Across Wages Markets
Lecture 1, January 10 2012
Announcements
(Many of these are on the supplementary syllabus)
Test 2 will be returned in Class on Friday, January 13th (10:00).
Reminder: Make-up Test is Friday, January 13th, 9:00-11:00, WI1017.
Only for those with previously approved medical accommodation
Term Paper Assignment will be distributed on Friday, January 20th (in
class)
Outline
Summarizing Wage Variation
What summary statistics?
Explorations based on LFS, November 2011
Introduce Earnings Function
Theoretical Model of Compensating Differentials
Demand side: Firm offers of wages and amenities
Supply side: Worker preferences for wages and amenities
Market Equilibrium: Deriving the Wage-Amenity locus
Application: Workplace Safety Regulation
Estimation of compensating differentials for job risk
Valuing human life
Problems of estimation
Last Semester
The focus was wage and employment determination in a single market, and
the theoretical framework was the supply and demand model.
Wages
Labour Supply
W*
Labour Demand
E*
Recall the combined assumptions:
Optimization (utility and profit maximization)
Equilibrium
Employment
Summarizing Wage Variation
Clearly, however, wages are not the same for everyone.
How can we summarize the degree of variation in wages?
Most informative would be showing the entire wage distribution, but
summary statistics are useful:
Percentiles (or quantiles), especially 10th, 25th, 50th, 75th, and 90th, e.g.,
W10 , W25 , W50 , W75 , W90
Or ratios of percentiles, e.g.,
W90 W10
Variance, standard deviation, coefficient of variation
Gini coefficient, etc.
Exploring Wages in Canada
Consider the distribution of wages in Canada.
Data come from the Labour Force Survey, November 2011
Pooled men and women, ages 20-59, with positive wage earnings.
Note: Average Hourly Earnings not quite the same as the wage.
The following distributions show:
Wages
Log Wages
Key percentiles (10th, 50th (median), and 90th)
0
.01
Density
.02
.03
.04
Distribution of Wages, November 2011
10
20
30
Source: Labour Force Survey
40
50
60
70
Average Hourly Earnings
80
90
100
0
.2
Density
.4
.6
.8
1
Distribution of Log Wages, November 2011
2
2.5
Source: Labour Force Survey
3
3.5
Log Average Hourly Earnings
4
4.5
Summary Statistics
Key results:
Average wage = $23.87 per hour
Median = $21.00 per hour
W10 = $11.00; W90 = $40.00
W90 W10 = 3.64
ln (W90 W10 ) = ln W90 ln W10 = 3.69 2.40 = 1.29
Links to overall inequality
While related, there is significant slippage between wage inequality and
income inequality:
Wages versus compensation;
Wages versus earnings:
ln wh = ln w + ln h
Earnings versus income;
Permanent versus transitory;
Taxes and transfers
Individual versus household;
Still, trends in wage inequality are an important area of research, and
related to overall inequality.
Consider the following recent (U.S.) evidence from Goldin and Katz.
Note the comparable Canadian level (difference in log 90/10 ratio) for men is 1.26.
141
Claudia Goldin and Lawrence F. Katz
Figure 2. Selected Measures of Weekly and Hourly Wage Inequality
Log wage ratio
Log wage ratio
March CPS Full-Time Weekly Wages, 19632005
1.7
0.65
1.6
0.60
1.5
1.4
1.3
Overall 90-10 ratio,a
males only (left scale)
0.55
0.50
1.2
Residual 90-10 ratio,b
males only (left scale) 0.45
1.1
1.0
Collegehigh school
wage differential,c both
sexes (right scale)
0.9
1965
1970
1975
1980
1985
1990
0.40
1995
2000
CPS MORG Hourly Wages, 19732006d
Source: Goldin and Katz, Brookings Papers on Economic Activity, 2007.
1.7
1.6
0.65
Modeling Wage Variation
We can imagine a model explaining wage determination as:
Or in logs:
wi = g ( x1i , x2 i , ..., xki , i )
ln wi = f ( x1i , x2 i , ..., xki , i )
What factors might we include in this function?
A linear approximation:
ln wi = 0 + 1 x1i + 2 x2 i + ... + k xki + i
OBSERVABLES
The population wage regression.
Which, given the right data, we can estimate by Ordinary Least Squares (OLS)
Over this semester
We will look at a variety of determinants of relative wages.
Compensating Wage Differentials
The general theoretical framework
Human Capital
Immigration
Discrimination: Factors that should not affect wages (but do)
Male-Female Wage differentials
Internal labour markets
Unions
Modeling relative wages
Why not just extend our analysis from last semester?
SS
SU
WS
W US
D
Unskilled
DS
U
Skilled
Start with Adam Smith
The five following are the principal circumstances which, so far as I have
been able to observe, make up for a small pecuniary gain in some
employments, and counter-balance a great one on in others: first, the
agreeableness or disagreeableness of the employments themselves;
secondly, the easiness and cheapness, or the difficulty and expense of
learning them; thirdly, the constancy or inconstancy of employment in
them; fourthly, the small or great trust which must be reposed in those who
exercise them; and fifthly, the probability or improbability of in
them.
success Key idea for us: Equilibrium wages must compensate individuals for the
disamenities associated with a job.
Hedonic Model
Modeling linkages between wages and working conditions
Workers will care about amenities (or disamenities)
It will be costly for firms to provide amenities (or provide fewer
disamenties).
For concreteness, consider the amenity, safety.
Need to examine firm payoffs/tradeoffs to providing different combinations
of wages and safety;
Then turn to workers, to see how willing they are to accept higher/lower
wages in return for different levels of safety.
Consider a single Firm
With two (or many) heterogeneous firms
Competition I1 = I 2
Turning to the worker side
Consider a single workers preferences over wages and safety:
Two (or more) Heterogeneous workers
Not everybody is the same:
Compare Marginal Rates of Substitution
Market Equilibrium
With a single firm and individual: No further gains from trade.
Equilibrium with several firms
The more relevant case: many firms and individuals
Implications
Individuals with different preferences will get paid different wages in
equilibrium:
Choose to work at firms that provide them with the best packages of wages and safety.
Can think of this as a market for amenities, as much as a labour market.
Individuals are willing to pay (in the form of lower wages) for amenities.
Firms sell amenities.
Implicit Assumptions:
Utility maximization (versus wage maximization, or some other objective)
Perfect information (workers are aware of the risks involved with the job)
Worker mobility (e.g., no monopsony)
An alternative portrayal
Can reverse the axis and express wages as a function of the disamenity
U3
(e.g., risk)
Wage
Equilibrium
Wage Risk Locus
U2
I3
U1
I2
I1
Risk
Policy Application: Safety Regulation
If the market works perfectly, workers are mobile, and they have complete
information, then the market solves any problems of workplace danger:
Socially optimal (Pareto Optimal) level of safety: neither firms nor workers
would want to change the combination.
Workers could switch firms if they did not like the tradeoff
If no one wanted to work there, dangerous firms would go out of business.
Optimal amount of safety is not infinite.
Impact of minimum safety standard
Consider the imposition of a minimum safety standard, Sr.
If the zero-profit constraint is satisfied, worker bears all of the cost:
Impact of safety standard
If the firm bears the cost:
Impact with multiple firms
Firm 3 is unaffected;
Firm 2 can adjust, as long as wage is lowered;
Firm 1 must shut down.
Imperfect information
What if workers believe that the level of safety is higher than it actually is?
With imperfect information, an externally imposed safety standard may
improve worker welfare, without harming firms:
Final Thoughts on Regulation
In the case of imperfect information, it is possible that safety regulation
would improve wellbeing (and be Pareto improving)
This is predicated on the regulator being able to observe the level of safety.
Why not just monitor safety and report to the workers, solving the information problem?
Aside from imperfect information:
Imperfect competition, or limited worker mobility
Behavioural economics (Psychology) also suggests that regulation may be
necessary.
Finally, if workers do not bear the full cost of their risk, society may be
subsidizing risky firms.
Empirical Evidence
Economists use the earnings function that we saw earlier to estimate the
value that workers place on workplace safety:
k
ln wi = 0 + j x ji + Pi + i
j =1
where Pi is the probability of injury of death on the job.
Basic result: Market seems to compensate workers for the risk of death.
Estimates range from $750 to $10,000 of extra pay per year for every
1/1000th increase in the probability of being killed in a given year.
These estimates can be used to estimate the implicit value of human life.
Valuing Human Life
Assume that $6,000 is a reasonable estimate of the Compensating
Differential for each 0.001 increase in the probability of a fatality.
This means that a group of 1,000 workers is willing to pay $6,000,000 to
reduce the rate of fatalities by one person per year.
Or viewed alternatively, willing to accept $6,000,000 in compensation for the extra death
per year.
Empirical Challenges
Can the estimated compensating wage differentials be taken at face value?
Consider estimation of an earnings function:
k
ln wi = 0 + j x ji + Amenityi + i
j =1
Can show that the OLS estimator can be written as:
= + Amenity,
Where Amenity, is the correlation between unobservables, and the
Amenity.
So if there are unobserved worker or job characteristics that are correlated
with Amenities, our estimates will be biased.
What if the unobservable is productivity
Next week
Human Capital: Chapter 9
Extend the idea of compensating differential to the cost of acquiring skills.
Selected problems from Chapter 8
They are all useful!
But for starters, please try Problems #1, #3, and #5.