression of real wage changes from the start of the job 

to the interview date on productivity changes weighted by the probability of a true, non-cost-of-living raise 

(estimated as part of the regression). Our point estimates indicate that all raises were true, productivity-related raises. 

Specifically, we assumed a wage equation of the form 

φ μ σ τ τ τ τ η

τ

− = + − + ∫ ln(wtt ) ln(w ) k ( , , )c(ln( p ,52 ) ln( p0, ))d

12

0 , where φ(μ,σ,τ) is a normal density function 

indicating the probability of a true wage increase at τ , ln( ) τ ,52 p is the log of average productivity from time τ until 

52 weeks, and ln( ) 0,τ p is the log of average productivity from time 0 until τ weeks. Our point estimates of μ and σ

are 13 and .7 if we use the entire sample and 13 and .9 if we restrict the sample to those who have a positive wage 

change), again indicating that that contract length is typically quite short. 
 23

associated with searching for, hiring, and training new workers. 26 As in Salop and Salop (1976), 

these costs may be factored into the starting wage (instead of being spread out into future 

wages). 

What is the source of identification for the b1 coefficient? To answer this question, we 

regress ∫

∞

∆ ≡ ξ − ξ ξ ξ 0

0 0 ( )) ( ) ) à ( )) ln( à ((ln( t t t t

typ H H H f d on the other variables in (9) to generate 

residuals capturing the identifying variation in ∆H. Regressing these residuals on the omitted 

instruments other than the log of relevant experience yields an R2 of .068. Adding the log of 

relevant experience to this regression raises the R2 to .793, indicating that the identifying 

variation in predicted ∆H is predominantly variation in relevant experience. 27

Recent theoretical work by Acemoglu and Pischke (1999) and Booth and Zoega (2004) 

has suggested that wage compression may make training more likely, arguing that employers are 

more willing to finance training if the returns to training accrue at least partially to the employer 

due to wages only partly responding to increases in productivity. Empirical analysis of this 

effect has been hampered by the lack information on productivity.28 To investigate this issue we 

divided the sample by hours of training for the typical worker and reestimated the variable 

contract length model. The estimates of b1 show little difference between the subsamples. 

Estimated c2 is 0.13 for the sample with training above the sample median and 0.32 for the lowtraining subsample, but the estimates are not significantly different from each other (t=1.22). 

 

26 One issue with interpreting this result is that it could at least partially be an artifact of functional form, as we 

assume a linear relationship between log productivity growth and log wage growth and only a few observations 

have zero or near-zero productivity growth. Further investigation of this question is outside the scope of this paper. 

27 The remaining unexplained variation is accounted for by the non-linear construction of the variable. 

28 Empirical studies include Brunello (2002), Almeida-Santos and Mumford (2004), Ericson (2004), and Peraita 

(2001). The findings are mixed. 
 24

IV. A Simple Sharing Model with Equity Norms

The foregoing results imply that predictable differences in employees' starting 

productivity based on their relevant job experience are not completely reflected in wages. This is 

contrary to traditional theory, which suggests that any rents earned by firms by paying 

experienced hires less than their productivity would be bid away by competing employers. 

While one can find explanations of wage compression in the literature, these seem for the 

most part unsatisfactory in the present context. Frank (1984) proposes a model where more 

productive workers derive utility from their status within the firm and are willing to accept a 

wage less than their marginal product in order to work side by side with workers who are paid 

less. However, it seems unlikely that workers who are more productive simply because they are 

more experienced would derive utility from this fact. Similarly, Akerlof and Yellen (1990) posit 

that large wage differentials between groups may be perceived as unfair and lead to reduced 

effort. However, since less-experienced workers will acquire experience (barring layoffs) it is 

not clear why they would feel aggrieved by steep wage-experience profiles. Explanations based 

on asymmetric information, as in Acemoglu and Pischke (1998,1999), Katz and Ziderman 

(1999), and Chang and Wang (1996) fail to account for the fact that predicted productivity as a 

function of relevant experience--a variable which is publicly observable--is not rewarded 

proportionately. 

As discussed by Acemoglu and Pischke (1999) and Zoega and Booth (2005), monopsony 

power by employers can lead to wage compression if search is more costly for higher skilled 

workers. However, this seems unlikely by itself to explain the magnitude of starting wage 

compression that we observe in the data. In fact, if one allows entry, the monopsony model does 

not unambiguously predict compression in the starting wage. There are two competing effects. 
 25

A more highly skilled worker for whom search is more costly will be in a weaker bargaining 

position than a less skilled worker with lower search costs. But knowing that he will be 

relatively immobile once he accepts the employerís job and thus subject to higher rent extraction 

by the employer in the future, the more highly skilled worker will bargain for a higher proportion 

of his compensation up front. If the second effect dominates the first, starting wages will vary 

more than proportionately with productivity. 

Here we suggest an explanation based on the interaction of equity considerations such as 

those in Akerlof and Yellen (1990) with employer sharing of the cost of human capital 

acquisition. If employers share the costs of human capital investment, they recoup these costs by 

paying employees trained by the firm less than their marginal product. Hiring trained outsiders 

at a wage equal to their marginal product implies that observationally equivalent workers are 

paid different wages. It is easy to imagine that an employerís senior workers will be unhappy 

and put forth less effort if they receive a lower wage than other experienced workers who are no 

more productive, but who simply began their careers at other firms. Such behavior seems 

consistent with both casual observation of the labor market and experimental studies cited in 

Akerlof and Yellen (1990). 29 We show that an ìequity normî will not only lead to wage 

compression, but also will amplify employer sharing of the return to general human capital 

acquisition, as the wage compression and sharing effects will reinforce each other. 

Our model is similar to that developed by Hashimoto (1981) to analyze the optimal 

division of the returns and costs to firm-specific human capital investment. Unlike Hashimoto 

(1981), we assume that human capital is purely general in that its expected value is the same 

 

29 In their experimental study, Charness and Kuhn (2005) find little response of effort to co-worker wages, but 

explicitly do not consider the case where workers know that they are identically productive. In our analysis, this 

would not be a ìknife-edgeî case since employers paying senior workers less than newly hired experienced workers 

would be differentiating on the basis of a characteristic that is known to be unrelated to productivity. 
 26

everywhere. Consider a match between an employer and an employee who is in the labor market 

for two periods. The worker is hired in period 1 and has a starting value of marginal product of 

H. As a result of on-the-job training and learning by doing, the workerís expected productivity is 

higher in period 2. The worker's actual period 2 productivity is random and is not observed until 

the start of that period. Letting h denote the value in period 2 of the human capital accumulated 

in the initial period and η denote the value of the productivity shock, the workerís actual value of 

marginal product in period 2 is H + h + η. 

The workerís utility in each period is equal to the wage he receives plus the amenity 

value ε he places on the employerís job. The worker observes ε after he starts the job. The 

worker receives a starting wage equal to w1 and a second period wage of w2. If the worker 

moves to a new job, he incurs the moving cost c = c(H + h). Assuming that the workerís human 

capital is general, he receives the alternative wage H + h. 

We assume that the cost of locating and moving to a new job increases with the workerís 

stock of human capital. More senior positions at an employer are typically filled from within by 

workers who have proved to be a good match. Consequently, a worker with more experience 

and training searching for a job typically has a smaller set of openings available to him and will 

generally find it more difficult and costly to find and relocate to an employer who can use his 

skills effectively.30 

 

30 This motivation differs from that in Acemoglu and Pischke (1999), who argue that locating another job requires a 

period of unemployment, which is more costly to higher paid workers. Zoega and Boothís (2005) model of wage 

compression assumes that the set of employers who can use more able, higher skilled workers is smaller than the set 

of employers who can use less skilled workers. This is more similar to our motivation except that Zoega and 

Boothís argument is applicable when one is comparing workers in high- and low- skilled occupations. In contrast, 

we are comparing workers who are in the same basic occupation. 
 27

Because the value of η is the private information of the employer and the value of ε is the 

private information of the worker, we assume, like Hashimoto, that the two parties cannot 

contract on the basis of the realized values of η and ε.

31 Letting 

(16) D = H + h - w2

denote the rent the employer extracts when η is zero, the employer dismisses the worker if η < 

- D. It pays for the worker to quit when ε < ε

c = D ñ c. The probability of a dismissal or layoff 

is ∫

−

−∞

=

D

L g(η)dη and the probability of a quit are thus given by ∫

−∞

=

c

Q f d

ε

(ε ) ε , where g(⋅) and f(⋅) 

denote the density functions of η and ε. 

The expected gain to the worker from his match with the employer is given by 

((1 )(1 ) ( | ) ((1 ) )( ) 1 2 U w L Q E w L Q L H h c c = + δ − − + ε ε ≥ ε + − + + − , where δ denotes the 

discount factor. The worker is willing to form a match with the employer if U is at least as great 

as the expected utility UA

 available to experienced workers elsewhere in the labor market. The 

employerís expected gain from his match with the worker is π = H - w1 + δ(1-L)(1-Q)E(D+η| η

≥ -D). 

The employer chooses first and second period wages to maximize π subject to the 

constraint that U ≥ UA

. Note that the first period wage simply serves to divide up the total return 

to the match between the employer and worker. In a competitive labor market, the first period 

wage is bid up until the employerís expected profit over the two periods is driven to zero, or 

(17) w1 = H + δ(1-L)(1-Q) E(D+η| η ≥-D). 

 

31 Mortensen (1978) shows that inefficient separations can be eliminated if the employee and employer post turnover 

bonds that provide compensation for losses imposed by the other's decision to separate. While one occasionally 

observes turnover bonds, as noted by Black and Loewenstein (1998), their general use is limited by the fact that they 

are hard to implement when the exact value of the match to one party is not known by the other party. In addition, 

as noted by Carmichael (1983), turnover bonds suffer from the disadvantage of providing the worker and employer 

with an incentive to induce the other party to initiate turnover. 
 28

When the employer decides whether or not to dismiss a worker, he does not take into account the 

potential loss that the dismissal imposes on the worker. Similarly, when the worker decides 

whether to quit, he does not take into account the potential loss that a quit imposes on the 

employer. The optimal second period wage, or, equivalently, the optimal D, minimizes the 

expected loss from inefficient separations. Differentiating and rearranging terms one finds that 

at the optimum 

(18) ε η η η ε ε ε ε

ε

f D g d g D f d c

c

D

c ( ) ( ) ( ) ( ) ( ) ( ) ∫ ∫

∞ ∞

−

+ = − − , 

or equivalently, (∂Q/∂D)(1-L)E(η+D|η>-D) = -(∂L/∂D)(1-Q)E(ε-ε

c

|ε>ε

c

): the reduction in the 

workerís expected capital loss from a marginal increase in D must just equal the increase in the 

employerís expected capital loss.32 

Let D0

 denote the optimal value of D. Differentiating (17) with respect to h, one finds 

that 

(19) ) / '( 0 ∂D ∂h = Mc H + h , 

 where 0 < M < 1.33 So if greater human capital accumulation is associated with higher mobility 

costs, the employer will share part of the return with the worker. Differentiating (17) yields 

(20) / '((1 ) ( )(1 )( ( ( )) ) 0 0

0 ∂ 1 ∂ = − + − + > ∫

∞

−D

c w h δc Q M f ε M D ηg η dη : 

 

32 The second-order condition to the maximization condition requires that / 0 2 2 ∂ G ∂D < , which is equivalent to 

A + B > 0, where ε ε ε η η η

ε

A g D f d f D g d c c D

c ( ) ( ) '( ) ( ) ( ) ∫ ∫

∞

−

∞

≡ − + + and 

(ε ) (η) η '( ) (ε ε ) (ε ) ε.

η ε

B f g d g D f d c c

c C

∫ ∫ ∞ ∞

≡ + − − This condition is satisfied provided that the responsiveness 

of the quit rate and of the dismissal rate does not decrease too much as the wage rate increases. Henceforth we 

assume that A and B are both positive. 

33 Specifically, A B

A M

+ = . 
 29

the higher rent earned by the employer in the second period is paid to the worker in the form of a 

higher first period wage (generating a positive value for the coefficient γ1g in equation (1) above, 

unlike the Becker model). Finally, differentiating (17) with respect to H yields 

(21) / 1 (1 ') '( (1 ) ( )(1 )( ( ( )) ) 1 0

0 ∂ 1 ∂ = + δ + φ − + ε − + η η η > ∫

∞

−D

c w H c M Q f M D g d . 

The increase in mobility costs from the higher H leads to rent extraction in the second period, 

which is compensated for by a higher wage in the first period. Thus the variation in the starting 

wage exceeds the variation in starting productivity, contrary to our empirical results. Note that 

we have assumed that an employer hiring a new worker does not have any monopsony power, so 

that the newly hired workerís expected lifetime compensation equals his expected lifetime value 

of marginal product. As mentioned above, allowing monopsony power breaks this equality, with 

the result that there is no clear prediction as to whether variation in the starting wage exceeds or 

is less than variation in starting productivity. 

Equity Norms

We now posit the existence of an ìequity normî that prevents an employer from paying 

retained workers less than equally productive experienced workers hired from the outside. Such 

a norm implies that a worker who moves to a new employer in period 2 will realize a smaller 

return to his initial general human capital investment and will be less likely to quit. Specifically, 

letting the wage the worker can receive at an alternative employer be given by H + h - DA

, the 

minimum value of ε such that the worker does not quit is now given by ε

c

 = D - DA- c. 

Other than the changed definition ε

c

, condition (18) is unchanged. This condition 

implicitly defines D as a function of DA

: D = χ(DA). Differentiating D with respect to DA, one 
 30

finds that χ'= M : a reduction in the alternative wage causes a partial reduction in the second 

period wage offered by a workerís initial employer. 

Competition for experienced workers will ensure that they do not receive less than 

retained workers. Thus, if all employers hire a mix of inexperienced and experienced workers, 

labor market equilibrium requires that D = DA

. Note that when D = DA, ε

c

 = - c. The equity 

norm equilibrium conditions therefore reduce to 

(22) f c D η g η dη g D c ε f ε dε

D c c

( ) ( ) ( ) ( ) ( ) ( ) ∫ ∫

∞

−

∞

−

− + = − + . 

Let D*

 denote the equilibrium value of D. It follows immediately that D* < D0 . 

Unlike the case without equity constraints, and consistent with our empirical results, the 

equity norm implies that the variation in starting productivity will generally exceed the variation 

in the starting wage. For example, suppose that starting differences in the stock of human capital 

are fully offset by differences in human capital accumulation during the first period of 

employment and let H denote the stock of human capital achieved by all workers in the second 

period. Then a new worker will not receive compensation for any starting human capital that 

exceeds H − D *. 

The existence of an equity norm also affects the extent to which employers share in the 

return to human capital accumulation. Specifically, differentiating (22), one finds after a little 

algebra that 

(23) ) / '( )/(1 * ∂D ∂h = Mc h − M . 

Comparing (23) and (19), one sees that that the existence of an equity norm amplifies the initial 

tendency by employers to share in the costs and returns to general human capital investment. In 
 31

terms of our empirical model, this implies a reduction in c2 and an increase in c1. While c1 is not 

precisely estimated, our model is consistent with low values of b1 and c2. 

In deriving the equity-norm equilibrium, we have assumed that employers hire a mix of 

inexperienced and experienced workers. This will be the case if inexperienced and experienced 

workers are strong complements in production, something which seems consistent with casual 

observation. For example, it may be efficient to place less skilled, inexperienced workers in less 

demanding tasks and let experienced workers concentrate on certain critical tasks for which they 

are better suited. Or part of experienced workersí higher value may stem from the informal 

training that they provide to less experienced workers.34

V. Conclusion 

Exploiting the richness of the EOPP data, this paper has analyzed the relationship 

between wages and productivity during the early years of an employment relationship. The 

EOPP data show that worker productivity grows substantially during the early part of the 

employment relationship: productivity after two years is on average eighty percent higher than at 

the start of the job. The data also indicate that most of the growth in productivity occurs at the 

very start of the job, with sixty-four percent of the growth in two year productivity occurring 

during the first three months. 

Even when one corrects for measurement error and the fact that expected productivity 

beyond the start of the job may be folded into the starting wage if wage revisions are not 

instantaneous, one finds that variation in productivity is only partially reflected in wages. One 

observes this along two dimensions. First, there is compression in the starting wage. Starting 

productivity differences for workers in the same job ñ in large part driven by differences in 

 

34 In their formally similar model, Akerlof and Yellen (1990) consider equilibria with segregation of different types 

of workers; detailed analysis of these equilibria in the present case is outside the scope of this paper. 
 32

relevant experience - are only partially reflected in starting wage differences even when one 

controls for differences in human capital acquisition. Second, productivity growth stemming 

from human capital accumulation while on the job is only partially reflected in wage growth, 

reflecting employer sharing of the costs and returns to human capital acquisitions and/or 

increased wage compression over time. 

Our empirical findings can be explained by adding equity norms to a simple model of 

employer sharing of the costs of human capital. Our model has two key features. First, similar 

to Zoega and Booth (2005), the cost of locating and moving to a new job increases with the 

workerís stock of human capital, reflecting the fact that more highly skilled workers typically 

have a smaller set of potential employers to choose from. Second (and to our knowledge unique 

to our model), in offering wages to new workers, an employer is constrained by the fact that his 

senior workers will be unhappy and uncooperative if they receive a lower wage than other 

workers who are no more productive. In equilibrium, there can be substantial wage compression: 

higher productivity resulting from the acquisition of human capital is only partially reflected in 

wages, whether the human capital accumulation occurs on the current job or at other jobs. 

Similar to Acemoglu and Pischke (1999) and Zoega and Booth (2005), a key feature of 

our model is the association of wage compression with employers' sharing the cost of human 

capital acquisition. Our estimate of the sharing effect is right signed, but the data are 

unfortunately insufficient to estimate the sharing effect precisely. Acemoglu and Pischke (1999) 

and Booth and Zoega (2004) suggest that compression may be associated with willingness of 

firms to train workers. Unfortunately, the data do not allow precise estimation of the difference 

in wage compression between low- and high-training firms. Thus, while the presence of wage 

compression receives strong support in our data, we have little to say empirically about the 
 33

implications of this finding. Further empirical analysis is required to test models associating 

wage compression with employer cost sharing or employer provision of training. This analysis 

is made difficult by the paucity of data sets with information on productivity. 
 34

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 37

Table 1 

Descriptive Statistics 

Variable Mean Std. Dev. Min Max

Ln Prod. Growth over initial 2 years 0.80 1.14 -1.10 6.91

Ln Prod. Growth over initial 3 months 0.51 0.94 -1.37 6.69

Ln Prod. Growth from third month until 

end of second year 

0.29 0.43 -1.25 6.22

Ln Wage Growth 0.18 0.20 -1.99 1.95

Age 27.00 9.08 16.00 64.00

Vocational schooling 0.28 0.45 0.00 1.00

Temporary or seasonal job 0.15 0.35 0.00 1.00

Part-time job 0.21 0.41 0.00 1.00

Union 0.11 0.28 0.00 1.00

Ln establishment size 2.91 1.51 0.00 8.60

Female 0.45 0.50 0.00 1.00

Tenure (weeks) 67.38 71.55 1.10 1152.67

High School Indicator 0.76 0.42 0 1

College indicator 0.12 0.32 0 1

Ln (formal tr. hours+ 1) 0.48 1.30 0.00 6.46

Ln (informal tr. hours + 1) 3.43 1.52 0.00 7.60

Ln (hours watch others, typical, + 1) 2.75 1.73 0.00 6.88

Ln (weeks until fully trained,typical, + 1) 2.21 1.23 0.00 6.03

Ln (weeks rel. experience + 1) 2.86 2.44 0.00 7.64

Ln (formal tr. , typical + 1) 0.50 1.34 0 6.69

Ln (informal tr. , typical, + 1) 3.56 1.48 0 7.60

Obs.* 1, 543 

*There are 1,471 observations with information on relevant experience and 1,538 observations with information on 

informal training. 
 38

Table 2 

OLS Wage Equations 

 Starting Productivity is 

average productivity during 

the first two weeks 

Starting Productivity is 

average productivity 

during the first three 

months 

Typical workerís log productivity 

growth over two years 

 0.027 

(0.004) 

 0.073 

(0.011) 

 

Difference between log starting 

productivity of typical worker and 

log starting prod. of most recent 

hire 

 0.015 

(0.008) 

 0.023 

(0.013) 

 

Union -0.011 

(0.018) 

-0.010 

(0.018) 

Log of establishment size 0.0005 

(0.0036) 

 0.0013 

(0.0036) 

Weeks tenure 0.0009 

(0.0001) 

 0.0009 

(0.0001) 

High School difference* 0.007 

(0.016) 

 0.007 

(0.016) 

College difference 0.036 

(0.021) 

 0.035 

(0.021) 

Vocational training difference -0.001 

(0.011) 

 0.006 

(0.011) 

Female difference 0.003 

(0.010) 

 0.003 

(0.010) 

Age difference 0.009 

(0.003) 

 0.009 

(0.003) 

Age squared difference/100 -0.01 

(0.00) 

-0.01 

(0.00) 

Temporary difference 0.002 

(0.014) 

 0.005 

(0.014) 

Part-time difference 0.005 

(0.014) 

 0.006 

(0.013) 

Constant 0.010 

(0.014) 

 0.095 

(0.014) 

 

Number of Observations 1,543 1,543 

2 R .13 .13 

*High School difference is the high school indicator for the typical worker minus the high school indicator 

for the most recent hire. The other dif variables in the table are defined analogously.
 39

Table 3 

Selected Coefficients, Productivity Growth Equation 

Ln (weeks rel. experience + 1) 0.032 

(0.007) 

Ln (formal tr. hours + 1) -0.16 

(0.10) 

Ln (informal tr. hours + 1) -0.23 

(0.04) 

Ln (weeks until fully trained, typical, + 1) 

 

-0.15 

(0.03) 

Ln (hours watch others, typical, l + 1) -0.13 

(0.03) 

Ln (formal tr. hours, typical, + 1 ) 0.23 

(0.10) 

Ln (informal tr. hours, typical, + 1) 0.12 

(0.04) 

Ln (formal tr. hours + 1) x (Tenure spline 1) 0.069 

(0.015) 

Ln (informal tr. hours + 1) x (Tenure spline 1) 0.045 

(0.014) 

Ln (weeks until fully trained,typical, + 1) x (Tenure spline 1) 0.049 

(0.012) 

Ln (watch others, typical, + 1) x (Tenure spline 1) 0.049 

(0.012) 

Ln (formal tr. hours, typical, + 1) x (Tenure spline 1) 0.018 

(0.035) 

Ln (informal tr. hours, typical, + 1) x (Tenure spline 1) -0.36 

(0.02) 

Ln (formal tr. hours + 1) x (Tenure spline 2) 0.009 

(0.028) 

Ln (informal tr. hours + 1) x (Tenure spline 2) 0.004 

(0.015) 

Ln (weeks until fully trained,typical, + 1) x (Tenure spline 2) 0.008 

(0.018) 

Ln (watch others, typical, + 1) x (Tenure spline 2) 0.008 

(0.013) 

Ln (formal tr. hours, typical, + 1) x (Tenure spline 2) -0.024 

(0.026) 

Ln (informal tr. hours, typical, + 1) x (Tenure spline 2) 

 

 0.000 

(0.014) 

 

Number of Observations 4,446 

R2

 0.21 
 40

Tenure spline 1 = min(ln(t+1),ln(12+1)) 

Tenure spline 2 = max(ln(t+1)-ln(12+1), 0) 
 41

Table 4 

IV Estimation of the Sharing Coefficients* 

Contract Length Difference 

between log 

starting 

productivity of 

typical worker 

and log starting 

prod. of most 

recent hire (b1) 

Difference 

between prod. 

growth of typical 

worker and prod. 

growth of most 

recent hire (c1) 

Productivity 

growth of typical 

worker over the 

two year period 

(c2) 

 

12 weeks 0.32 

(0.07) 

0.19 

(0.29) 

0.19 

(0.03) 

18 weeks 0.32 

(0.08) 

0.12 

(0.41) 

0.33 

(0.08) 

26 weeks 0.32 

(0.08) 

0.02 

(0.43) 

0.46 

(0.16) 

38 weeks 0.32 

(0.09) 

-0.13 

(0.49) 

0.58 

(0.24) 

52 weeks 0.31 

(0.09) 

-0.43 

(0.58) 

 0.61 

 (0.26) 

Variable 0.32 

(0.10) 

0.17 

(0.46) 

0.26 

(0.05) 

n = 1518 

* Standard errors generated by bootstrapping. 
 42

Table 5 

Probit Equation: Probability of a Wage Change 

 

Typical workerís log productivity growth 

over the first two years 

 0.57 

(0.41) 

 

Typical workerís log productivity growth 

x weeks tenure 

 0.012 

(0.007) 

 

Typical workerís log productivity growth 

x (weeks tenure)2

/100 

-0.0013 

(0.0008) 

 

Weeks tenure 0.064 

(0.025) 

(Weeks tenure)2

/100 -0.068 

(0.037) 

Tenure >= 1 year 1.18 

(0.41) 

Weeks tenure x (Tenure >= 1 year) -0.058 

(0.024) 

(Weeks tenure)2 x (Tenure >= 1 year)/100 0.067 

(0.037) 

Constant -1.21 

(0.49) 

 

Number of Observations 1686