Wage Dispersion (1) Indicators & Determinants of Wages

Question 1

What does the CDF describe?

Answer 1

The proportion of individuals (p) earning less than a certain wage level

Question 2

How is the PDF related to the CDF?

Answer 2

PDF is effectively the slope of the CDF

Question 3

What is the optimum point on the PDF in relation to the CDF?

Answer 3

It is the “inflection point”.

Where function stops rising at increasing rate and starts rising at decreasing rate

Question 4

Give 3 indicators of wage inequality

Answer 4

Quantiles

Variance

Coeff of variation

Question 5

What is the formula for the coefficient of variation?

Answer 5

σ(W))/E(W)

Question 6

What is the problem with using variance as an indicator?

How can this be overcome?

Answer 6

It is sensitive to the scale

Overcome by dividing s.d. through by the mean (coefficient of variation)

Question 7

What is the benefit of quantiles?

Answer 7

Explain where inequality lies in a distribution

Question 8

What is the quantile function?

Answer 8

The inverse of the CDF

The wage level such that a given proportion (p) of individuals earns less than it

(look at proportion first to compute wage level)

Question 9

What are R-ratios?

2 things

Answer 9

The ratio of quantiles taken at different points on a distribution

Capture the difference in wages between high and low earners, tells us where the inequalities are in a distribution

Question 10

What is the Gini coefficient?

What does a high Gini coeff mean?

Answer 10

A measure of how far a distibution is from equality

A higher Gini coeff means that there is more inequality

Question 11

What is S(p)?

Answer 11

The cumulative wage of the proportion of individuals earning below a certain wage

Question 12

What are the axes of the Lorenze curve?

Answer 12

y-axis = cumulative total income

x-axis = cumulative population percentage

Question 13

What does the Lorenz curve show?

Answer 13

A graphical representation of the distribution of income/wealth in an economy

Question 14

On a Lorenz curve diagram, the area between the curve and 45 degree line is A and the remaining area under the curve is B. What is the formula for the gini coeff in this case?

Answer 14

Gini coeff = A/A+B

Question 15

What does the Gini coeff capture?

What is its value for i) Perfect inequality ii) Perfect equality

Answer 15

How far from equality a wage distribution is

Perfect inequality => GC=1
Perfect equality => GC=0

Question 16

In terms of wage determination, give an example of asymmetric information

Answer 16

If the worker knows their own level of productivity but the firm does not

Question 17

What wage will the firm offer when

i) There is no screening
ii) All agents are risk neutral
iii) There are two types of workers: p1=high prod p2=low prod and the proportion of high prod workers = θ

(verbal explanation and equation)

Answer 17

Firm offers wage = expected productivity

E(p) = θp1 + (1-θ)p2

Question 18

Why is there no wage dispersion when there is adverse selection?

(2 points)

Answer 18

If θ is high (many high prod workers) then the average wage is high. Everyone works for the same wage

If θ is low (few high prod workers) then average wage is close to p2, so only low prod workers participate, all earning the same wage

Question 19

What is adverse selection and why does is occur?

2 points

Answer 19

Where high productivity workers suffer because firms cannot distinguish them from low productivity workers

Occurs due to asymmetric information

Question 20

What are the benefits of signalling and screening?

Answer 20

It is one way to overcome adverse selection

Question 21

What 3 assumptions do we make for signalling?

Which one of these is potentially problematic?

Answer 21

Workers can signal their productivity by taking some level of education

It is cheaper for high prod workers to take education

Taking education does not increase productivity, it is just a signal [Potentially problematic]

Question 22

What potential equilibrium(s) can occur in a signalling world?

Explain. Where does wage dispersion occur?

Answer 22

2 equilibriums:

Separating: low-prod workers don’t take educ, high-prod workers do. Firms can tell them apart so there is wage dispersion

Pooling: All workers take the same level of education. Firms can’t tell them apart so all are paid the same wage i.e. no wage dispersion

Question 23

How does screening work?

Answer 23

Firms offer higher wages for more difficult jobs and lower wages for easier jobs. So workers self-select

Question 24

What equilibrium(s) can occur in a screening world?

Explain. Where does wage dispersion occur?

Answer 24

There can only be a separating equilibrium because workers won’t accept a job that does not suit their type

Hence their is wage dispersion

Question 25

What is problematic about the screening world?

Answer 25

The data doesn’t consider that wage dispersion is caused by the difference in job difficulty

Question 26

Is(are) the equilibrium(s) in the signalling world efficient?

Why/why not?

Answer 26

No, neither equilibrium is efficient

Workers have to pay to produce a signal, which is costly

Question 27

Is(are) the equilibrium(s) in the screening world efficient?

Answer 27

No, the separating equilibrium is not efficient

Question 28

What is the formula for the gender wage gap?

Answer 28

Av.wage(M) - Av.wage(F)

Question 29

Why is the gender wage gap supposedly smaller for S.European countries than the UK/US?

Answer 29

There is stronger selection bias because the participation rates for women are lower in Southern Europe

Hence the wage gap appears smaller in S.Europe

Question 30

What is the Oaxaca-Blinder decomposition?

Answer 30

An approach to distinguishing between explained and unexplained components of the wage gap

(see page 4 of your notes for practice!)

Question 31

What are the 3 components in the Oaxaca-Blinder decomposition (give their expressions)

Answer 31

Explained component (X̅m - X̅f)

Unexplained component (βm - βf)

Unobserved component (U̅m - U̅f)

Question 32

Where does the explained component of the O-B composition come from?

Answer 32

The intrinsic differences between mens and womens characteristics

Question 33

What is the UNexplained component of the O-B composition also known as?

Answer 33

The “price effect”

Question 34

Where might the unobserved component of the O-B composition come from?

(3 points)

Answer 34

Differences in unobserved characteristics
OR
Discrimination

Hence we cannot clearly interpret this

Question 35

Give another way of writing the female unobserved component

Rewrite the equation for women’s wages based on this

What is the key assumption in order to obtain unbiased estimates of βf and μf?

Answer 35

Ufi = μf + εfi

Where ε̅f = 0 and μf is a constant

Wfi = βfXi + μf + εi

Key assmn: E(ε|X=x)=0 i.e. no correlation between unobserved and observed characteristics

Question 36

What is the potential problem with the assumption that E(ε|X=x)=0 in the extended O-B composition?

Answer 36

There might be correlation between observed and unobserved characteristics, in which case estimates will be biased

Question 37

In an extended O-B composition, E(ε|X=x)=0. Why might there still be problems?

Answer 37

There may be selection bias

Question 38

Explain positive selection bias in the context of the observed gender wage gap

(3 verbal points + eqn)

Answer 38

Employed women have higher unobserved characteristics (e.g. ability) than the average

=> mean observed wage is higher than the average popn wage

E(ε|X, L=1)>0

=> Observed gender wage gap will be decreased (smaller than the true wage gap)

Question 39

Explain negative selection bias in the context of the observed gender wage gap

Answer 39

Employed women have lower unobserved characteristics than the average

=> mean observed wage lower than the average popn wage

E(ε|X, L=1) Observed gender wage gap will be increase (larger than the true wage gap)

Question 40

What are the implications of selection bias on the gender wage gap over time

Answer 40

Even if the true wage gap remains constant, if participation changes over time then the observed wage gap may change

Question 41

What do empirical results say about selection bias/the wage gap?

(4 points)

Answer 41

SB is substantial for women

Stronger in S. Europe

SB has been positive for the last 30 years

Once selection bias is accounted for there is no narrowing of the gender wage gap between 1970 and 2000

Question 42

Give the formula for the estimate of a CDF function

Answer 42

F ̂(w)=1/N ∑(i=1)^N 1{wi≤w}