Wages, employment, and statistical discrimination: evidence from the laboratory.
Dickinson, David L. ; Oaxaca, Ronald L.
I. INTRODUCTION
While taste-based discrimination (Becker 1957) is driven by
prejudice, research on statistical discrimination attempts to explain
differential treatment of individuals unrelated to prejudice. In
essence, statistical discrimination results when the actual or assumed
statistical properties of a group are applied to anyone belonging to
that group. Differential treatment based on lower average outcomes of
one's group (e.g., minorities, females) was considered a starting
point for modeling of statistical discrimination (see Phelps 1972).
However, labor market researchers then considered that statistical
discrimination could result from measures other than the average
outcomes of one's group (see Aigner and Cain 1977; Lundberg and
Startz 1983). Theoretical models have explored various reasons why
statistical discrimination might arise in varied contexts. Most notable
are the models based on differential screening or communication costs
(Cornell and Welch 1996; Lang 1986), noisier productivity signals (see
discussion in Aigner and Cain 1977), or incomplete information (Lundberg
and Startz 1983). (1)
Field studies, some of which involve experimental manipulations,
have uncovered evidence of statistical discrimination in mortgage
lending (Ladd 1998), auto sales (Ayers and Siegelman 1995; Goldberg
1996; Harless and Hoffer 2002), sports card price negotiations (List
2004), law enforcement decisions (Applebaum 1996), exam grading (Hanna
and Linden 2012), taxi fare negotiations (Castillo et al. 2013), and
vehicle repair estimates (Gneezy and List 2006). In labor markets, some
discrimination may be due to factors other than productivity
characteristics (Neumark 1999), but the evidence for statistical
discrimination based on race has been elusive (see Altonji and Pierret
2001). Identifying statistical discrimination from field data is
complicated by the fact that it may arise as first-moment or
second-moment statistical discrimination, and they are difficult to
disentangle empirically.
More controlled laboratory studies have also examined statistical
discrimination (Anderson and Haupert 1999; Castillo and Petrie 2010;
Davis 1987; Dickinson and Oaxaca 2009; Fershtman and Gneezy 2001;
Masclet, Peterle, and Larribeau 2012). (2) Findings from these
laboratory studies indicate that statistical discrimination may result
from aversion to risk, mistaken stereotypes, biased probability
assessments, or incomplete information. The benefit of the laboratory
approach is our ability to control and cleanly identify the source of
the discrimination, if it exists.
Whether taste-based or statistical, discrimination is most always
measured along a single dimension, such as vehicle pricing, labor market
wages, group choice, or job assignments. (3) However, in many instances
multiple avenues for discrimination exist simultaneously and to focus on
only one may produce a systematically biased view of the prevalence of
statistically based discrimination. (4) In this paper, we examine
statistical discrimination in a controlled experimental environment.
Statistical discrimination in our study can only be based on
productivity-distribution risk attached to worker groups. We not only
cleanly separate taste-based from statistical discrimination, but we
also cleanly isolate second-moment statistical discrimination in a way
not possible from field data. Building on Dickinson and Oaxaca (2009),
our key contribution is to examine an environment in which
discrimination may be exercised simultaneously along the dimensions of
both wages and employment rates. This more closely approximates the
field environments we hope to study, where discrimination may exist in
terms of labor market wages and/or hiring practices, auto sales prices
and/or sales rates, mortgage rates and/or home sales.
As in Dickinson and Oaxaca (2009), subjects negotiate in a
simulated labor market where worker subjects are given an induced
common-knowledge productivity distribution. In the present design, our
environment allows workers of distinct productivity-distribution groups
to compete against each other in negotiating with employers for a wage
contract. The environment is designed such that there is equilibrium
unemployment, allowing us to compare both wage and unemployment rates of
workers belonging to distinct productivity-distribution groups.
Additionally, these data allow us to examine the bias in discrimination
estimates that would exist if we only had data on one dimension or the
other from our experimental market (i.e., only hiring data or only wage
data).
Our results indicate that, while higher variance in a worker's
productivity decreases the negotiated wage, there is evidence that
experimental employers substitute hiring choice and wage contracts. More
specifically, workers with higher productivity variance are more likely
to be hired, but they receive lower wages. An alternative measure of
productivity risk (i.e., the distributional support) significantly
decreases the likelihood of being employed while not significantly
impacting the wage if hired. (5) These results are intriguing and highly
relevant to naturally occurring labor markets where hiring and pay
decisions are often made over potential workers from heterogeneous
statistical worker groups. Our evidence that experimental employers
practice statistical wage discrimination and statistical employment
reverse-discrimination indicates that a focus on wages alone may
overestimate the real incidence of statistical discrimination.
II. EXPERIMENTAL DESIGN
The experimental environment is an oral double-auction market, with
employer and worker subjects negotiating wage contracts in an open pit.
There is no central auctioneer, and no actual labor task is involved.
Rather, we use the context of a labor market so that it would be easier
for subjects to comprehend the trading environment. We replicate the
methods of Dickinson and Oaxaca (2009) to the extent possible, which
facilitates comparison of our results. The design is a context-specific
use of classic market experiment techniques discussed in Smith (1982).
That is, supply and demand are induced upon subjects, and all decisions
have monetary consequence. See Appendix SI, Supporting Information, for
experiment instructions.
Each experimental session consists of 15 subjects. Five of these
subjects are randomly assigned to be "employer" subjects, and
the rest are assigned as "worker" subjects. A worker can sell
at most one unit of labor, and an employer can hire only one unit of
labor, during each round of the experiment. Workers have an induced
reservation wage of $0.80, such that they are guaranteed this payment
for a round in which they are not employed and this reservation wage is
private information to workers. The expected productivity of a unit of
labor to the employer is 3 units of output, which sell for a normalized
$ 1.00 per unit (the price per unit of output is private employer
information). Thus, expected revenue to an employer from hiring a unit
of labor is $3.00. Profits to a worker subject are either the
reservation wage, [W.sub.R], or the negotiated wage, W, which we did not
bound so that workers enjoying utility from making a contract may choose
to negotiate W < [W.sub.R]. Employer profits are the realized
productivity of the worker (times output price $1.00) minus the
negotiated wage. The thicker supply side of the market guarantees
equilibrium unemployment of five workers (50% unemployment) per round.
(6) Figure 1 shows the simulated labor market for each round of the
experiment.
An experiment session consists of four treatments of four decision
rounds each, for a total of 16 decision rounds per experimental session.
The labor pool in each treatment consists of workers belonging to one of
two distinct worker productivity types. A worker's type or
"group" for a given round is identified by an ID badge worn by
the subject. At the outset of an experimental session workers are
assigned to a productivity distribution through random allocation of the
10 ID badges, that is, 5 ID badges for each productivity-distribution
group. For subsequent treatments in an experimental session, each group
cohort is randomly assigned to one of two groups corresponding to the
particular treatment. This procedure is much simpler to implement but
may potentially retain negotiating power asymmetries across the two
competing worker groups. In the conduct of the experiment, there was
never any evidence of group "bonding" or group consciousness.
As will be seen below, worker and worker-employer pair random effects
were taken account of in the econometric analysis of the experimental
results. (7)
[FIGURE 1 OMITTED]
The design choice to randomly assign workers to
productivity-distribution groups implies that workers are effectively
identical within these groups. This reflects our focus on the
employers' wage and hiring choices. As such, actual worker subjects
may not seem necessary in our experiments, but we choose to not
mechanize the worker choice in order to maintain the labor negotiations
context of our experiments. Additionally, the market exchange
environment leverages the well-documented power of the double-auction
institution to produce the competitively predicted wage outcomes. This
allows one to attribute outcome differences across worker groups to the
productivity group differences with minimal concern that bargaining
heterogeneity is driving the results.
We used a total of six different worker productivity distributions
in all. The productivity-distribution information of each worker group
is shown in Table 1. As in Dickinson and Oaxaca (2009), the worker
productivity distributions are intended to explore three distinct
measures of "risk": the distributional variance, the support
of the distribution, and the probability that earnings will be less than
mean earnings ($3.00) for an employer. (8) As can be seen in Table 1,
hiring a worker identified as belonging to Group 1 guarantees the
employer a certain productivity of 3 units of output. Hiring a worker
from any of the other groups involves risk of some sort. Upon hiring a
worker from a risky productivity-distribution group, a random draw from
the appropriate productivity distribution determines the worker
productivity to the employer for that round. Productivity draws are
independent each and every round, such that employers are aware that
negotiating a wage contract with the same subject in two distinct rounds
or with any subject from the same productivity group as in a previous
round may not lead to the same productivity outcome. We do not include
any risk or loss aversion instrument in our design, and so heterogeneity
in either of these individual preference dimensions may add noise to our
data that will be dealt with in the econometric analysis.
As noted above, employer choice involves two dimensions: hiring
workers from one group or the other and the choice of wage. With six
distinct worker productivity groups, there are 15 possible binary group
comparisons. An experiment session, however, involves only four
treatments, and so we select treatments so that each session involves
one treatment that pairs the certain productivity group, GI, with one of
the other groups, and then three treatments with labor pools comprised
of (G2,G5), (G2.G6), and (G3,G4) productivity group pairings (treatments
randomly ordered within a session). The (G2,G5) pairing captures the
risk associated with the probability of earnings less than mean earning,
and the (G2,G6) pairing captures the risk associated with changing the
support by extending the maximum outcome to 5 versus 4. In the case of
the (G3,G4) pairing, the variance is higher for G4 but the support is
missing outcomes 2 and 4 which are symmetric around the distribution
mean of 3. The distributional information in Table 1 highlights how
these binary comparisons vary the risk measures. Table 2 shows the
productivity comparisons used in each of the five experimental sessions
we ran, and the location of any particular treatment within the set of
four treatments was varied across sessions. Because each subject was
administered four of the many possible treatment pairings (see Table 2),
our design is a mixed design with both within- and between-subjects
components.
III. THEORETICAL FRAMEWORK
In our environment, employers make a simultaneous choice of
employment and wage rate. Thus, a simple choice framework for employers
would be a traditional model of choice where employer utility, U, is a
function of expected profits, [pi], and employment risk (i.e.,
productivity risk), r. U = U([pi],r), where [U.sub.[pi]]' > 0,
[U.sub.r]' < 0, [U.sub.[pi]]" < 0, [U.sub.r]" >
0. Because expected productivity is fixed across all worker groups, [pi]
varies inversely with the wage rate. Assuming employers are risk averse,
we borrow from optimal portfolio theory of Markowitz (1952) and
formulate an employer's utility maximization decision. (9) As seen
in Section IV (Table 3), our data indicate that expected profits are
higher (i.e., wages lower) for the risky productivity groups relative to
certain productivity. Thus, the labor market "portfolio"
constraint describing combinations of expected profits and productivity
risk available to employers appears as the upward sloping line in Figure
2, as one would expect.
In this framework, employers with a higher marginal disutility of
productivity risk (bold indifference curves in Figure 2) will choose to
hire workers from groups considered a lower productivity risk, paying
them higher wages (resulting in lower expected profits, it). Conversely,
employers with lower marginal disutility of risk (dashed indifference
curves) will hire from riskier worker groups and face higher expected
profits. We reiterate here that higher expected profits are not due to
higher levels of average productivity--average worker productivity is
constant in our experimental design--but rather due to lower market
wages for the same level of average productivity. The risk-reward
trade-off is at the core of this framework.
[FIGURE 2 OMITTED]
This framework assumes a continuous risk choice dimension, but our
experimental framework has employers choosing between hiring a worker
from one group or another. Within this framework, choices of workers
from one group or the other will generate the employment rates in our
data. An underlying assumption is that there is a market wage for each
worker group and employers take that wage as given. Although this is not
true in our two-sided auction market, the simplification captures the
idea that both empirical employment and wage models should be the
functions of worker groups as well as the variables capturing the
particular worker group pairing facing the employer in a given choice
round. For example, consider two worker groups, [G.sub.x] and [G.sub.y].
A worker from [G.sub.x] will be hired over [G.sub.y] if the hire offers
the employer higher utility. So an employment indicator for the worker
from [G.sub.x], can be defined as [E.sub.Gx] = 1[U([[pi].sub.Gx],
[r.sub.Gx]) - U([pi][G.sub.y], [r.sub.Gy]) > 0]. Such a framework is
basically a random utility model that lends itself to probit estimation
techniques with regressors that capture the relevant worker group
information. In Figure 3 we see that the employer with indifference
curves as shown would prefer hiring a [G.sub.y] worker over a [G.sub.x]
worker, but would employ a [G.sub.z] worker over a [G.sub.y] worker. The
probability of employment for a worker from a given group depends on the
alternative available to the employer.
[FIGURE 3 OMITTED]
It is clear from this framework that one can view the hiring and
wage choices of employers in a general way that focuses on risk and
compensating differentials. While it is true that our experiments can
therefore apply to risky choice in general, in many instances such a
risky choice decision is cast as a simple individual choice task. This
would be more applicable to choice over risky assets in a portfolio
choice problem, but the two-sided negotiations context we employ has
greater external validity for labor markets. It is also worth
highlighting that the few studies examining a dual-dimension of
discrimination possible do so only empirically, without offering a
theoretical basis. In some instances, econometric modeling choices may
even constrain coefficients on wage and employment outcomes to imply
discrimination on both dimensions (see our comments in Section IV on the
Tobit model). A framework that suggests employers might substitute wages
for employment risk is novel for labor markets, and gives us reason to
suggest caution regarding empirical strategies for labor market
discrimination studies that address employment and wages simultaneously.
IV. RESULTS
We consider a series of random effects models for wage and
unemployment rate determination. For wage determination, we estimate
wage equations based on contract pair (employer-worker) random effects,
based on employer random effects, and based on worker random effects.
(10) In any given experimental session there were 5 employers, 10
workers, 4 treatments, and 4 rounds per treatment. With a total of 5
sessions, we therefore have 25 employers and 50 worker subjects in the
data set. In our design, 5 of the 10 workers are unemployed each round.
Thus, our data include 400 total wage contracts and consequently 400
observations for contract pair random effects and 400 observations for
employer random effects. On the other hand, there are a total of 800
observations for work random effects.
In the case of contract pairs, there were 161 distinct
employer-worker pairings. The random effects wage determination model
corresponding to contract pair random effects is an unbalanced design
and is parsimoniously specified by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where {ij} denotes each unique employer(i)-worker(j) contract pair,
[G.sub.jt] is a vector of dummy variables for the group association of
the jth worker, [T.sub.t] is a vector of dummy variables for the
treatments (corresponding to which two worker groups are competing for
wage contracts), [R.sub.t] is a vector of dummy variables corresponding
to the four rounds per treatment, [C.sub.{ij}t] is a vector of dummy
variables for employer-worker gender pairings, the [beta]'s are
conforming parameter vectors, [u.sub.{ij}] is a normally distributed
mean zero, constant variance contract pair random effect, and
[[epsilon].sub.{ij}t] is a normally distributed mean zero, constant
variance idiosyncratic error term.
When considering employer random effects, we have a balanced
design. The wage determination model in this case is specified as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where variables are defined as above (i indexes employers, j
indexes workers).
Since in any given period, half of the workers will be unemployed,
we model the wage determination process for workers as a balanced design
random effects Tobit:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Here, [X.sub.jt] is a vector of worker personal characteristics
corresponding to gender, minority status, and citizenship. (11) From the
estimated Tobit model, we can examine unemployment rates. Specifically,
we back out the probability of being employed
P (Employed = 1) = [PHI](I/[sigma])
where [PHI] is the standard normal cumulative distribution
function, [sigma] is the standard deviation of worker wages, and / is
the index function defined earlier by
I = [[beta].sub.0] + G[[beta].sub.G] + T[[beta].sub.T] +
R[[beta].sub.R] + X[[beta].sub.X].
Considering the wage effect coefficients of the random effects
models for contract pairs and employers, all worker groups with some
productivity risk exhibited negative wage effects compared with Group G1
with the certain productivity outcome (see Table 4). These negative wage
effects were statistically significant in two cases, Groups G3 and G4.
When considering the random effects Tobit model for workers, we find
that relative to G1 all of the other groups exhibit consistently
negative wage effects. These were statistically significant in two
cases, Groups G2 and G5.
Table 5 reports the estimated treatment effects for isolated
productivity risk variables: variance, support, and probability of
productivity less than the mean. With respect to the contract pairs and
employer random effects model, the results suggest that higher variances
are associated with statistically significantly lower wage contracts.
The G4-G3 treatment shows that higher variance and two omitted outcomes
symmetric around the mean productivity outcome depress wage contracts.
The G4-G5 comparison is not a treatment but is rather a cross-subject
design to estimate the wage-contract effects of the higher variance
associated with G4 and the same two omitted outcomes. The estimated
impact on wage contracts is even greater than the G4-G3 treatment. The
only difference in these two variance/support comparisons is that the
difference in variances for G4-G5 is nearly twice as large as that of
the G4-G3 treatment. This would suggest that the variance effect is the
driver of the wage contract effects. Indeed the statistically
significant negative G3-G5 cross-subject estimate in Table 5 is exactly
the difference between G4-G5 and G4-G3. As the supports are identical,
this effect is solely the result of the variance difference between G3
and G5. At the same time, there were no statistically significant wage
contract effects of productivity distribution support or the probability
of productivity less than the mean. On the other hand, the random
effects Tobit model for workers shows no statistically significant
coefficients associated with membership in higher variance groups or in
groups with a higher probability of generating productivity less than
the mean. Yet, there is a statistically significant negative coefficient
for membership in groups with a higher support range.
We use the estimated probabilities of employment from the Tobit
model evaluated at the overall sample mean to estimate the marginal
effects of our risk measures on the probability of employment. We find
no statistically significant employment effect of the higher variance
with symmetrically omitted outcomes of G4 against G3 but we do find
statistically significant positive employment effects of the higher
variances of G3 and G4 against G5. We find no statistically significant
employment effect from a higher probability of drawing productivity less
than the mean.
As already pointed out, while all three of the variance-related
treatments had statistically significant negative impacts on wage
contracts in the contract pairs and employer RE models, they had no
direct wage impacts when taking account of worker random effects.
Interestingly, two of the variance treatments (G4 vs. G5 and G3 vs. G5)
had positive effects on employment. These positive employment effects
were accompanied by negative wage contract effects for employers. The
variance/support treatment for G4 vs. G3 had no statistically
significant employment effect to offset the employer/contract pair
negative wage contract effect. In the case of the higher support range
treatment, there was no contract pair/employer wage contract effect, but
there was a negative wage and employment impact when taking account of
worker random effects. When considering the probability of productivity
draws less than the mean, we find no evidence of wage or employment
effects.
The contract pair and employer-based random effects estimations
look at the data from the employer perspective, without considering the
unemployment risk as is the case when looking at the worker random
effects Tobit estimations. If we consider the workers' perspective,
the expected wage is determined according to
[W.sup.e] = E(W|X) = (W|W > 0) x ([pi]),
where [W.sup.e] is the worker's expected wage, W | W > 0 is
the wage conditional upon being employed, and [pi] is the probability of
being employed. This expected wage is simply a weighted average of W = 0
when unemployed and W > 0 when employed. The change in the expected
wage associated with group "k" compared with group
"j" can be calculated as follows:
[DELTA] [W.sup.e.sub.kj] = [W.sup.e.sub.k] - [W.sup.e.sub.j].
In the case of a Tobit model, the marginal effects of continuous
variables are constrained to have the same sign for the conditional mean
wage effects and the employment effects. This correspondence would
generally carry over when looking at the marginal effects of binary
variables. Thus, we use the Tobit model to estimate employment effects,
but focus on the random effects wage equations for estimated wage
effects as these are not constrained by the Tobit model to have the same
sign as the employment effects. (12)
Column 6 of Table 5 (Wage Effect | X) reports the expected wage
effects using the predicted wages and probabilities evaluated at overall
sample means. Three of the risk treatments show a negative effect on
mean expected wages but only the negative support treatment effect is
statistically significant. In the case of employer and contract pair
random effects, the support treatment does not produce a statistically
significant wage effect. With the exception of the G4-G3 comparison, the
variance treatments show statistically significant positive effects on
worker average wages (including 0 wages when unemployed). These same
variance treatment comparisons show negative and statistically
significant wage effects for employer and contract pair random effects.
Thus, the expected or "average" wage results seem to conflict
with the contract wage effects of the variance treatments when
considering employer and contract pair random effects. It is clear that
the employment probability effects are driving these results.
Our findings suggest that the variance treatments depress wage
contracts for employers and contract pairs, but raise the probability of
a worker being employed in two of the three variance treatments (see
far-right column of Table 5). These wage contract effects are consistent
with the theoretical framework outlined earlier, which stressed the
risk-reward trade-off to an employer of wages and productivity risk of
hiring certain workers. Regarding overall risk effects, the positive
employment effects of two of the variance treatments in the worker RE
Tobit model generate positive estimated effects on mean wages and
conditional mean wages. While in some sense overcorrecting our worker RE
Tobit results demonstrate that the effects of risk on wage contracts
alone do not reveal the full extent of statistical discrimination.
Certainly, the negative risk effects of productivity variance on
employer contract wages overstate the extent of statistical
discrimination because the same measure of risk increases the
probability of employment. In the case of the support treatment, the
lack of wage contract effects actually understates the extent of
statistical discrimination because the negative employment effects
reduce the expected wages of these workers. The probability of
productivity draws less than the mean had little effect on wage
contracts, conditional wages, employment probabilities, and expected
wages.
Among the control variables in our models, the round/period effects
were never statistically significant. In the contract pairs and employer
RE models (relative to contracts between male employers and male
workers), the presence of a female in the contract is associated with
higher wage contracts. The highest contract is associated with female
employers and female workers (C_ff in Table 4), followed by contracts
with male employers and female workers (C_mf), and finally by contracts
between female employers and male workers (C_fm). However, the estimated
wage contract effect for C_fm is not statistically different from a male
employer/male worker contract. In the RE Tobit wage model for workers,
we controlled for gender, minority status, and noncitizen. For the most
part these variables were not statistically significant though minority
status exhibited a marginally significant negative effect on wages and
because of the restrictions imposed by a Tobit model, a small negative
effect on the probability of employment. We should highlight that the
race and gender variables are used only as controls and cannot be used
to identify taste-based discrimination in our study, as these variables
may correlate with other relevant variables.
Given that the subject workers assume a relatively passive role
compared with the subject employers, columns 2 and 3 of Table 5 provide
our best estimates of the wage contract effects of our risk measures,
while column 6 provides the sole estimates of the employment effects of
the risk measures. With this in mind, a main result of this paper is
that our estimations suggest that belonging to a risky productivity
group has a negative effect on wage contracts while it may yet have a
positive effect on the probability of being employed. Thus, our
laboratory evidence suggests that employers may view hiring choices and
wage contracts as substitute goods. That is, a higher productivity
variance increases the likelihood that one will be employed, but
conditional on employment there is a lower wage contract. Reverse
statistical discrimination in hiring choices is perhaps used by
employers to help leverage wage negotiations (i.e., those high-variance
workers willing to accept lower wages increase their likelihood of being
employed). It would therefore be an incomplete view of statistical
discrimination if one were to focus simply on wage effects among the
employed. In some cases, doing so in our data would upwardly bias
one's estimate of the negative effects of productivity variance in
the labor pool because it would fail to take into account any increased
probability of employment. In other cases, there can be a downward bias
in the estimate of statistical discrimination, such as when we find no
significant wage effect among employed workers, but a decreased
likelihood of employment.
V. DISCUSSION
Our previous work (Dickinson and Oaxaca 2009) found a significant
effect of loss probabilities on depressing wage contracts, a result we
do not replicate in these data. However, the availability of more than
one way to statistically discriminate in the present experiments implies
the results we report here are not directly comparable to our previous
research. The present experiments generate a richer data set for
exploring how worker productivity risk impacts the dual choice faced by
employers. The result is that this current work is more externally valid
and applicable to field labor markets.
Our data are consistent with employers exercising trade-offs
between hiring choices and wage contracts in an environment where
competing heterogeneous workers have identical expected labor
productivity but differ with respect to the riskiness of their labor
productivity. We implement a design where there is equilibrium
unemployment such that employers may simply choose to not hire workers
from less-preferred worker groups. For worker groups with a higher
variance of labor productivity, we estimate lower wages from the
contract-pair and employer random effects models, but we also find that
these same workers often face an increased probability of being
employed. Thus, our data overall show statistically based discrimination
in wages but reverse statistical discrimination in hiring choices.
The offsetting wage and employment effects we find imply that
expected wages of the worker may actually be higher as a result of
belonging to a high risk worker pool, when defining risk as a higher
variance of labor productivity. However, we also isolate an alternative
measure of risk, the support of the productivity distribution, and find
that typical wage estimates may underestimate statistical discrimination
as a result of that alternative risk measure. As a result, we cannot
make a general claim as to the direction of the likely bias in typical
wage discrimination estimates, but it is clear that ignoring hiring
choices in one's analysis can generate significant wage effect
biases. These results make the case for considering employment, wages,
and earnings in empirical research as a way to more fully assess whether
discrimination has any net impact on labor market outcomes. In doing so,
we suggest caution in interpreting earnings data because, although they
capture the impact of wages joint with employment, earnings are also a
function of worker preferences as well.
Although there exists a body of literature on statistical
discrimination, researchers have yet to examine environments where
"statistical" discrimination may be exercised on multiple
dimensions. Our contribution is that we study such an environment in a
controlled laboratory setting. This research highlights, however, that
multiple avenues for potential discrimination do not necessarily imply
discrimination on multiple fronts. Indeed, evidence suggests that
individuals may discriminate along one dimension but simultaneously
reverse-discriminate along the other. This may be more likely with
statistical discrimination than with taste-based discrimination, as
Aeberhardt et al. (2010) find evidence for taste-based discrimination in
both employment and wages, although there is insufficient research to
make this claim.
A practical implication of this research is to say it would be
incorrect to assume that sufficiently risk-averse employers will
statistically discriminate across all dimensions. Rather, we suggest
that employers may value the trade-off between wages and employment
similar to how one balances risk and reward in other contexts. Our
results also have important implications for our estimates of the extent
of statistical discrimination, and highlight the likely bias that exists
in such estimates when data analysis only examines one possible
dimension for discrimination. We focus on non-prejudiced based
discrimination, but this is likely an important message for all types of
discrimination research.
doi: 10.1111/ecin. 12103
Online Early publication May 28, 2014
SUPPORTING INFORMATION
Additional Supporting Information may be found in the online
version of this article:
Appendix S1. Experiment Instructions.
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(1.) Charles and Guryan (2008) conducted an empirical study with
data on community-level prejudice from the 1972-2004 waves of the
General Social Survey. They conclude that prejudice-based discrimination
accounts for only one-quarter of the black-white wage gap. Other
mechanisms suggested as the source of the remaining wage gap include
statistical discrimination.
(2.) Another paper, Rodin and Ozcan (2011), finds evidence of
discrimination in a laboratory experiment in Sweden. Subjects not
perceived as stereotypically Swedish are rated as worse performers,
which could be consistent with either taste-based or statistical
discrimination. Providing information on performance outcomes does not
explain or eliminate the negative beliefs regarding subjects with
foreign-accented speech, which suggests taste-based discrimination.
(3.) Two exceptions we are aware of both focus on taste-based
discrimination. Groothuis and Hill (2013) examine the effect that exit
discrimination may have in biasing wage equations using professional
basketball player data. They fail to find evidence of discrimination
using 1990-2008 data, but note that residual methods of identifying
discrimination are prone to pitfalls. Aeberhardt et al. (2010) find
evidence for taste-based discrimination in at both the hiring stage as
well as in wage data of French workers with African origins. Their study
is based on a typical assumption that unexplained residual differences
in the data imply discrimination.
(4.) Heckman (1998) notes that differential outcomes clearly need
not imply discrimination, but it is also true that the absence of
differentials need not imply the absence of discrimination. For example,
estimates of labor market discrimination would be biased downwards if
females or minority workers were discriminated against in hiring, and
yet discrimination estimates were based solely on wage data. Those
employers most averse to the statistical characteristics attached to
certain workers do not hire those workers, and the remaining employers
require a lesser wage discount to employ workers from the female or
minority group. One might plausibly argue, however, that employers
averse to minority or female workers (on statistical grounds) might
choose to hire these workers if the market wage discount is large enough
and employers view hiring choice and wage payments as substitutes. Thus,
the direction of bias is not so clear.
(5.) In total, we examine three distinct measures of productivity
risk that can be identified through our experimental treatments:
productivity variance, the support of the productivity distribution, and
the probability of worker productivity being less than the group
average. Each of these ways to think of risk has a basis in the
literature (see Dickinson and Oaxaca 2009).
(6.) Of course, we assume that all workers not employed were
actually attempting to secure a wage contract, which is reasonable given
that worker subjects were not allowed to simply disengage themselves
completely from the pit negotiations. Of course, some subjects tried
harder than others, but this is a feature of real world job search as
well.
(7.) In addition to answering all subject questions prior to
beginning the experiment rounds, any misunderstanding on the part of
subjects regarding the differences in productivity distribution groups
were quickly resolved due to the spirited and open nature of the double
auction exchange environment coupled with real monetary incentives.
(8.) This measure of risk may be thought of as similar to studying
loss aversion. If expected (average) profits are considered the
reference point of the employer, then earnings less than mean earnings
in a decision round would be a type of loss. Actual negative earnings
were not possible, however. Also, though workers typically received
wages well below the marginal revenue product generated to the employer,
this maximum retail price was private employer information. Workers only
knew that they would earn either their negotiated wage, or a reservation
wage of $.80 if not employed.
(9.) In some instances employers may value productivity variance
for the upside option value when low productivity workers can be
terminated (see Lazear 1998). However, our environment does not allow
for this given that each wage contract is a one-period contract
independently drawn from the relevant productivity distribution.
(10.) For the wage determination models, we reject ordinary least
squares in favor of random effects in all cases.
(11.) Our overall sample was 33% female, 40% minority, and 11%
non-U.S. citizen. Regarding the subsample of worker subjects the values
are 36% female, 38% minority, and 12% non-U.S. citizen.
(12.) We considered the possibility of estimating a traditional
two-stage Heckit model as an alternative. However, it is difficult to
find plausible exclusion restriction for the wage equations in our case.
Moreover, the addition of the inverse mills ratio in the panel data
setting would not yield consistent estimators. Although we did estimate
a random effects probit model for employment, which yielded virtually
identical results to our reported Tobit results, the addition of the
wage information using the Tobit model produces a more efficient
estimator for our employment probability parameters.
DAVID L. DICKINSON and RONALD L. OAXACA *
* The authors thank Tim Perri and Pete Groothuis, seminar
participants at Appalachian State University, and participants at the
2013 WEAI Pacific Rim meetings in Tokyo for valuable comments on the
paper.
Dickinson: Department of Economics, Appalachian State University,
Boone, NC 28608. Phone 828-262-7652, Fax 828-262-6105, E-mail
dickinsondl@appstate.edu
Oaxaca: Department of Economics, University of Arizona and IZA,
Tucson, AZ 85721. Phone 520-621-4135, Fax 520-621-8450, E-mail
rlo@email.arizone.edu
TABLE 1
Experiment Treatment Design
Worker Productivity
Group (G) (Probability) Mean Variance
G1 3 (1.00) 3 0
G2 1,2,3,4,5 3 1
(,1,.1,.6,.1,.1)
G3 1,2,3,4,5 3 2
(.2,.2,.2,.2,.2)
G4 1,3,5 (.4,.2,.4) 3 3.2
G5 1,2,3,4,5 3 1
(.01,.39,
.27,.25,.08)
G6 1,2,3,4 3 1
(.15,.05,.45,.35)
Likelihood
of
Worker Distribution Productivity
Group (G) Support < Mean
G1 3 0
G2 1,2,3,4.5 0.2
G3 1,2,3,4,5 0.4
G4 1,3,5 0.4
G5 1,2,3.4,5 0.4
G6 1,2,3,4 0.2
TABLE 2 Pairings Used in Each Session
Session Number
Treatment
Pairings (T) of 1 2 3 4 5
Worker Groups (G)
Risky choice T1 = G2 and G5 X X X X X
options that T2 = G2 and G6 X X X X X
identify unique T3 = G3 and G4 X X X X X
risk factor
Certain versus T4 = G1 and G2 X
risky choice T5 = G1 and G3 X
employer T6= G1 and G4 X
options T7= G1 and G5 X
T8= G1 and G6 X
Total treatments 4 4 4 4 4
Note: The ordering of treatments was varied across sessions.
TABLE 3
Summary Wage and Employment Data
(Averaged across All Treatments and Sessions)
Worker Wage minWage maxWage Employment
Group (G) Rate
G1 1.41 .79 10.00 .55
G2 1.08 .50 2.80 .46
G3 1.18 .75 2.50 .49
G4 1.07 .75 2.50 .52
G5 0.99 .50 3.00 .47
G6 0.99 .65 1.80 .56
TABLE 4
Group Wage Effects
Random
Effects (MLE) Effects (MLE)
Wage Effect Wage Effect
Coefficients Coefficients
Variables (Standard Errors) (Standard Errors)
Constant 1.022 *** (0.212) 1.023 *** (0.208)
G2 -0.086 (0.190) -0.079 (0.187)
G3 -0.699 *** (0.219) -0.788 *** (0.220)
G4 -0.929 *** (0.220) -1.020 *** (0.220)
G5 -0.084 (0.211) -0.101 (0.205)
G6 -0.186 (0.209) -0.143 (0.198)
T2 0.091 (0.129) 0.058 (0.130)
T3 0.775 *** (0.297) 0.878 *** (0.296)
T4 -0.003 (-0.199) 0.010(0.199)
T5 0.688 ** (0.279) 0.708 *** (0.272)
T6 1.452 *** (0.279) 1.548 *** (0.276)
11 -0.177 (0.212) -0.151 (0.216)
T8 -0.069 (0.212) 0.051 (0.213)
C_ff 0.527 *** (0.164) 0.388 *** (0.135)
C_mf 0.269 ** (0.109) 0.267 *** (0.083)
C_fm 0.138 (0.126) 0.178 (0.114)
Female -- --
Minority -- --
Noncitizen -- --
Log Likelihood -395.975 -398.730
N 400 400
Effects (MLE)
Wage Effect
Coefficients
Variables (Standard Errors)
Constant 0.561 * (0.325)
G2 -0.486 * (0.283)
G3 -0.333 (0.337)
G4 -0.336(0.335)
G5 -0.514 * (0.312)
G6 -0.149 (0.308)
T2 -0.165 (0.191)
T3 -0.135 (0.450)
T4 -0.256 (0.297)
T5 -0.096 (0.417)
T6 0.287 (0.405)
11 -0.323 (0.300)
T8 -0.456 (0.315)
C_ff --
C_mf --
C_fm --
Female 0.166 (0.148)
Minority -0.268 * (0.156)
Noncitizen 0.027 (0.234)
Log Likelihood -936.843
N 800
Note: Round dummies-suppressed for space-were
all statistically insignificant.
*, **, *** indicate significance at the .10, .05, and .01 levels,
respectively, for the two-tailed test.
TABLE 5
Employment Models Risk Effect Identification
(Binary Groups Comparisons)
Contract
Pair Random
Groups Effects
(MLE) Wage
Risk [G.sub.x]- Effect
Measure [G.sub.y] Coefficients
Variance/ G4-G3 -0.230 ** (0.126)
Support
Variance/ G4-G5 -0.846 *** (0.301)
Support
Variance G3-G5 -0616 ** (0.309)
Support G2-G6 0.100 (0.125)
Prod < avg G5-G2 0.002 (0.124)
Log-L -395.975
N 400
Employer
Random
Effects
(MLE) Wage (MLE) Wage
Risk Effect Effect
Measure Coefficients Coefficients
Variance/ -0.232 ** (0.126) -0.003 (0.194)
Support
Variance/ -0.919 *** (0.301) 0.179 (0.450)
Support
Variance -0.684 ** (0.301) 0.181 (0.465)
Support 0.065 (0.127) -0.337 * (0.189)
Prod < avg -0.022 (0.126) -0.037 (0.187)
Log-L -398.730 -936.843
N 400 800
Worker Random Effects Tobit
Risk Effect on
Employment Probability
(Marginal Effects)
[psi] ([x.sup.'][beta]/
[[sigma]).sub.Gx=1] -
Risk Wage Effect | X [psi] ([x.sup.'][beta]/
Measure (At Sample [[sigma]).sub.[Gy=1]]
Means) (At Sample Means)
Variance/ -0.001 (0.014) -0.001 (0.009)
Support
Variance/ 0.087 *** (0.033) 0.058 *** (0.022)
Support
Variance 0.088 *** (0.035) 0.059 *** (0.023)
Support -0.176 *** (0.033) -0.109 *** (0.016)
Prod < avg -0.013 (0.021) -0.009 (0.016)
Log-L -- --
N 800 800
*, **, *** indicate significance at the .10, .05,
and .01 levels, respectively, for the two-tailed test.
