Download Lecture 6: Compensating Wage Differentials

Lecture 6: Compensating
Wage Differentials
The model of competitive labor markets
implies that as long as workers or firms can
freely enter and exit the marketplace, there
will be a single wage in the economy if all
jobs are alike and all workers are alike.

All jobs are not the same. Adam Smith in 1776
argued that compensating wage differentials arise to
compensate workers for the nonwage characteristics
of jobs. It is not the wage that is equated across jobs
in a competitive market, but the “whole of the
advantages and disadvantages” of the job.
 Workers differ in their preferences for job
characteristics and firms differ in the working
conditions that they offer. The theory of
compensating differentials tells a story of how
workers and firms “match and mate” in the labor
market.
1. Workers’ and Firms’ Choice with Risky Jobs
E.g. Employer X: NT.$100 per hour, clean, safe work conditions
Employer Y: NT.$100 per hour, dirty, noisy factory
→ Most workers would undoubtedly choose employer X.
If employer Y decides not to alter working conditions, it must
pay wage above NT.$100 to be competitive in the labor
market.
→ The extra wage it must pay to attract workers is called a
compensating wage differential because the higher wage is
paid to compensate workers for the undesirable working
conditions.
After the wage rise of firm Y, if both firms could obtain the
quantity and quality of works they wanted, the wage
differential would be an equilibrium differential, in the sense
that there be no forces causing the differential to change.
* The compensating wage differential
serves two purposes:
1.
2.
It serves a social need by giving people an incentive
to voluntarily do dirty, dangerous, or unpleasant
work or a financial penalty on employers offering
unfavorable working conditions.
At an individual level, it serves as a reward to
workers who accept unpleasant jobs by paying them
more than comparable workers in more pleasant
jobs. Those who opt for more pleasant conditions
have to buy them by accepting lower pay.
→ Compensating wage differentials provide the key to
the valuation of the nonpecuniary aspects of
employment.
Note:
The predicted outcome of the compensating wage
differential theory of job choice is not that employees
working under “bad” conditions receive more than
those working in “good” conditions. The prediction is
that, holding worker characteristics constant,
employees in bad jobs receive higher wages than
those working under more pleasant conditions.
* The compensating wage differential
theory is based on three assumptions:
Utility Maximization
Workers seek to maximize their utility, not their
income. Compensating wage differentials will only
arise if some people do not choose the highestpaying job offered, preferring instead a lowerpaying but more pleasant job.
→ Wages do not equalize in this case. The net
advantage – the overall utility from the pay and the
psychic aspects of the job – tend to equalize for the
marginal workers.
1.
2. Worker Information
Workers are aware of the job characteristics of
potential importance to them.
→ Company offering a “bad” job with no compensating
wage differential would have trouble recruiting or
retaining workers, trouble that would eventually
force it to raise its wage.
Note: Our predictions about compensating wage
differentials hold only for job characteristics that
workers know about.
3. Workers Mobility
Workers have a range of job offers from which to
choose. It is the act of choosing safe jobs over
dangerous ones that forces employers offering
dangerous work to raise wages.
2. The Hedonic Wage Function
A wage theory based on the assumption of
philosophical hedonism that workers strive to
maximize utility.
To simplify our discussion, we shall analyze just one
dimension –risk of injury on the job – and assume
that the compensating wage differentials for every
other dimension have already been established.
→ To obtain a complete understanding of the job
selection process and the outcomes of that process, it
is necessary to consider both the employer and
employee sides of the market.
(1) Employee Considerations
Some combinations of wage rates and risk levels that would yield
the same level of utility can be represented by indifference curve
map.
W
U3
U2
U1
Risk
U2 slopes upward because
risk of injury is a “bad” job
characteristics. i.e., if risk
increases, wage must rise if
utility is to be held constant.
Highly Averse to Risk
W
Moderately
Averse to Risk
UL
UH
Risk
People differ in their aversion to
the risk of being injured. Those
who are very sensitive to this
risk will require large wage
increases for any increase in risk
(UH), while those who are less
sensitive will require smaller
wage increases to hold utility
constant (UL).
(2) Employer Considerations
Assumptions:
a. It is presumably costly to reduce the risk of
injury facing employees.
b. Perfect competition → Firms operate at zero
profits.
c. All other job characteristics are presumably
given or already determined.
→ If a firm undertakes a program to reduce the
risk of injury, it must reduce wages to remain
competitive.
Forces on the employer side of the market tent
to cause low risk to be associated with low
wages and high risk to be associated with high
wages, holding other things constant.
→The employer trade-offs between wages and
levels of injury risk can be graphed through the
use of isoprofit curves , which show the
various combinations of risk and wage level
that yield a given level of profits.
W
The concavity of isoprofit
curves is a representation of
our assumption that there are
diminishing marginal returns
to safety expenditures.
M
N
→ The cost of reducing risk
levels is reflected in the slope
of the isoprofit curve.
Risk
Y’
W
X’
X
Y
Risk
Employers differ in
the ease (cost)
with which they can
eliminate
hazards.
→ Firm X can reduce
risk more cheaply
than firm Y.
(3) The Matching of Employer and Employees
Graphing worker indifference curves and employer isoprofit
curves together can show which workers choose which offers.
B2
Y’
W
B1
WBY
X’
WAX
A2
Y
X
A1
RAX
RBY
Risk
A’s choice: (WAX, RAX)
→ value safety higher
If A took B’s offer
A1 < A2
B’s choice: (WBY, RBY)

Since X can produce safety more cheaply than Y, X
will be a low-risk producer who attracts employees,
like A, who value safety highly. Y attracts people like
B, who have a relatively strong preference for money
wages and a relatively weak preference for safety.
 Note: The only offers of jobs to workers with a
chance of being accepted lie along XR’Y’.
 → The curve XR’Y’ can be called an “offer curve”,
because only along XR’Y’ will offers employers can
afford to make be potentially acceptable to employees.
W
Offer Curve
Risk
The more types of firms there
are in a market, the smoother
this offer curve will be. It will
always slope upward because of
our assumptions that risk is
costly to reduce and that
employees must be paid higher
wages to keep their utility
constant if risk is increased.
* Major Insights:
1.
2.
Wages rise with risk, other things equal.
→ There will be compensating wage
differentials for job characteristics that are
viewed as undesirable by workers.
Workers with strong preferences for safety will
tend to take jobs in firms where safety can be
generated most cheaply.
→ Firms and workers offer and accept jobs in
a fashion that makes the most of their strengths
and preferences.
3. Policy Application: How Much is a Life Worth?
Empirical Evidences
Many studies estimate the hedonic function relating wages
and the probability of injury on the job. This literature
typically estimates regressions of the form:
wi = γρi + other variables
Where wi gives the wage of worker i and ρi. gives the
probability of injury on the worker’s job. The
coefficientγgives the wage change associated with a
one-unit increase in the probability of injury.
Many empirical studies report a positive relationship
between wages and hazardous or unsafe work conditions,
regardless of how the hazard or the unsafe nature of the
work environment is defined.
1.
2. Calculating the Value of Life
The correlations of the wages and the probability of injury on the
job allow us to calculate the “value of life.”
Example:
Firm
X
Y
Probability of Fatal Injury
ρx
ρx + .001
Annual Earnings
wx
wx+ $5,000

The data suggests that each of the workers in firm Y
is willing to give up $5,000 per year to reduce the
probability of fatal injury in their job by 0.001 units.
Put differently, the 1,000 workers employed in firm Y
are willing to give up $5 million (or $5,000x 1,000
workers) to save the life of the one worker who will
almost surely die in any given year. The workers in
firm Y, therefore, value a life at $5 million.
 This calculation instead gives the amount that
workers are jointly willing to pay to reduce the
likelihood that one of them will suffer a fatal injury in
any given year. It is the statistical value of a life.