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Frictional Wage Dispersion in Search
Models: A Quantitative Assessment

WP 06-07

Andreas Hornstein
Federal Reserve Bank of Richmond
Per Krusell
Princeton University
Giovanni L. Violante
New York University

This paper can be downloaded without charge from:
http://www.richmondfed.org/publications/

Frictional Wage Dispersion in Search Models:
A Quantitative Assessment ∗
Andreas Hornstein†

Per Krusell‡

Giovanni L. Violante§

Federal Reserve Bank of Richmond Working Paper 2006-07
Abstract
Standard search and matching models of equilibrium unemployment, once properly calibrated, can generate only a small amount of frictional wage dispersion, i.e.,
wage differentials among ex-ante similar workers induced purely by search frictions.
We derive this result for a specific measure of wage dispersion—the ratio between
the average wage and the lowest (reservation) wage paid. We show that in a large
class of search and matching models this statistic (the “mean-min ratio”) can be
obtained in closed form as a function of observable variables (i.e., interest rate, value
of leisure, and statistics of labor market turnover). Looking at various independent
data sources suggests that, empirically, residual wage dispersion (i.e., inequality
among observationally similar workers) exceeds the model’s prediction by a factor
of 20. We discuss three extensions of the model (risk aversion, volatile wages during
employment, and on-the-job search) and find that, in their simplest version, they
can improve its performance, but only modestly. We conclude that either frictions
account for a tiny fraction of residual wage dispersion, or the standard model needs
to be augmented to confront the data.
Keywords: labor market, wage inequality, search frictions, job search
JEL Classification: D83, E24, J31, J41, J63, J64
∗

We are grateful for comments from Gadi Barlevy, Bjoern Bruegemann, Zvi Eckstein, Chris Flinn,
Rasmus Lentz, Dale Mortensen, Giuseppe Moscarini, Fabien Postel-Vinay, Richard Rogerson, Robert
Shimer, and Philippe Weil, and from seminar participants at the Cleveland Fed, the Cowles Foundation
Workshop, ESSIM 2004 (Cyprus), Georgetown, NYU, Philadelphia Fed, Penn State, Princeton, SED
2006, Southern California, Yale, and York University. Greg Kaplan and Matthias Kredler provided excellent research assistance. The views expressed here are those of the authors and do not necessarily reflect
those of the Federal Reserve Bank of Richmond or the Federal Reserve System. Our e-mail addresses are:
andreas.hornstein@rich.frb.org, pkrusell@princeton.edu, and gianluca.violante@nyu.edu
†
Federal Reserve Bank of Richmond
‡
Princeton University, CEPR, and NBER
§
New York University and CEPR

1

Introduction

The economic success of individuals is largely determined by their labor market experience. For centuries, economists have been interested in studying the determinants of
earnings dispersion among workers. The standard theories of wage differentials in competitive environments are three. Human capital theory suggests that a set of individual
characteristics (e.g., individual ability, education, labor market experience, job tenure) are
related to wages because they correlate to productive skills, either innate or cumulated
in schools, and on the job. The theory of compensating differentials posits that wage
dispersion arises because wages compensate for non-pecuniary characteristics of jobs and
occupations such as fringe benefits, amenities, location, and risk. Models of discrimination assume that certain demographic groups are discriminated against by employers and,
as such, they earn less for similar skill levels.
Mincerian wage regressions based on cross-sectional individual data proxy all these
factors through a large range of observable variables, but typically they can explain at
most 1/3 of the total wage variation. A vast amount of residual wage variation is left
unexplained. In practice, measurement error is large, and the available covariates capture
only imperfectly what the theory suggests as determinants of wage differentials. However,
even if we could perfectly measure what these competitive theories require, we should not
expect to explain all observed wage dispersion.
Theories of frictional labor markets which build on the seminal work of McCall (1970),
Mortensen (1970), Lucas and Prescott (1974), Burdett (1978), Pissarides (1985), Mortensen
and Pissarides (1994), and Burdett and Mortensen (1998) predict that wages can diverge
among ex-ante similar workers looking for jobs in the same labor market (e.g., the market
for janitors in Philadelphia) because of informational frictions and luck in the search and
matching process. We call this type of wage inequality inherently associated to frictions
frictional wage dispersion.1
The canonical search and matching model provides a natural starting point for thinking
about frictional wage dispersion. We begin by asking how much frictional wage dispersion
the model can generate, and we arrive at a surprisingly general answer. We show that in
1

Mortensen (2005), which reviews the theoretical and empirical investigations on the subject, calls it
pure wage dispersion.

1

the three standard models (the sequential search model, the island model, and the random
matching model) one obtains the same analytical expression for a particular measure of
frictional wage dispersion: the ratio between the average wage and the lowest (reservation)
wage paid in the economy. We call this measure the mean-min (M m) ratio. The M m
ratio has the convenient property that it does not depend directly on the shape of the
wage-offer distribution, which is hard to observe, but only on a small set of structural
parameters that can be readily calibrated to reproduce well known features of the U.S.
economy. It must also be noted here that our result, since it merely exploits rational
search by workers, is consistent with many views on where the wage-offer distribution
comes from, including different sorts of search-matching theory as well as efficiency-wage
theory.
A calibration of the model—for plausible values of the job finding rate, separation rate,
worker’s discount/interest rate, and “flow utility value of being unemployed”—predicts
M m = 1.036. I.e., the model only generates a 3.6% differential between the average wage
and the lowest wage. The reason is that in the search model “good things come only
to those who wait”, but the data on unemployment duration show that workers do not
wait for very long. Thus, the observed search behavior of workers rationalizes only a tiny
amount of dispersion in the wage distribution.
The natural follow-up question is: how large is frictional wage dispersion in actual
labor markets? Ideally, one would like to access individual wage observations for ex-ante
similar workers searching in the same labor market. These requirements pose several
challenges that we can only partially address, given data availability. We exploit three
alternative data sources: the November 2000 survey from the Occupational Employment
Statistics (OES) program, the 1967-1996 waves of the Panel Study of Income Dynamics
(PSID), and the 5% Integrated Public Use Microdata Series (IPUMS) sample of the 1990
U.S. Census. Overall, from the empirical work we gauge that the observed M m ratios are
at least twenty times larger than what the model predicts.
Residual wage dispersion measured in the data includes both wage differentials due
to frictions, and wage differentials due to unobservable, possibly time-varying, skills that
cannot be fully controlled for, given data constraints. Thus, the large discrepancy between
model and data we document can be resolved in two ways. First, one can “blame the

2

data”: unobserved heterogeneity would account for the large M m ratios we document,
and the remaining frictional wage dispersion is very small, as predicted by the theory.
Second, one can “blame the theory”: more elaborate, or different, search models need to
be explored in order to account for our recorded M m ratios. We remain agnostic. We
do, however, consider it important to pursue each possibility further. As for further data
analysis, this paper contains rather detailed analysis already; in particular, our PSID data
does control for fixed (time-invariant) individual effects. However, it would be valuable
to try to measure more individual-specific components (directly measured time-invariant
variables, such as test scores, and time-varying factors such as events altering the value
of leisure, e.g., fertility or health shocks). This work is important, but it is beyond the
scope of this paper to pursue it here.
As for developing theory—which one would need if indeed our M m estimates represent
true frictional wage dispersion—that can overcome the spectacular failure of the baseline
model, we do begin this pursuit here. Our investigation maintains focus on the M m ratio.
This statistic is naturally obtained from the reservation wage equation, a cornerstone of
virtually every search model, and in all the three extensions we study, we are able to
derive simple closed-form expressions for the M m.
The first extension introduces risk aversion: risk-averse workers particularly dislike the
low-income state (unemployment) and set a low reservation wage, which allows the model
to generate a larger M m ratio. We find that even when we exclude agents from using any
form of insurance, a very high risk-aversion coefficient (around eight) is needed to generate
what we see in the data. Moreover, we know that the availability of self-insurance (say,
with precautionary saving) would help consumers a lot, thus requiring much higher risk
aversion still.
The second extension allows for stochastic wage fluctuations during employment, with
endogenous separations. If wages vary over the employment spell, then the wage offer
drawn during unemployment is not very informative about the value of a job, so a large
dispersion of wages could coexist with a small dispersion of job values which is what
drives unemployment duration. Also in this case, though, for reasonable calibration the
quantitative improvement of the model is modest: wages need to be virtually i.i.d. during
the employment relationship for the model to produce a high M m ratio; in reality, wages

3

are instead close to a random walk.
The third extension allows for on-the-job search, along the lines of the basic jobladder model of Burdett (1978).2 The ability to search on the job for new employment
opportunities makes unemployed workers less demanding, which reduces their reservation
wage and allows the model to generate a higher M m ratio. This latter modification is
the one that shows most promise but, at least in its simplest form, it still falls short
of explaining the data. To generate dispersion, this model needs a high arrival rate of
offers on the job. However, the high arrival rate implies separations at a frequency that
is almost twice that observed.
In conclusion, we find that for plausible parameterizations a remarkably large class of
search models has trouble generating the observed amount of residual wage dispersion.
This result is also helpful for understanding why the existing empirical structural search
literature (see Eckstein and Van den Berg, 2005, for a recent survey) systematically finds
very low (negative and large) estimates of the value of non-market time, extremely high
estimates of the interest rate, or very large estimates of measurement error or of unobserved worker heterogeneity. Finally, we note that our findings indicate a link between the
struggle in understanding the cross-sectional wage distribution and the recently discussed
difficulty of replicating the time series of unemployment and vacancies using search theory
(see, e.g., Hall, 2005, and Shimer, 2005b): parameter values that help resolve the former
problem make it harder to resolve the latter, and vice versa.
The rest of the paper is organized as follows. Section 2 derives the common expression
for the M m ratio in three canonical search models and quantifies their implications.
Section 3 contains the empirical analysis. Section 4 makes a number of first attempts
at rescuing the canonical model. Sections 5, 6, and 7 then outline the three significant
extensions of the model mentioned above and evaluate them quantitatively. Section 8
discusses the empirical search literature from our perspective. Section 9 concludes the
paper. Finally, some of the theoretical propositions in the present paper are proved in a
separate Technical Appendix: Hornstein, Krusell, and Violante (2006).
2

Since none of our derivations depend on the shape of the wage offer distribution, our results hold
in the wage-posting equilibrium versions of the job-ladder model (e.g., Burdett and Mortensen, 1998) as
well.

4

2

Frictional wage dispersion in canonical models of
equilibrium unemployment

The three canonical models of frictional labor markets are the sequential search model
developed by McCall (1970) and Mortensen (1970), the island model of Lucas and Prescott
(1974), and the random matching model proposed by Pissarides (1985).
In what follows, we show that all three models lead to the same analytical expression
for a particular measure of frictional wage dispersion: the mean-min ratio, i.e., the ratio
between the average wage and the lowest wage paid in the labor market to an employed
worker. Then, we explore the quantitative implications of this class of models for this
particular statistic of frictional wage dispersion.

2.1

The basic search model

We begin with the basic sequential search model formulated in continuous time. Consider
an economy populated by ex-ante equal, risk-neutral, infinitely lived individuals who discount the future at rate r. Unemployed agents receive job offers at the instantaneous rate
λu . Conditionally on receiving an offer, the wage is drawn from a well-behaved distribution
function F (w) with upper support w max . Draws are i.i.d. over time and across agents.
If a job offer w is accepted, the worker is paid a wage w until the job is exogenously
destroyed. Separations occur at rate σ. While unemployed, the worker receives a utility
flow b which includes unemployment benefits and a value of leisure and home production,
net of search costs. Thus, we have the Bellman equations
rW (w) = w − σ [W (w) − U ]
Z wmax
rU = b + λu
[W (w) − U ] dF (w) ,

(1)
(2)

w∗

where rW (w) is the flow (per period) value of employment at wage w, and rU is the flow
value of unemployment. In writing the latter, we have used the fact that the optimal
search behavior of the worker is a reservation-wage strategy: the unemployed worker
accepts all wage offers w above w ∗ = rU , at a capital gain W (w) − U . Solving equation
(1) for W (w) and substituting in (2) yields the reservation wage equation

5

λu
w =b+
r+σ
∗

Z

w max

[w − w ∗ ] dF (w) .

w∗

Without loss of generality, let b = ρw̄, where w̄ = E [w|w ≥ w ∗ ] . Then,
w

∗

Z max
λu [1 − F (w ∗ )] w
dF (w)
= ρw̄ +
[w − w ∗ ]
r+σ
1 − F (w ∗ )
w∗
λ∗u
= ρw̄ +
[w̄ − w ∗ ] ,
r+σ

(3)

where λ∗u ≡ λu [1 − F (w ∗ )] is the job-finding rate. Equation (3) relates the lowest wage
paid (the reservation wage) to the average wage paid in the economy through a parsimonious set of structural parameters of the model.
If we now define the mean-min wage ratio as M m ≡ w̄/w ∗ and rearrange terms in (3),

we arrive at

Mm =

λ∗u
r+σ
λ∗u
r+σ

+1
+ρ

.

(4)

The mean-min ratio M m is our new measure of frictional wage dispersion, i.e., wage
differentials entirely determined by luck in the random meeting process. This measure
has one important property: it does not depend directly in any way on the shape of
the wage distribution F . Put differently, the theory allows predictions on M m without
requiring any information on F. The reason is that all it is relevant to know about F ,
i.e., its probability mass below w ∗ , is already contained in the job finding rate λ∗u that we
can measure directly through labor market flows from unemployment to employment and
treat as a parameter.
The model’s mean-min ratio can thus be written as a function of a four-parameter
vector, (r, σ, ρ, λ∗u ), which we can try to measure independently. Thus, looking at this relation, if we measure the discount rate r to be high (high impatience), for given estimates
of σ, ρ, and λ∗u , an increased M m must follow. Similarly, a higher measure of the separation rate σ increases M m (because it reduces job durations and thus decreases the value
of waiting for a better job opportunity). A lower estimate of the value of non-market time
ρ would also increase M m (agents are then induced to accept worse matches). Finally, a
lower measure of the contact rate λ∗u pushes M m up, too (because it makes the option
value of search less attractive).
6

2.2

The search island model

We outline a simple version of the island model as in Rogerson, Shimer, and Wright
(2006). Consider an economy with a continuum of islands. Each island is indexed by its
productivity level p, distributed as F (p) . On each island there is a large number of firms
operating a linear technology in labor y = pn, where n is the number of workers employed.
In every period, there is a perfectly competitive spot market for labor on every island.
An employed worker is subject to exogenous separations at rate σ. Upon separation, she
enters the unemployment pool. Unemployed workers search for employment and at rate
λu they run into an island drawn randomly from F (p) .
It is immediate that one can obtain exactly the same set of equations (1)-(2) for the
worker, while for the firm in each island, we can write its flow value of producing as
rJ (p) = pn − wn.
Competition among firms drives profits to zero, and thus in equilibrium w = p. At this
point the mapping between the island model and the search model is complete.3 The
search island model yields the same expression for M m as in (4) .

2.3

The basic random matching model

There are three key differences between the search setup described above and the matching
model (e.g., Pissarides, 1985). First, there is free entry of vacant firms (or jobs). Second,
the flow of contacts m between vacant jobs and unemployed workers is governed by an
aggregate matching technology m (u, v). Let the workers’ contact rate be λu = m/u and
the firm’s contact rate be λf = m/v. Third, workers and firms are ex-ante equal, but upon
meeting they jointly draw a value p, distributed according to F (p) with upper support
pmax , which determines flow output on their potential match. Once p is revealed, they
bargain over the match surplus in a Nash fashion and determine the wage w (p). Let β
be the bargaining power of the worker; then the Nash rule for the wage establishes that
w (p) = βp + (1 − β) rU,
3

(5)

One can also allow firms to operate a constant returns to scale technology in capital and labor, i.e.,
y = pk α n1−α . If capital is perfectly mobile across islands at the exogenous interest rate r, then firms’
optimal choice of capital allows us to rewrite the production technology in a linear fashion, and the
equivalence across the two models goes through.

7

where rU is the flow value of unemployment.4 This equation uses the free entry condition
of firms that drives the value of a vacant job to zero.
From the worker’s point of view, it is easy to see that equations (1)-(2) hold with a
slight modification:
rW (p) = w (p) − σ [W (p) − U ]
Z pmax
rU = b + λu
[W (p) − U ] dF (p) ,
p∗

i.e., the value of employment is expressed in terms of the value p of the match drawn;
similarly, the optimal search strategy is expressed in terms of a reservation productivity p∗ . Rearranging these two expressions, we arrive at an equation for the reservation
productivity
λu β
p =b+
r+σ
∗

Z

pmax
p∗

[p − p∗ ] dF (p) ,

(6)

where we have used the fact that p∗ = rU. Substituting (5) into (6) , we obtain
Z max
λu [1 − F (p∗ )] p
dF (p)
∗
w = b+
[w (p) − w ∗ ]
r+σ
1 − F (p∗ )
p∗
λ∗u
= b+
[w̄ − w ∗ ] .
r+σ
Using the definition b = ρw̄ in the last equation, we again obtain the formula in (4) for
the mean-min ratio. Finally, note that nothing in this derivation depends on the shape
of the matching function.

2.4

Quantitative implications for the mean-min ratio

How much frictional wage dispersion can these models generate when plausibly calibrated?
We set the period to one month.5 An interest rate of 5% per year implies r = 0.0041.
Shimer (2005a) reports, for the period 1967-2004, an average monthly separation rate σ
(EU flow) of 2% and a monthly job finding probability (UE flow) of 39%. These two numbers imply a mean unemployment duration of 2.56 months, and an average unemployment
rate of 4.88%.
4

See, for example, Pissarides (2000), Section 1.4, for a step-by-step derivation of this wage equation.
The M m ratio has the desirable property of being invariant to the length of the time interval.
A change in the length of the period affects the numerator and denominator of the ratio λ ∗u / (r + σ)
proportionately, leaving the ratio unchanged. The parameter ρ is unaffected by the period length.
5

8

The OECD (2004) reports that the net replacement rate of a single unemployed worker
in the U.S. in 2002 was 56%. The fraction of labor force eligible to collect unemployment
insurance is close to 90% (Blank and Card, 1991) which implies a mean replacement rate
of roughly 50%. Of course, unemployment benefit are only one component of b. Others
are the value of leisure, the value of home production (both positive), and the search
costs (negative). Shimer (2005b), weighting all these factors, sets ρ to 41%. As discussed
by Hagedorn and Manovskii (2006), this is likely to be a lower bound. For example,
taxes increase the value of ρ since leisure and home production activities are not taxed.
Since higher values for b will strengthen our argument, we proceed conservatively and set
ρ = 0.4, and in Section 4 we perform a sensitivity analysis.
This choice of parameters implies M m = 1.036: the model can only generate a 3.6%
differential between the average wage and the lowest wage paid in the labor market. 6 This
number appears very small. What explains the inability of the search/matching model to
generate quantitatively significant pure wage dispersion? In the model, workers remain
unemployed if the option value of search is high. The latter, in turn, is determined by
the dispersion of wage opportunities. The short unemployment durations, as in the U.S.
data, reveal that agents in the model do not find it worthwhile to wait because frictional
wage inequality is tiny. The message of search theory is that “good things come to those
who wait”, so if the wait is short, it must be that good things are not likely to happen.
We now turn to the obvious next question: how large is frictional wage dispersion in
actual labor markets?

3

An attempt to measure frictional wage dispersion

The aim of our analysis is to quantify the empirical counterpart of the model’s meanmin ratio M m. Ideally, one would like to access individual wage observations for ex-ante
similar workers searching in the same labor market. This requirement poses three major
challenges that we address by exploiting three alternative data sources: the November
2000 OES survey, the 1967-1996 waves of the PSID, and the 5% IPUMS sample of the
1990 U.S. Census.
6
The reason why this ratio is close to one is that the term λ∗u / (σ + ρ) is very large—around 16—
compared to both 1 and ρ, the other two terms of the expression in 4.

9

The first challenge is to define a “labor market”. The most natural boundaries across
labor markets are, arguably, geographical, sectoral, and occupational, and possibly combinations of all these dimensions. The PSID sample is too small to construct detailed
labor markets. OES and Census data, however, allow us to look at the wage distribution
in thousands of separate labor markets in the U.S. economy.
Second, differences in annual earnings may reflect differences in hours worked. To
avoid this problem, one should focus on hourly wages. However, it is well known that
measurement error in hours worked plagues household surveys, and large measurement
error will generate an upward bias in estimates of wage dispersion. The OES is an establishment survey where measurement error should be negligible. PSID and Census
information on hourly wages, though, may suffer from measurement error bias. In particular, estimates of the reservation wage through the lowest wage observation are especially
subject to outliers due to reporting or imputing errors. As an alternative, we estimate the
reservation wage from the 1st, 5th, and 10th percentile of the wage distribution. These
percentiles are less volatile, even though upward biased, estimators of the reservation
wage in the empirical wage distribution. We denote the corresponding mean-min ratios
as M p1, M p5, and M p10, respectively.
Third, we would like to eliminate all wage variation due to ex-ante differences across
individuals in observable characteristics (e.g., experience, education, race, gender, etc.), as
well as all wage variation due to heterogeneity in unobservables (e.g., innate ability, value
of leisure, etc.). The OES does not provide any demographic information on workers. In
the Census data, we can control for a wide set of observable characteristics. When using
the PSID, we can exploit the panel dimension to also purge fixed individual heterogeneity
from the wage data.
Overall, none of the three data sets is ideal, but each of them is informative in its own
way.

3.1

OES Data

The first data source we use is the OES. Appendix A contains a description of the survey
and of the sample selection criteria we adopt.

10

Table 1: Dispersion measures from the 2000 OES

Occupation

Number of
labor mkts
637

Ratio of mean wage
to 10th percentile
1.68

Occ./Industry

6,293

1.60

Occ./Geog Area

106,278

1.48

OES data are collected at the level of the establishment. Each establishment reports
the average hourly wage paid within each occupation. To the extent that there are withinestablishment differences in wages due to luck or frictions among similar workers, these
data underestimate frictional wage dispersion.
We use three different levels of aggregation: nation-wide data by occupation (3-digit),
occupation × metropolitan area data, and occupation (3-digit) × industry (2-digit) data.
The publicly available survey reports the average, the 10th, 25th, 50th, 75th and 90th

percentiles of the hourly wage distribution.
The best possible estimate (which clearly is downward-biased) of the mean-min ratio is
the ratio between the average wage and the 10th percentile (M p10). We exclude all those
cells where hourly wage data are not available, and those where the 90th percentile is top
coded (at $70 per hour)—a sign that wages are heavily censored in that cell.7 In each
cell (i.e., a labor market) we compute the M p10, and then we calculate the median M p10
ratio across labor markets. The median is preferable to the mean because we consistently
found that the empirical distributions of mean-min ratios are very skewed to the right,
and we are interested in the mean-min ratio of the wage distribution in a typical labor
market.
The median M p10 ratio across occupations in the U.S. economy is 1.68. For the
classification of labor markets based on 2-digit industry (58 industries) and occupation,
the median M p10 ratio is 1.60. Finally, when we define labor markets by metropolitan
area (337 areas) and occupation, the median M p10 ratio is estimated to be 1.48. Table 1
summarizes the results.
7

The first restriction mainly excludes workers in the Education sector (25-000), while the second
mainly excludes Healthcare Practitioners (29-000).

11

As the definition of labor market becomes more refined, wage dispersion falls for
two reasons. First, there is less worker heterogeneity within a specific occupation in a
given industry, or in a given geographical area than at the country level. Second, as we
keep disaggregating, the number of establishments sampled within each cell falls. For
example, for cells defined by occupation and metropolitan area, we have on average only
11 establishments per cell. With such a low number of observations, the estimate of
the 10th percentile could be severely upward biased, and in turn the mean-min ratio
underestimated.

3.2

PSID Data

Our second data source is the Panel Study of Income Dynamics (PSID). In Appendix
B, we describe in detail our sample selection. With our final sample in hand, for every
year in the period 1967-1996, we run an OLS regression on the cross-section of individual log hourly wages where we control for gender, 3 race dummies (white, non-white,
Hispanics), 5 education dummies (high-school dropout, high-school degree, some college,
college degree and post-graduate degree), a cubic in potential experience (age minus
years of education minus five), a dummy for marital status, 6 regional dummies, 25 twodigit occupation dummies, and interaction between occupation and experience to capture
occupation-specific tenure profiles. We face a trade-off in the choice of covariates between
(1) the appropriate filtering out of the variation in hourly wages due to observable individual characteristics which are rewarded in the labor market, and (2) the risk of overfitting
the data. On average, these year-by-year regressions yield an R 2 between 0.42 and 0.45.
Next, we use the panel dimension of the data and identify individual-specific effects in
wages. Let εit be the residual of the first stage for individual i = 1, ...I in year t = 1, ..., T .
We limit the sample to those whose number of wage observations in the panel (Ni ) is at
P i
I
least ten and estimate ε̄i = N
t=1 εit /Ni for every individual. The vector {ε̄i }i=1 captures
the variation in fixed unobserved individual factors (e.g., innate ability, preference for

leisure) which affect wages. Let w̃it = exp (εit − ε̄i ) . For each year t, we then calculate

our indexes of residual inequality across workers on w̃it .

We report our results for the PSID in Figure 1. For comparison with the other data
sources, we comment on the values for the last part of the sample (the 1990-1996). The
12

ratio between mean wage and lowest wage residual from the basic Mincer regressions
is M m = 4.47, but the estimate is clearly very noisy. When the reservation wage is
estimated from the 1st and the 5th percentile of the wage distribution, the noise is much
reduced and we obtain, respectively, M p1 = 2.73 and M p5 = 2.08. The coefficient of
variation of the regression residuals is 0.50.
Controlling for individual effects drastically cuts the estimate of the mean-min ratios
by more than half. For the period 1990-1996, we estimate M m = 3.11, M p1 = 1.90, and
M p5 = 1.46. The coefficient of variation of the residuals net of individual effects falls
to 0.25.8 One should be cautious in interpreting these results, however. The estimated
fixed effects confound worker-specific characteristics with match- (or firm-) specific effects.
This is especially true for long-lived matches. Removing the estimated fixed effects may
therefore eliminate some of the variation in the data we want to explain.
To facilitate the comparison with the OES data, we also report ratios between the
mean and the 10th percentile. The M p10 on the residuals of the first-stage regression
equals 1.77, and the M p10 on the residuals net of individual-specific means is 1.32. The
corresponding statistics for the OES data all lie somewhere in between (see Table 1).

3.3

Census Data

Our third data source is the 5% Integrated Public Use Microdata Series (IPUMS) sample
of the 1990 United States Census. In Appendix C, we outline our sample selection. As for
the PSID, we run an OLS regression on the log of individual hourly wage to control for
the variation in wages due to observable characteristics which are rewarded in the labor
market. Among the covariates, we include gender dummies, 3 race dummies, 5 education
dummies, and a cubic in potential experience. We weight each observation by its Census
sample weight. The regression explains 31% of the total variation in log hourly wages. 9
Next, we group the (exponent of the) regression residuals by labor markets. Our
8

In passing, we note that Figure 1 is consistent with the views that residual wage dispersion has risen
significantly over the period, and that the rise in prices for unobserved innate characteristics is a key
component of this phenomenon.
9
This R2 is sizeably lower than the one for the PSID regression, and it is more in line with typical
Mincerian regressions. The reason is that in the PSID regression we included occupational dummies
and occupation-specific experience profiles, which have strong explanatory power. Moreover, the PSID
sample is smaller by a factor of 1,500 compared to the Census sample. See Appendices B and C.

13

first definition of labor market is the individual occupation. The Census allows us to
distinguish between 487 distinct occupations (variable OCC). Our second definition is the
combination of occupation and place of work (for the main job). Our indicator for place
of work is constructed as follows. Whenever possible, we use the 329 metropolitan areas
(PWMETRO). For rural areas we use a variable (PWPUMA) which defines a geographical
area by following the boundaries of groups of counties, or census-defined “places” which
contain up to 200,000 residents. Overall, we end up with 799 different geographical areas.
For each cell identified as a labor market, we calculate the mean-min ratio and we report
the median mean-min ratio across labor markets.
In the top panel of Figure 2, we show one example of the wage distribution for Janitors and Cleaners, excluding Maids and House Cleaners (code 453) in the Philadelphia
metropolitan area (code 616). These are the wage residuals of a regression that controls
for the demographics listed above, restricted to those working full time (35-45 hours per
week), full year (48-52 weeks per year) to reduce the role of measurement error. Overall,
we have 572 observations. As reported in the figure, the ratio between the mean and
the first percentile is 2.24. In the bottom panel, we display the distribution of M p1 ratios, obtained exactly as for the Philadelphia cell, for Janitors and Cleaners across all
geographical areas in the U.S. economy for which we have at least 50 individual wage
observations (131 areas). There are local labor markets displaying more and markets
displaying less residual dispersion than in Philadelphia, but the bottom line seems to be
that, even within a very unskilled occupation such as Janitors, and even after selecting
the sample to minimize the role of measurement error, wage differentials remain large:
the median M p1 ratio for Janitors across the U.S. is 2.20.
Table 2 reports our results in a number of formats. We use various estimators of
the mean-min ratio: M m, M p1, M p5, and M p10. We condition on cells with at least 50
observations and with at least 200. Larger cells usually display higher M m ratios both
because of higher unobserved heterogeneity that we did not capture in the first-stage
regression, and because they permit a less biased estimate of the low percentiles of the
wage distribution.

14

Table 2: Dispersion measures for hourly wage from the 1990 Census
Min. obs.
per cell
(1) Occupation

Number of
labor mkts

Ratio of mean wage to
1st pct.
5th pct.

CV

min.

487

4.54

2.83

2.13

1.83

0.47

10th pct.

(2) Occ./Geog. Area

(N≥50)
(N≥200)

13,246
2,321

2.94
3.85

2.66
2.88

2.04
2.13

1.76
1.82

0.41
0.44

(3) Occ./Geog. Area
Full time/Full year

(N≥50)
(N≥200)

7,195
1,117

2.74
3.58

2.49
2.68

1.92
1.98

1.66
1.71

0.35
0.37

(4) Occ./Geog. Area
Experience ≤ 10

(N≥50)
(N≥200)

2,810
406

2.64
3.33

2.46
2.57

1.92
1.97

1.68
1.73

0.40
0.44

(5) Occ./Geog. Area
Unskilled Occ.

(N≥50)
(N≥200)

1,152
191

2.51
2.95

2.37
2.57

1.98
2.08

1.77
1.83

0.45
0.49

(6) Occ./Geog. Area
Within cell regression

(N≥50)
(N≥200)

13,246
2,321

2.61
3.33

2.39
2.66

1.88
2.02

1.64
1.75

0.39
0.42

To get at the measurement error issue, we condition our analysis on full-time, full-year
workers who report weekly hours between 35 and 45 and annual weeks worked between
48 and 52. Going from row (2) to row (3) in Table 2, wage dispersion falls with respect
to the full sample, but it remains very high.10
To eliminate the importance of individual-specific differences in cumulated skills not
perfectly correlated with experience (accounted for in the first-stage regression), we condition on workers with less than 10 years of experience, Table 2 row (4), and on a set of
very low-skilled occupations, Table 2 row (5), where occupation and firm-specific skills
are arguably not very important.11 Once again, going from row (2) to either row (4) or
row (5) the findings are barely affected.
10

The coefficient of variation falls by 16%. For comparison, Bound and Krueger (Table 6, 1991) compare
matched Current Population Survey data to administrative Social Security payroll tax records and find
that the measurement error explains between 7% and 19% of the total standard deviation of log earnings.
Recall that the standard deviation of the logs has the same scale of the coefficient of variation.
11
This list includes, inter alia, Launderers and ironers, Crossing guards, Waiters and waitresses, Food
counter, fountain and related occupations, Janitors and cleaners, Elevator operators, Pest control occupations, and Baggage porters and bellhops.

15

Finally, we also run the first-stage regressions within each occupation/area cell, to
account for the fact that the role of demographic characteristics in wage determination
may be different across occupations. Going from row (2) to row (6), estimates of dispersion
fall by less than 10%.
We conclude that, except for estimates of M m based on the lowest observed wage
that are quite volatile, all the other statistics in Table 2 remain very robust to all these
controls and strongly support the view that residual wage dispersion is large.

3.4

Summary and interpretation

Our three independent data sources offer a fairly consistent view of the size of residual
wage dispersion within narrowly defined labor markets. If we focus our attention on the
M p5 estimate of the mean-min ratio, a review of our findings yields M p5 = 1.46 from
PSID. The PSID estimate could be upward-biased because of measurement error, but at
the same time the individual wage demeaning could filter out too much variation, including
variation due to “persistent luck” components that should be included in measures of
frictional dispersion. From the Census sample restricted to full-time, full-year workers
(where measurement error in hours should be negligible) we have estimated M p5 = 1.98.
Given the OES estimate of the M p10, and the fact that the other two data sets suggest
that M p5 are roughly 10%-15% larger, we conjecture that the M p5 in the OES data may
be around 1.67. An average across the three data sets yields 1.70, which we use as a
target in the rest of our analysis.
This appraisal of residual wage dispersion—based not on the minimum wage observed,
but on the 5th percentile, and hence quite conservative—is about 20 times larger than
that implied by the textbook models of Section 2. How can we resolve this enormous
discrepancy between the size of residual dispersion in the data and the model-implied
frictional dispersion?
One reaction to our findings is that the actual wage data hide large differentials due to
unobservable skills that we cannot fully control for with our given data. This is possible,
though one has to bear in mind that with our PSID data, we have controlled for unobserved heterogeneity that is fixed over time.12 Thus, for heterogeneity to explain our large
12

In an unreported set of regressions on PSID data, we also allowed fixed differences in (linear and

16

M m ratios, it would have to involve time-varying, unobserved skills, or preferences, which
influence remuneration in the labor market. Such heterogeneity cannot be ruled out a
priori, and it is important to continue incorporating more detailed worker information to
isolate this source in future work.13
One can also imagine the presence of firm-specific skills that are not perfectly correlated with experience. Estimates of returns to firm tenure vary widely. Topel (1991) estimates that 10 years of seniority increase log hourly wages by 25%. Altonji and Shakotko
(1987) report estimates below 7%. Recently, Altonji and Williams (2004) have reassessed
the evidence, concluding that returns to tenure over 10 years could be around 11%, most
of them occurring in the first 5 years of the employment spell.14 If we assume that average
tenure is roughly 4 years (see section 7), then this factor may account for at most 1/10th
of the wage difference between the average worker (with average tenure) and the lowest
paid worker (with zero tenure) in a given occupation/geographical area. Residual wage
dispersion remains very high.
In conclusion, we have made efforts along several fronts to isolate frictional wage
dispersion as well as possible, and our “residual” measure remains large—much larger
than what textbook models predict. If indeed this discrepancy is due to poor data and,
after all, unobservable worker characteristics (which vary over time) do account for the
bulk of our computed M m ratios, then one would hope that more careful future work will
reveal this. We do not, however, consider it satisfactory to simply stop here. Many hold
the prior that “markets are close to frictionless, because any significant wage differences for
identical workers would be exploited by profit-maximizing employers” but, after all, this
is a belief, and we must strive to update and test our beliefs, especially when preliminary
data analysis suggests that such priors may be off. Therefore, we also proceed on a parallel
quadratic) time trends across workers—possibly capturing differences in learning ability—and this did
not significantly change our findings either.
13
Incidentally, a large class of quantitative macroeconomic models of the Bewley-Huggett-Aiyagari style
implicitly takes this view, presuming idiosyncratic risks which are modelled as a stochastic process for
efficiency units of labor, priced in a frictionless labor market. An example of this approach in the search
literature is Ljungqvist and Sargent (1998).
14
Kambourov and Manovskii (2004) argue that the bulk of returns to specific human capital is
occupational-specific: 5 years of occupational tenure increase wages between 12% and 20%. They find
that once occupation is taken into account, returns to human capital specific to industry and employer become virtually zero. Hence, their findings would change the nature of wage differentials due to unobserved
heterogeneity specific skills, but not their magnitude.

17

front, which is to examine the consequences of the data at hand actually revealing large
true frictional wage dispersion: what, then, is so spectacularly wrong with textbook
theory? To find out, we first make some attempts to rescue the baseline model, without
changing its key features. Next, we investigate ways to augment the model so as to
improve its performance.

4
4.1

Five attempts to rescue the baseline model
Unemployment vs. wage dispersion

In defense of the model, one might argue that it is designed to explain unemployment, not
wage dispersion. This argument is flawed: in the search model, there is a tight link between
the existence of unemployment and the existence of wage dispersion. Unemployment
exists because of the option value of searching for better wage opportunities. Let us
reverse our logic and suppose that, given the amount of frictional wage dispersion observed
empirically, we want to predict unemployment duration, i.e., use equation (4) and the
empirical value of M m = 1.7 to compute the implied value for λ∗u . We would obtain
λ∗u = 0.011. In other words, a search model consistent with the amount of wage dispersion
in the data predicts an expected unemployment duration of 91 months, 35 times the
average duration in U.S. data.15

4.2

Alternative parameterizations

To calibrate the pair (λ∗u , σ), we used the UE and EU flow data. One could argue that
we should also incorporate flows in and out of the labor force. Taking this into account,
Shimer (2005a) reports the monthly separation rate to be 3.5%, and the monthly job
finding rate to be 61%. For the same values of r and ρ used in the baseline calibration,
we obtain M m = 1.038.16
15

In one of the most commonly used search setups, Mortensen and Pissarides (1994), unemployment
duration is not connected to wage dispersion, because in that model, unemployed workers always receive
the maximum wage upon employment: they never consider turning down a job offer. There, however,
the separation rate is determined by a reservation-wage strategy since there are wage shocks on the job.
Thus, that model instead links wage dispersion to the observed separation rate. We explore this link in
Section 6 below.
16
Since, under the new parameterization, both the job finding rate and the separation rate increase,
the effect on the M m ratio is negligible.

18

With respect to the interest rate r, we have used a standard value, but it is possible
that unemployed workers, especially the long-term unemployed, face a higher effective
interest rate if they wanted to borrow. Much less is known about ρ. To assess the
robustness of our conclusions to the choice of values for these two parameters, in Figure
3, we plot the pairs (r, ρ) which are consistent with an M m ratio of 1.7, together with
the region of “reasonable pairs” based on our prior. This region covers the area where
ρ ∈ (0, 1) and r is at most 27% per year.

The results are striking and suggest the baseline model cannot be rescued: even for

annual interest rates around 40% per year, one would need agents to value one month of
time away from the market the equivalent of minus three times the average monthly wage.
Positive net values of non-market time are consistent with the observed wage dispersion
only for interest rates beyond 1,350% per year.17

4.3

Ability differences

Wage inequality can, of course, naturally arise from ability differences. A very simple
illustration, extending the above search setting, goes as follows: there are two worker
types, and type 1 is more productive than type 2 by µ percent in the following sense:
F2 (w) ≡ F (w) and F1 (w) = F (w/(1 + µ)) for all w. Suppose also that the workers have
the same values for ρ, r, σ, and λu . Then

λu (1 − Fi (wi∗ ))
(w̄i − wi∗ )
(7)
r+σ
R
for each type i. It is easy to show that if w2∗ and w̄2 = w∗ wF (dw) solve (7) for i = 2,
wi∗ = ρw̄i +

2

then, using the assumed symmetry, w1∗ = (1 + µ)w2∗ implies F1 (w1∗ ) = F2 (w2∗ ) and w̄1 =
R
wF1 (dw) = (1 + µ)w̄2 , and therefore solves (7) for i = 1. Thus, in this model the
w∗
1

observed wage distribution for the type-1 worker is a µ-percent scaling up of that of type-2
workers, and w̄1 /w1∗ = w̄2 /w2∗ , which will be a small number given the above analysis.
17

A number of authors in the health and social behavioral sciences have argued that unemployment
can lead to stress-related illnesses due to financial insecurity or to a loss of self-esteem. This psychological
cost would imply an additional negative component in b. Economists have argued that this empirical
literature outside economics has not convincingly solved the serious endogeneity problem underlying
the relationship between employment and health status and even have, at times, reached the opposite
conclusion, i.e., that there is a positive association between time spent in non-market activity and health
status (e.g., Ruhm 2003).

19

However, for the population, w̄ = αw̄1 + (1 − α)w̄2 , where α is the share in population

of type 1. So the population-wide mean-min ratio, which the econometrician observes,
will equal
αw̄1 + (1 − α)w̄2
Mm =
=
w2∗



w̄1
α
+1−α
w̄2



w̄2
w̄2
= (1 + αµ) ∗ .
∗
w2
w2

Thus, if µ is large and α is not too small, we can obtain large population mean-min values,
even though mean-min values within groups are small. In particular, large enough ability
difference will generate any desired mean-min ratio for the overall population.
The model just described, however, is not one of frictional wage inequality, but rather
one of ability-driven wage differences. Moreover, our PSID-based empirical analysis eliminates individual-specific effects, and we still find very large values for the mean-min ratio.
A related model could also be constructed assuming that the types are random; perhaps
they follow a Markov chain, depicting the evolution of human capital on (and perhaps
also off) the job. Similar settings have been used by Ljungqvist and Sargent (1998) and
Kambourov and Manovskii (2004). One can use arguments along the lines of those above
to demonstrate that such settings also allow larger wage inequality, but only due to the
skill differences between types being large: for a given type, wage inequality is still small,
and thus large frictional wage inequality—as we view it—does not result here either.

4.4

Targeting European data

In Section 2.4 we have indicated that the short duration of unemployment in the U.S.
reveals that frictional wage dispersion must be small. It is well known that in Europe
unemployment spells last much longer, on average. For example, Machin and Manning
(1999, Table 1) document that in 1995 the proportion of workers unemployed for more
than 12 months was less than 10% in the U.S., but over 40% in France, Germany, Greece,
Italy, Portugal, Spain, and the United Kingdom. Does this observation give hope to
the model to be more successful in explaining European wage dispersion? To answer this
question, recall that in a stationary equilibrium, unemployment is u = σ/ (σ + λ∗u ) . Using
this formula in expression (4) allows one to rewrite the M m ratio as
Mm =

σ 1−u
r+σ u
σ 1−u
r+σ u

+1
+ρ

20

≈

1−u
u
1−u
u

+1
,
+ρ

where the “approximately equal” sign is obtained by setting r = 0, a step justified by the
fact that r is second order compared to the other parameters in that expression. Setting
the unemployment rate to 10%, with ρ = 0.4, one obtains M m = 1.076. The reason
for the small improvement is that in European data both unemployment duration and
employment spells are much longer than in the U.S. labor market. While the first fact is
consistent with larger equilibrium wage dispersion, the second implies that unemployed
workers are more selective and set their reservation wage high, which reduces frictional
wage dispersion.
For the argument to be fully convincing, one would need to document the extent of
residual wage dispersion, as well as the magnitude of the value of non market time, in
European countries. A systematic investigation goes beyond the scope of this paper,
but conventional wisdom would suggest that while inequality is lower in Europe, social
benefits for the unemployed are much more generous.18

4.5

Implications for other dispersion measures

Admittedly, the mean-min ratio is not a common index of dispersion. One may argue
that even though the model fares poorly in terms of this statistic, its performance along
more common measures of dispersion, such as the coefficient of variation (cv), could be
satisfactory. To answer this question, we need to make further assumptions about the
equilibrium wage distribution. Given a parametric specification for this distribution, we
can map predicted mean-min ratios into cv’s, i.e., we can determine the value of the cv
corresponding to a certain value for the mean-min ratio.
The Gamma distribution (see Mood et al., 1974, for a standard reference) is a convenient choice because it is a flexible parametric family and has certain properties that are
useful in our application. Let wages w be distributed according to the density


∗

w−w ∗ γ−1
exp − w−w
∗
α
α
g (w; w , α, γ) =
,
αΓ (γ)

(8)

with γ, α > 0, and with Γ (γ) denoting the Gamma function. The value for w ∗ is the
location parameter and determines the lowest wage observation, α is the scale parameter
18

For example, Hansen (1998) calculates benefits replacement ratios with respect to the average wage
up to 75% in some European countries.

21

determining how spread out the density is on its domain, whereas γ is the parameter that
determines the shape of the function (e.g., exponentially declining, bell-shaped, etc.).19
The mean and standard deviation of a random variable distributed with g (w; w ∗ , α, γ)
√
are given by, respectively, m̄ = w ∗ + αγ and sd = α γ. Recalling that M m = m̄/w ∗ , it is
easy to obtain a relation between the coefficient of variation cv and the mean-min ratio,
and this relation only depends on the shape parameter γ:


1 Mm − 1
cv = √
.
γ
Mm

(9)

The empirical analysis of section (3) suggest that cv = 0.30 and M m = 1.7 are
reasonably conservative estimates for the coefficient of variation and the mean-min ratio
of the wage distribution within labor markets.20 From equation (9), this implies γ = 1.88.
A search model generating a mean-min ratio of 1.036, under the Gamma wage offer
distribution assumption, would generate a coefficient of variation for hourly wages of
0.025, i.e., 1/12th of the coefficient of variation in the wage data. We conclude that the
failure of the model generalizes to more common measures of dispersion.

4.6

Non-pecuniary job attributes

In many jobs, wages are only one component of total compensation. In a search model
where a job offer is a bundle of a monetary component and a non-pecuniary component,
short unemployment duration can coexist with large wage dispersion, as long as nonpecuniary job attributes are negatively correlated with wages so that the dispersion of
total job values is indeed small.
This hypothesis, which combines the theory of compensating differentials with search
theory, does not show too much promise. First, it is well known that certain key nonmonetary benefits such as health insurance tend to be positively correlated with the wage,
e.g., through firm size.21 Second, illness or injury risks are very occupation-specific and our
measures of frictional wage dispersion are within-occupation indexes. Third, differences
19

The Gamma family is very flexible: it includes the Weibull (hence, the exponential) distribution for
γ = 1 and the lognormal, in the limit as γ → ∞.
20
This value for cv is an average between the PSID estimate (0.25) and the estimate on Census sample
of full-time, full-year workers (0.35).
21
For example, the mean wage in jobs offering health insurance coverage is 15%-20% higher than in
those not offering it; see Dey and Flinn (2006).

22

in work shifts and part-time penalties are quantitatively small. Kostiuk (1990) shows
that genuine compensating differentials between day and night shifts can explain at most
9% of wage gaps. Manning and Petrongolo (2005) calculate that part time penalties for
observationally similar workers are around 3%.
We now examine three extensions of the baseline search model that go, qualitatively,
in the direction of producing more frictional wage dispersion: risk aversion, stochastic
wages during the employment relationship, and on-the-job search.

5

Risk aversion

Risk-averse workers particularly dislike states with low consumption, like unemployment.
Compared to risk-neutral workers, ceteris paribus, they lower their reservation wage in
order to exit unemployment rapidly, thus allowing M m to increase.
Let u (c) be the utility of consumption, with u0 > 0, and u00 < 0. To make progress
analytically, we assume workers have no access to storage, i.e., c = w when employed,
and c = b when unemployed. It is clear that this model will give an upper bound for the
role of risk aversion: with any access to storage, self-insurance or borrowing, agents can
better smooth consumption, thus becoming effectively less risk-averse.
To obtain the reservation wage equation with risk aversion, observe that in the Bellman
equations for the value of employment and unemployment, the monetary flow values of
work and leisure are simply replaced by their corresponding utility values. The reservation
wage equation (3) then becomes
u (w ∗ ) = u (ρw̄) +

λ∗u
[E (u (w)) − u (w ∗ )] .
r+σ

(10)

A second-order Taylor expansion of u (w) around the conditional mean w̄ yields
1
u (w) ' u (w̄) + u0 (w̄) (w − w̄) + u00 (w̄) (w − w̄)2 .
2
Take the conditional expectation of both sides of the above equation and arrive at
1
E (u (w)) ' u (w̄) + u00 (w̄) var (w) .
2

(11)

Let u (w) belong to the CRRA family, with θ representing the coefficient of relative risk
23

aversion. Then, using (11) in (10) , and rearranging, we obtain
" λ∗
# 1


1
2
1−θ θ−1
u
1
+
(θ
−
1)
θcv
(w)
+
ρ
w̄
2
M m ≡ ∗ ' r+σ
.
λ∗u
w
+1
r+σ

(12)

It is immediate to see that, for θ = 0, the risk-neutrality case, the expression above equals
that in equation (4) .
To assess the quantitative role of risk aversion, we use the same parameterization of the
risk-neutral case, and based on the evidence provided in section 3, we set cv (w) = 0.30.
Figure 4 plots the pairs of (ρ, θ) consistent with M m = 1.70. For θ = 8, the model
can match the data. Recall, however, the upper-bound nature of our experiment: in
fact, plausibly calibrated models of risk-averse individuals who have access to a risk-free
bond for saving and borrowing are much closer to full insurance than to autarky (see,
e.g., Aiyagari, 1994). For example, it is well known that as r → 0, the bond economy

converges to complete markets (Levine and Zame, 2002).

6

Wage shocks during employment

We now extend the basic search model by allowing wages to fluctuate stochastically along
the employment spell.22 Unemployed workers draw wage offers from the distribution F (w)
at rate λu , but now these wage offers are not permanent. At rate δ, the wage changes,
and the worker draws again from F (w). Draws are i.i.d. over time. Separations are now
endogenous and will occur at rate σ ∗ ≡ δF (w ∗ ) , where w ∗ is the reservation wage.

The reason why this generalization can potentially generate a larger M m ratio is that

the particular value drawn from F (w) by an unemployed worker is not a good predictor
of the continuation value of employment, if the wage is very volatile. Unemployed workers
will therefore be more willing to accept initially low wage offers, which reduces w ∗ and
increases dispersion.
The Bellman equations for employment and unemployment are, respectively,
Z wmax
rW (w) = w + δ
[W (z) − W (w)] dF (z) − δF (w ∗ ) [W (w) − U ]
∗
w
Z wmax
rU = b + λu
[W (z) − U ] dF (z) .
w∗

22

The Technical Appendix, Hornstein et al. (2006), contains the details of all the derivations in this
and the next sections.

24

With respect to equation (1) , the value of employment is modified in two ways. First,
the endogenous separation rate is now δF (w ∗ ) . Second, there is a surplus value from
accepting a job at wage w which is given by the second term on the right-hand side.
Exploiting the definition of reservation wage W (w ∗ ) = U , integrating by parts, and using
W 0 (w) = 1/ (r + δ), we arrive at
λu − δ
w =b+
r+δ
∗

Z

w max
w∗

[1 − F (z)] dz.

Now, using the definition of the conditional mean wage w̄, we obtain
w∗ = b +

(λu − δ) [1 − F (w ∗ )]
(w̄ − w ∗ ) .
r+δ

Therefore, imposing b = ρw̄, and rearranging, we can write the M m ratio in this model
as
w̄
Mm = ∗ =
w

λ∗u −δ+σ ∗
r+δ
λ∗u −δ+σ ∗
r+δ

+1
+ρ

.

(13)

As δ → 0, the M m ratio converges to equation (4) with σ ∗ = 0, since without any shock
during employment every job lasts forever. As δ → λu , unemployed workers accept every

offer above b since being on the job has an option value equal to being unemployed.

The parameter δ maps into the degree of persistence of the wage process during employment. In particular, in a discrete time model where δ ∈ (0, 1) the autocorrelation

coefficient of the wage process is 1 − δ.23 Individual panel data suggest that residual

wages are very persistent, indeed near a random walk, so plausible values of δ are close
to zero.

We repeat the exercise in Section 4 on the (r, ρ) pair. Given values for (λ∗u , σ ∗ , r) one
can search for the values of (δ, ρ) that generate M m ratios of the observed magnitude.
Figure 5 reports the results. Once again, the model is very far from the data for reasonable
values of ρ and of the degree of wage persistence of wage shocks. For example, for δ = 0.1
(corresponding to an annual autocorrelation coefficient of 0.9) the model requires ρ = −13.
Only for virtually i.i.d. wage shocks (δ ≈ 1) would the model succeed.

The setup of Mortensen and Pissarides (1994) is similar to that described here, with

one difference: upon employment, all workers start with the highest wage, w max , and thus
23

It is easily seen that a discrete time version of this model leads exactly to equation (13) .

25

they only sample from F (w) while employed. This model, however, does not offer higher
mean-min ratios: the resulting M m ratio can be shown to be strictly bounded above by
that in equation (13).

7

On-the-job search

Allowing on-the-job search goes, qualitatively, in the right direction for reasons similar to
the model with stochastic wages. If the arrival rate of offers on the job is high, workers are
willing to leave the ranks of unemployment quickly since they do not entirely forego the
option value of search. This property breaks the link between duration of unemployment
and wage dispersion that dooms the baseline model. However, for a proper test, we
now need to explore the implied labor-market flows, which now include employment-toemployment transitions.
We generalize the model of Section 2 and turn it into the canonical job ladder model
outlined by Burdett (1978). A worker employed with wage ŵ encounters new job opportunities w at rate λw . These opportunities are drawn from the wage offer distribution
F (w) and they are accepted if w > ŵ.
A large class of equilibrium wage posting models, starting from the seminal work by
Burdett and Mortensen (1998), derives the optimal wage policy of the firms and the
implied equilibrium wage offer distribution as a function of structural parameters. It is
not necessary, at any point in our derivations, to specify what F (w) looks like. Our
expression for M m will hold in any equilibrium wage posting model that satisfies the
following two assumptions. First, employed workers accept any wage offer above their
current wage; second, every worker (employed or unemployed) faces the same wage offer
distribution. Moreover, without loss of generality, to simplify the algebra, we posit that
no firm would offer a wage below the reservation wage w ∗ ; thus, F (w ∗ ) = 0.
The flow values of employment and unemployment are
Z wmax
rW (w) = w + λw
[W (z) − W (w)] dF (z) − σ [W (w) − U ]
w
Z wmax
rU = b + λu
[W (z) − U ] dF (z) ,
w∗

26

and the reservation wage equation becomes
Z wmax
∗
w = b + (λu − λw )
w∗

1 − F (z)
dz.
r + σ + λw [1 − F (z)]

(14)

It is easy to see that, in steady state, the cross-sectional wage distribution among employed
workers is
G (w) =

σF (w)
.
σ + λw [1 − F (w)]

(15)

Using this relation between G (w) and F (w) in the reservation wage equation (14), and
exploiting the fact that the average wage is
Z wmax
∗
w̄ = w +
[1 − G(z)] dz,

(16)

w∗

we arrive at the new expression for the M m ratio,
Mm ≈

λu −λw
r+σ+λw
λu −λw
r+σ+λw

+1
+ρ

,

(17)

in the model with on-the-job search.24
Note that, if the search technology is the same in both employment states and λw =
λu , the reservation wage will be equal to b, since searching when unemployed gives no
advantage in terms of arrival rate of new job offers. Indeed, for λw > λu , unemployed
workers optimally accept jobs below the flow value of non-market time b in order to access
the better search technology available during employment.
The crucial new parameter of this model is the arrival rate of offers on the job λw . To
pin down λw , note that average job tenure in the model is given by


Z wmax
dG (w)
σ + λw /2
1 1
τ =
=
∈
,
.
σ + λw [1 − F (w)]
σ (σ + λw )
2σ σ
w∗

(18)

Since we set the monthly separation rate σ to 0.02, the model can only generate average
tenures between 25 and 50 months. Based on the CPS Tenure Supplement, the BLS
24

The “approximately equal” sign originates from one step of the derivation where we have set
r+σ
σ
≈
,
r + σ + λw [1 − F (z)]
σ + λw [1 − F (z)]

a valid approximation since, for plausible calibrations, r is negligible compared to σ.

27

(2006, Table 1) reports that median job tenure (with current employer) for workers 16
years old and over, from 1983-2004, was 3.64 years, or 43.7 months.25
An alternative way to restrict the choice of λw is to compute the average separation
rate χ implied by the model, which is given by
Z
σ (λw + σ) log
χ = σ + λw
[1 − F (w)] dG (w) =
λw
w∗

σ+λw
σ




,

(19)

where the first equality states that the separation rate equals the EU flow rate (σ) plus
the EE flow rate (the integral). Recent studies (Fallick and Fleischman, 2001; Nagypal,
2005) estimate the data counterpart of χ to be around 4%.26
In what follows, we ask whether the on-the-job search model can generate the observed
M m ratio while, at the same time, being consistent with tenure lengths higher than 43.7
months or, alternatively, a monthly average separation rate of 4%. Since the M m ratio is
increasing in λw , it should be clear that the model will have a good chance to generate
a large M m ratio for low job tenures/high separation rates (which imply high values of
λw ).
Figure 6 illustrates that, once λw is chosen so that the model can generate transitions
as in the U.S. data, the model will produce high M m ratios only for negative values of
ρ. Although the model is still far from a success, it is clear that the introduction of
on-the-job search represents a significant quantitative improvement. Compare Figure 3
with Figure 6. In the former graph, one needs ρ = −5 to reproduce M m = 1.70, whereas

in the latter setting ρ = −0.5 allows the model to roughly match both the separation and

the wage dispersion facts.27 However, the independent evidence on average job tenure
seems to put more strain on the model: wage dispersion and average tenure are jointly
replicated only for values of ρ around -4.
This result contains an important lesson. One may be tempted to think that, given
the relationship between F (w) and G (w) in equation (15), it suffices to assume enough

dispersion in firms’ productivities, and hence in the wage offer distribution F (w), to
25

For two reasons, this number is a lower bound as the empirical counterpart of τ . First, the implied
average job tenure would be longer, since tenure distributions are notoriously skewed to the right. Second,
the BLS data refer to the truncated tenure distribution. A higher estimate for average tenure strengthens
our argument.
26
There is no inconsistency between average tenure exceeding 44 months and an average separation
rate of 4%, since the employment hazard is not constant.
27
For ρ = 0.4, the model calibrated to match the aggregate separation rate gives rise to M m = 1.10.

28

generate large wage differentials among employed workers. Equation (14), instead, tells
us that a high variation in F (w) is consistent with a low reservation wage, and thus a
high M m ratio, only for negative values of b, or high values of r.
Finally, there exist versions of on-the-job search models which have much weaker
implications for workers’ flows, because it is possible that many outside offers to workers
do not result in job-to-job flows, but rather in a matching of the outside offer by the
current employer.28 While this is common in the economics profession, however, it is
arguably (as emphasized and discussed in some detail in Mortensen, 2005) more rare in
the broader labor market.
Arguably, models with on-the-job search today represent the most vibrant research
area within search theory. Next, we analyze two recent theoretical developments of this
class of models and evaluate their potential to generate frictional wage dispersion.

7.1

Endogenous search effort

Recently, Christensen et al. (2005, CLMNW therafter) have generalized Burdett’s on-thejob search model by introducing an endogenously chosen level of search intensity that
determines the contact rate λ.29 The model assumes full symmetry between employment
states in the sense that the search effort cost c (λ)—a convex function of the offer arrival
rate chosen by the worker—is the same for unemployed and employed workers. Given
that this cost function is independent of the income earned, whereas the return to search
is clearly declining in such income, the optimal policy λ (w) is decreasing in the wage w
for employed workers.
In this model, the reservation wage w ∗ equals the flow value of leisure b, and thus
M m = 1/ρ. The model, therefore, has the same potential to generate sizeable frictional
wage dispersion as the standard on-the-job search model with λu = λw . The advantage is
that, while this latter parameterization induces implausibly high workers’ flows, CLMNW
show that their model, estimated on employer-employee matched Danish data, can replicate the empirical separation rate as a. function of wage, χ (w) = σ + λ (w) [1 − F (w)] ,
as well.
28
29

For a model of this sort, see, e.g., Postel-Vinay and Robin (2002).
See also the recent work by Lise (2006).

29

This extension of the basic job ladder model appears, at first sight, a quick and
reasonable fix to the fundamental shortcoming we discuss throughout the paper. However,
a more careful look reveals that this is not the case, for two reasons.
First, under this symmetric specification for the disutility of search, the model has
the implication that unemployed workers and workers employed at the reservation wage
make the same optimal search effort choice, i.e., the hazard rate from unemployment
must equal the job-to-job flow rate at w ∗ . CLMNW (Table 2) estimate the latter to be
0.07 at the monthly frequency, with an extremely tight standard error due to their large
sample size. They do not, however, use data on worker flows out of unemployment and do
not test this implication. Rosholm and Svarer (2004) document that, for Denmark, the
monthly exit rate from unemployment is 0.11, so one would strongly reject the hypothesis
that the job finding rate equals the job-to-job transition rate at the lowest wage—a key
prediction of this model.30 In particular, for the model to be consistent with this aspect of
the data, the symmetry assumption must be abandoned in favor of a specification where
unemployed workers (i) face extra costs of being unemployed (so they have the incentive
to exit unemployment more quickly), which is exactly the type of problem we encountered
in all the models studied so far, or (ii) they search more cheaply than employed workers.31
In the latter case, though, the reservation wage becomes higher than b, again making it
harder for the model to generate wage dispersion.
The second reason why the CLMNW model does not provide an entirely satisfactory
solution is related to one of the key observations of our paper: to generate sizeable wage
dispersion, the search model needs a large and implausible disutility of unemployment.
Recall that in the CLMNW model, the disutility flow from being jobless is b − c (λ∗ ) .
Therefore, one should investigate how large the search cost component c (λ∗ ) is once the

model is calibrated.
Through a number of manipulations of the FONC for search effort, it is possible to
derive a bound on the marginal search cost as a discounted value of the expected gain
30

This rejection is for the Danish data. It remains to be studied whether U.S. labor market data, on
which we based all our empirical analysis, would be more favorable to the model. At the moment, data
constraints prevent one from performing such exercise.
31
For example, one could assume that searching for a job takes time out of work or leisure; then the
effective search cost is lower for the unemployed, and is increasing in the wage for employed workers.

30

from search:

w̄ − w ∗
.
r + σ + λ∗
Assuming an iso-elastic specification for the cost function, as done in CLMNW, i.e.,
c0 (λ∗ ) ≥

c(λ) = λγ , and using the fact that in the model M m = 1/ρ we have that
c(λ∗ )
1 λ∗ (1 − ρ)
≥
,
w̄
γ r + σ + λ∗
which establishes a lower bound for the search cost of the unemployed in terms of the
average wage. Using the baseline parameterization of the paper (λ∗ = 0.39, r = 0.004, σ =
0.02, ρ = 0.4) together with γ = 2 based on the elasticity estimated by CLMNW, one
obtains that the model requires a search cost for the unemployed that is at least 28% of
the average wage paid in the economy. This magnitude, once again, seems very large: it
implies a net utility flow from unemployment b − c (λ∗ ), of at most 12% of the average
wage.

7.2

Reallocation shocks

Micro data indicate that a non-negligible fraction of job-to-job movers receive a wage
cut. In line with this observation, some recent contributions (e.g., Jolivet et al., 2006)
advocate that on-the-job search models, to be successful, must introduce “reallocation
shocks”, i.e., a situation where employed workers receive a job offer with an associated
wage drawn from F (w) that cannot be rejected. In other words, under the scenario of
a reallocation shock the outside option of a worker is not keeping the current job (and
the current wage), but becoming unemployed which is always dominated by accepting
any new job offered. This category of employment to employment (EE) transitions may
include, for example, search activity during a notice period, or a geographical move for
non-pecuniary motives.
If we let φ be the arrival rate of such an event, it is easy to see that the mean-min
ratio in the model becomes
Mm ≈

λu −λw −φ
r+σ+λw +φ
λu −λw −φ
r+σ+λw +φ

+1
+ρ

,

(20)

a magnitude that is increasing in φ.32 Ceteris paribus, the reallocation shock shortens
the life of a job and makes unemployed workers less picky, and thus they reduce their
32

The approximately equal sign holds here for the same reason as in equation (17) .

31

reservation wage, which helps raising frictional wage dispersion. Moreover, it is straightforward to derive that the average separation rate in this model is exactly as in (19) with
σ replaced by σ + φ.
Even though this extension goes in the right direction, quantitatively it falls short of
succeeding because, as in the standard on-the-job search model, the model with forced
job-to-job mobility cannot reconcile the observed wage dispersion with labor turnover
data. To replicate M m = 1.70 with positive values of ρ, the separation rate would have
to be implausibly high.
A variant of the reallocation shock story which shows more promise is suggested by
Nagypal (2006). In her model, employed workers move within the wage distribution in
two ways: through job-to-job movements following on-the-job search with contact rate
λw , and through shocks occurring at rate φ that change the wage during an employment
relationship without inducing a separation: at rate φ, workers make another wage draw
from F (w) that is uncorrelated to their current wage and that has to be accepted, or else
separation takes place. Effectively, this model is a combination of the canonical on-the-job
search model and the model with stochastic wages we presented in Section 6.
The mean-min ratio in this model has exactly the same form as in (20) , but now
raising φ does translate into a wage change without increasing the separation rate. To
gauge the quantitative implications of this version of the on-the-job search model, we
perform the following exercise: keeping the values for (σ, ρ) unchanged relative to our
previous analysis, we set the pair (λw , φ) to match the aggregate separation rate (4%)
and M m = 1.70. Then, we calculate the average arrival rate κ of a wage cut among
employed workers in the model. It is given by the formula



σ+φ+λw
Z
(σ
+
φ)
(λ
+
σ
+
φ)
log
w
σ+φ
σ+φ
.
κ = φ F (w) dG (w) = φ 1 +
−
2
λw
λw

The model implies that 9.5% of the workforce is subject to a wage cut every month, i.e.,
70% of the stock of employees experience at least a salary cut from month to month, in
any given year.33 This extreme implication is similar to our finding of Section 6, where
33

The calibration yields a value for the Poisson arrival rate κ of 10% which implies a monthly probability
of receiving a wage cut of 1 − exp(−κ)=9.5%.

32

we concluded that the model with wage shocks (but without on-the-job search) generates
individual wage profiles that are too volatile.

8

The literature on structural estimation of search
models

Since the pioneering effort of Flinn and Heckman (1983), a rather vast literature on
structural estimation of search models has developed (see Eckstein and van den Berg,
2005, for a recent survey). We view these contributions as having generated many valuable
insights. From our perspective here, it is important to comment on how the literature has
dealt with the baseline model’s apparent inability to generate frictional wage dispersion.
We summarize our reading of the literature as follows: it has either (1) simply “accepted”
implausible parameter estimates for the value of non-market time and the interest rate,
or (2) introduced unobserved skill heterogeneity and measurement error that soak up the
large wage residuals in the data. We now proceed to discussing a number of selected
papers in more detail.
In one of the first attempts at a full structural estimation, Eckstein and Wolpin (1990)
estimate the Albrecht and Axell (1984) search model with worker heterogeneity in the
value of non-market productivity and conclude that their model cannot generate any significant wage dispersion, and that almost all of the observed wage dispersion is explained
through measurement error. Eckstein and Wolpin (1995) reach a far better match between
model and data, by introducing a five-point distribution of unobserved worker heterogeneity within each race/education group (8 groups in total). In spite of such heterogeneity,
however, for many of the groups the estimates of b remain extremely small or negative
(see their Table 7, page 284). In this work, thus, wage dispersion is for the most part
accounted for by heterogeneity in observable and unobservable characteristics. In our
view, this procedure, which is quite frequent in this literature, can perhaps be categorized
more as part of the human-capital theory of wages: it does not deliver large frictional
wage dispersion.34
34

There is also a theoretical argument against models of frictional wage dispersion based on heterogeneity. Gaumont et al. (2006) demonstrate that wage dispersion in an Albrecht and Axell (1984) model
with worker heterogeneity in the value of leisure is fragile. As soon as an arbitrarily small search cost
is introduced, the equilibrium unravels and we are back to the “Diamond paradox”, i.e., a unique wage

33

Negative estimates of the net value of non market time are quite common. The survey
paper by Bunzel et al. (2001) estimates several models with on the job search on Danish
data. When firms are assumed to be homogeneous, the point estimate for ρ is −2. With
heterogeneity in firms’ productivity it increases just about to ρ = 0. Only the model with

measurement error produces a large and positive estimate of ρ.35 Flinn (2006) estimates
a Pissarides-style matching model of the labor market, without on-the-job search, to
evaluate the impact of the minimum wage on employment and welfare. In his model, as
is typical in estimation exercises, the pair (ρ, r) is not separately identified. Setting r to
5% annually in his model implies roughly ρ = −4.36

Another example of extreme parameter estimates that can be found in Postel-Vinay

and Robin (2002). Under risk neutrality, their estimates of the discount rate r always
exceed 30% per year in every occupational group, reaching 55% for unskilled workers,
where they find no role for unobserved heterogeneity. Risk aversion (in the form of log
utility, without storage) does not help: the estimates of r decline by just 3 percentage
points on average. Recall, from Figure 3, that a negative value for ρ and a high value for
r are two sides of the same coin.
Whenever authors have restricted (r, ρ) to plausible values ex-ante, not surprisingly,
they end up with finding that frictions play a minor role. For example, Van den Berg
and Ridder (1998) estimate the Burdett-Mortensen model on Dutch data allowing for
measurement error and observed workers’ heterogeneity (58 groups defined by education,
age and occupation). They set r to zero and b to equal the average unemployment benefit
for each group, i.e., roughly 60% of the average wage. They conclude that observed
heterogeneity and measurement error account for over 80% of the empirical wage variation.
Moscarini (2003) develops an equilibrium search model where workers learn about their
match values, based on Jovanovic (1979). When the model is calibrated, r is set to 5%
annually and ρ to 0.6. His model generates a M m ratio of just 1.16 (Moscarini, 2005,
Table 2).
One may note that a number of papers in the literature do claim that the (on-thearising in equilibrium.
35
These values for ρ are obtained from Bunzel et al. (2001) by dividing the estimates of b for the entire
sample, in Tables II and V, by the average wage from Table I.
36
Calculations are available upon request.

34

job search) model is successful in simultaneously matching the wage distribution and
labor market transition data (see, e.g., Bontemps et al., 2000, and Jolivet et al., 2005).
These claims of success, clearly, need to be properly reinterpreted in light of our findings.
The typical strategy in these papers is, first, to estimate the wage distribution G(w)
non-parametrically without using the search model. Next, the model is used to predict
the wage-offer distribution F (w) through a steady-state relationship like (15), where the
structural parameters of the relationship (σ, λu , λw ) are estimated by matching transition
data. Success is then expressed as a good fit (in some specific metric). However, the
exercise is not a full success because it neglects the implications of the joint estimates of
F (w) and of the transition parameters for the relative value of leisure ρ (or, similarly, for
the interest rate r). The key additional “test” that we are advocating would thus entail
using the estimated F (w) in the reservation-wage equation (14) and, given an estimate
of w ∗ (for example, the bottom-percentile wage observed), backing out the implied value
for ρ. In light of our results, we maintain that ρ would be negative, or in any case
unreasonably low.
In conclusion, while we are definitely of the view that there is an important amount of
progress in this empirical literature, the success is really only partial: the literature has
not yet managed to match the data with plausible parameter values. In short, important
parameters such as b and r (the value of leisure and the discount rate, respectively) are
considered free parameters, and estimates that are far from what we view as reasonable
are thus “accepted”. Alternatively, unobserved heterogeneity or measurement error must
be introduced, also with amounts that are free parameters, in order to match the data.
Our contribution in this context is thus to point to a specific prediction—which is quite
sharp in most search models and which has not been noted before—that arguably is
somewhat of an Achilles heel for this class of models: the mean-min wage ratio is too
low. Marked improvements in model performance may thus benefit from further analysis
of the determinants of this measure of wage dispersion.

9

Conclusions

Search theory maintains that similar workers looking for jobs in the same labor market
may end up earning different wages according to their luck in the matching process. This
35

paper has proposed a simple strategy for evaluating the quantitative ability of search
models to generate frictional wage dispersion. The strategy is based on a particular
measure of wage differentials, the mean-min ratio, that arises very naturally, in closed
form, from the reservation wage equation, the cornerstone of a vast class of search models.
We have demonstrated that, when plausibly calibrated, the textbook search and
matching model implies that frictions play virtually no role in the labor market: the
mean-min ratio is less than 4%. We have made several attempts to save the model. The
most promising extension is the one with on-the-job search. However, within the simplest
version of the job ladder model, it is hard to produce large wage dispersion while, at
the same time, being consistent with the observed labor market transition data. Other
attempts seem far less promising. Risk aversion can be successful only if one believes that
self insurance is unimportant, but a decade of quantitative investigations of Bewley-type
models speaks against this possibility. Volatility in wages during employment can be successful only if one believes that wages are as volatile during an employment spell as in
the cross-section.
The data we have analyzed tell a striking story: residual wage dispersion among
observationally similar workers in narrowly defined labor markets (by occupation and geographical area) is twenty times larger than what predicted by the model. This leaves
two possible, but radically different, conclusions on the table. First, residual wage inequality in the data is attributable to unobserved (and probably time-varying) skills that
are remunerated in a near frictionless labor market; put differently, the role of frictions is
actually small in the data as well. This conclusion is viewed as plausible by many, but it
does call for more careful testing. In particular, one must look for more individual-specific
information (both time-invariant, like test scores or attitudes towards leisure and work,
and time-varying, like significant events altering the value of leisure, e.g., need for child or
health care in individuals’ lives) in order to reduce the current residual dispersion. One
may also be able to look more deeply at implications for on-the-job wage variability, which
should be quite large if indeed individual-specific and time-varying skill heterogeneity accounts for the wage dispersion. Alternatively, the second possible conclusion which puts
more faith in the measures of frictional wage dispersion reported here, is that our basic
search theory needs further development. Distinguishing between these two conclusions

36

should be a central task in macroeconomics and labor economics: the relative roles of
skills and luck in the labor market lie at the heart of policy design.
Finally, an implicit but interesting implication of the present work is closely connected
to the recent debate on whether the matching model is able to generate enough time-series
fluctuations in aggregate unemployment and vacancies; see Shimer (2005b), Hagedorn and
Manovskii (2006), and Hall (2005). There, it is pointed out that the matching model, at
least if one is to avoid the incorporation of significant real-wage rigidity, requires a very
high benefit of non-market time (denoted ρ above, expressing this benefit as a fraction of
the average wage) in order to produce sharp movements in vacancy and unemployment
rates. But, as we showed here, the higher is the value of ρ, the more difficult it is to explain
wages cross-sectionally. More specifically, the time-series facts necessitate a value of ρ close
to 1 to explain the data, and our cross-sectional facts demand a value significantly below
0. We believe that it is important in future work to keep both “puzzles” in mind while
developing and using search-matching theories of the labor market.

37

10

Appendix

A: the occupational employment statistics program
The Occupational Employment Statistics (OES) program collects data on employees in approximately 200,000 non-farm establishments to produce employment and wage estimates for
821 occupations classified based on the Standard Occupational Classification (SOC).
Since November 2003, the program samples 200,000 establishments semi-annually. Before
then, it sampled 400,000 once a year. The OES survey is designed to produce occupational
wage and employment estimates using six panels (3 years) of data. The BLS Employment Cost
Index is used to adjust survey data from prior panels before combining them with the current
panel’s data. The full six-panel sample of 1.2 million establishments allows the construction
of occupational estimates at detailed levels of geography and industry. Estimates based on
geographic areas are available at the National, State, and Metropolitan Area levels. Industry
classifications correspond to 3, 4, and 5-digit North American Industry Classification System
(NAICS) industry groups.
The OES survey form sent to establishments defines wages as straight-time, gross pay, exclusive of premium pay. Base rate, cost-of-living allowances, guaranteed pay, hazardous-duty
pay, incentive pay including commissions and production bonuses, tips, and on-call pay are included. Excluded are back pay, jury duty pay, overtime pay, severance pay, shift differentials,
non-production bonuses, employer cost for supplementary benefits, and tuition reimbursements.
The OES survey groups wages in 12 discrete intervals. In November 2004, the lowest interval
was “Under $6.75” and the highest was “$70 and over”. Mean hourly wage rate for an occupation
equals total wages that all workers in the occupation earn in an hour divided by the total
employment of the occupation. The same concept applies to more disaggregated levels such as
occupations within metropolitan areas or industries. The mean and percentiles for an occupation
are calculated by uniformly distributing the workers inside each wage interval, ranking the
workers from lowest paid to highest paid.
B: the panel study of income dynamics
The Panel Study of Income Dynamics (PSID) began collecting information on a sample
of approximately 5,000 households in 1968. Of these, about 3,000 are representative of the
U.S. population as a whole (core sample), while the rest are low-income families (SEO sample).
Since then, both the original households and their split-offs (members of the original household
forming a family of their own) have been followed over time. Questions on labor income and
hours are retrospective: information collected in the year t wave refers to the calendar year t − 1.
Our initial sample comprises every head and spouse between 20-60 years old in the 1968-1997
waves of the PSID core sample. We then exclude individuals currently in school, self-employed,
or disabled, and those with annual hours below 520 and above 5096 to reduce the role for
measurement error in hours, which leaves 80,979 individual/year records in the sample. 37 Next,
we exclude all individuals whose earnings are top-coded or whose hourly wage (computed as
annual earnings divided by annual hours) is below the federal minimum wage, which eliminates
37

French (2005) uses the PSID Validation Study to assess the size of measurement error in hourly
wages. He concludes that it accounts for 24% of the standard deviation of log wages. By trimming the
hours distribution below 520 and above 5096, we eliminate many outliers that are due to reporting errors.

38

around 4,141 individual/years observations. At the end of this selection, we are left with 76,848
individual/year observations in our final sample, i.e., roughly 2,500 per year.
The estimation of the individual fixed effect described in the main text is based on workers
with at least ten reported wage observations which reduces the sample size to 49,010 individual/year observations, i.e., 1,633 per year on average.
C: the 5% ipums sample of the 1990 census
The 1990 Census of the U.S. population uses a single long-form questionnaire for sample
questions completed by one half of persons in locations with a population under 2,500, one sixth
of persons in other tracts and block numbering areas with fewer than 2,000 housing units, and
one eighth of persons in all other areas. Overall, about one sixth of all housing units complete a
long form. Within each state, the Bureau divides the sample questionnaires into an appropriate
number of 1-percent samples. For example, if 20 percent of the population of a state completed
long forms, the sample questionnaires for that state are divided into twenty subsamples of equal
size. The 5-percent files are then selected at random from the 1-percent subsamples for each
state. Weights are attached to each case representing the number of individuals in the general
population represented by any particular case in the sample.
The original data set contains over 12,500,000 person-level observations. To create our
sample, first we exclude every person below 20 and above 60 years old, as well as every individual
currently in school, self-employed, or disabled, which leaves 4,636,759 individual records in the
sample. Next, we exclude all individuals who report zero wage income or zero weeks worked
over the year, and individuals whose annual earnings are top-coded, i.e. higher than $140,000
(19,890 cases). We also remove altogether occupational groups where more than 3% of all
workers are top coded. Eleven occupations are excluded based on this criterion, e.g., Airplane
pilots, Athletes, Dentists, Physicians, Podiatrists, and Judges. Finally, we eliminate individuals
for whom estimated hourly wages are below the federal minimum wage ($3.35 in 1989), i.e.,
roughly 400,000 observations.38 We are then left with 3,923,744 individual records in our final
sample.
We construct hourly wage as annual wage and salary income (variable INCWAGE) divided
by the product between the number of weeks worked last year (WKSWRK1) and usual weekly
hours worked (UHRSWORK).39

38

Through validation with CPS data, Baum-Snow and Neal (2006) find that a significant fraction of
workers report usually working 8 hours per week on the census’ long form when they actually usually
worked 40 hours per week; thus, they respond as if the question meant to report “usual hours per day”.
However, this type of measurement error which plagues the 1980 Census is much less frequent in the 1990
census. Moreover, these respondents are excluded from our selection criteria on annual hours.
39
See Ruggles et al. (2000) for a detailed explanation of the IPUMS Census data.

39

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43

PSID: mean to minimum

PSID: mean to first percentile ratio

6.5

3

6

1st stage residuals

1st stage residuals

2.8

2nd stage residuals

2nd stage residuals

5.5

2.6
5
2.4

4.5

2.2

4
3.5

2

3
1.8
2.5
1.6

2
1.5

1970

1975

1980

1985

1990

1.4

1995

1970

1975

Year

1980

1985

1990

1995

Year

PSID: mean to fifth percentile ratio

PSID: mean to tenth percentile ratio

2.3

2

2.2

1st stage residuals

1st stage residuals

1.9

2nd stage residuals

2.1

2nd stage residuals
1.8

2
1.7

1.9
1.8

1.6

1.7

1.5

1.6
1.4
1.5
1.3

1.4
1.3

1970

1975

1980

1985

1990

1995

1970

Year

1975

1980

1985

1990

1995

Year

Figure 1: Empirical analysis on PSID data. The first stage residuals refer to the regression
on observable covariates. The second stage residuals are the first stage residuals demeaned
individually.

44

1.5
1
Density
0

.5

Mean / first percentile = 2.24

1

1.5
2
Wage residual

2.5

3

Density

1

1.5

.5

0

.5

Median = 2.20

1.5

2

2.5
Mean / first percentile

3

3.5

Figure 2: Top panel: Residual wage distribution for full-time, full-year janitors and cleaners in the Philadelphia area. Bottom panel: Distribution of mean-min ratios for full-time,
full-year janitors and cleaners across U.S. geographical areas.

45

Net value of leisure as a fraction of w (ρ)

1
0

Reasonable
pairs
−1
Pairs of (ρ,r) consistent
with Mm=1.70

−2
−3
−4
−5
−6
−7
0

0.05

0.1

0.15

0.2

0.25

0.3

Monthly interest rate (r)

Figure 3: Pairs of the value of non-market time and the interest rate that can generate
Mm=1.70

46

0.7

Net value of leisure as a fraction of w (ρ)

0.6

Pairs (ρ,θ) consistent with Mm=1.70
0.5

0.4

0.3

0.2

0.1

0

θ=8

5

10

15

20

25

30

35

40

45

Relative risk aversion (θ)

Figure 4: Pairs of the value of non-market time and risk aversion that can generate
Mm=1.70

47

Pairs of (1−δ) and ρ consistent with Mm=1.70
0

Reasonable
pairs

Net value of leisure as a fraction of w (ρ)

−2
−4
−6
−8
−10
−12
−14
−16
−18
−20
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Annual autocorrelation coefficient of wage process (1−δ)

Figure 5: Pairs of the value of non-market time and the wage autoregression coefficient
that can generate Mm=1.70

48

Net value of leisure as a fraction of w (ρ)

Net value of leisure as a fraction of w (ρ)

1
0
−1
Reasonable pairs
−2
−3
−4
−5

Pairs of (ρ,λ )
w

consistent with Mm=1.70

−6
−7

0

0.1

0.2

0.3

0.4

1
0
−1
−2
−3
−4
−5

Pairs of (ρ,λ )
w

consistent with Mm=1.70

−6
−7

Monthly offer arrival rate on the job ( λw )

50

Reasonable pairs

0

0.1

0.2

0.3

0.4

Monthly offer arrival rate on the job ( λw )

0.065

45

40

Monthly separation rate

Mean job duration (months)

0.06

BLS estimate of
average job tenure

35

30

0.055
0.05
0.045
0.04
0.035
CPS−based estimate of
average separation rate

0.03
0.025

25

0

0.1

0.2

0.3

0.02

0.4

Monthly offer arrival rate on the job ( λw )

0

0.1

0.2

0.3

Figure 6: Top panels: pairs of the value of non-market time and the job offer rate during
employment that can generate Mm=1.70. Bottom panels: mapping between the arrival
rate of offers on the job and average job tenure (left panel), and separation rate (right
panel).

49

0.4

Monthly offer arrival rate on the job ( λw )