Lecture 6: Compensating Wage Differentials

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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.

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• 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.

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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.

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The compensating wage differential serves two
purposes

• 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.

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• ? 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.

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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
  highest-paying job offered, preferring instead a
  lower-paying 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.

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• 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.

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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.

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(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.
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.
W
U3
U2
U1
Risk
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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).
Highly Averse to Risk
W
Moderately Averse to Risk
UL
UH
Risk
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(2) Employer Considerations

• Assumptions
• It is presumably costly to reduce the risk of
  injury facing employees.
• Perfect competition ? Firms operate at zero
  profits.
• 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.

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• 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.

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W
The concavity of isoprofit curves is a
representation of our assumption that there are
diminishing marginal returns to safety
expenditures. ? The cost of reducing risk levels
is reflected in the slope of the isoprofit curve.
M
N
Risk
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W
Y
Employers differ in the ease (cost) with which
they can eliminate hazards. ? Firm X can reduce
risk more cheaply than firm Y.
X
X
Y
Risk
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(3) The Matching of Employer and Employees

• Graphing worker indifference curves and
  employer isoprofit curves together can show which
  workers choose which offers.

B2
W
Y
As choice (WAX, RAX) ? value safety higher If
A took Bs offer A1 lt A2 Bs choice (WBY,
RBY)
B1
WBY
X
WAX
A2
Y
X
A1
Risk
RAX
RBY
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• 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 XRY.
• ? The curve XRY can be called an offer curve,
  because only along XRY will offers employers
  can afford to make be potentially acceptable to
  employees.

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W
Offer Curve
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.
Risk
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Major Insights

• 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.

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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 ??i other variables
• Where wi gives the wage of worker i and ?i.
  gives the
• probability of injury on the workers job.
  The coefficient?gives 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.

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• 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 Probability of Fatal Injury
  Annual Earnings
• X ?x
  wx
• Y ?x .001
  wx 5,000

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• 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.