Wage Dispersion (1) Indicators & Determinants of Wages Flashcards
1. Indicators 2. Determinants of Wages
What does the CDF describe?
The proportion of individuals (p) earning less than a certain wage level
How is the PDF related to the CDF?
PDF is effectively the slope of the CDF
What is the optimum point on the PDF in relation to the CDF?
It is the “inflection point”.
Where function stops rising at increasing rate and starts rising at decreasing rate
Give 3 indicators of wage inequality
Quantiles
Variance
Coeff of variation
What is the formula for the coefficient of variation?
σ(W))/E(W)
What is the problem with using variance as an indicator?
How can this be overcome?
It is sensitive to the scale
Overcome by dividing s.d. through by the mean (coefficient of variation)
What is the benefit of quantiles?
Explain where inequality lies in a distribution
What is the quantile function?
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)
What are R-ratios?
2 things
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
What is the Gini coefficient?
What does a high Gini coeff mean?
A measure of how far a distibution is from equality
A higher Gini coeff means that there is more inequality
What is S(p)?
The cumulative wage of the proportion of individuals earning below a certain wage
What are the axes of the Lorenze curve?
y-axis = cumulative total income
x-axis = cumulative population percentage
What does the Lorenz curve show?
A graphical representation of the distribution of income/wealth in an economy
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?
Gini coeff = A/A+B
What does the Gini coeff capture?
What is its value for i) Perfect inequality ii) Perfect equality
How far from equality a wage distribution is
Perfect inequality => GC=1
Perfect equality => GC=0
In terms of wage determination, give an example of asymmetric information
If the worker knows their own level of productivity but the firm does not
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)
Firm offers wage = expected productivity
E(p) = θp1 + (1-θ)p2
Why is there no wage dispersion when there is adverse selection?
(2 points)
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
What is adverse selection and why does is occur?
2 points
Where high productivity workers suffer because firms cannot distinguish them from low productivity workers
Occurs due to asymmetric information
What are the benefits of signalling and screening?
It is one way to overcome adverse selection
What 3 assumptions do we make for signalling?
Which one of these is potentially problematic?
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]
What potential equilibrium(s) can occur in a signalling world?
Explain. Where does wage dispersion occur?
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
How does screening work?
Firms offer higher wages for more difficult jobs and lower wages for easier jobs. So workers self-select
What equilibrium(s) can occur in a screening world?
Explain. Where does wage dispersion occur?
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
What is problematic about the screening world?
The data doesn’t consider that wage dispersion is caused by the difference in job difficulty
Is(are) the equilibrium(s) in the signalling world efficient?
Why/why not?
No, neither equilibrium is efficient
Workers have to pay to produce a signal, which is costly
Is(are) the equilibrium(s) in the screening world efficient?
No, the separating equilibrium is not efficient
What is the formula for the gender wage gap?
Av.wage(M) - Av.wage(F)
Why is the gender wage gap supposedly smaller for S.European countries than the UK/US?
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
What is the Oaxaca-Blinder decomposition?
An approach to distinguishing between explained and unexplained components of the wage gap
(see page 4 of your notes for practice!)
What are the 3 components in the Oaxaca-Blinder decomposition (give their expressions)
Explained component (X̅m - X̅f)
Unexplained component (βm - βf)
Unobserved component (U̅m - U̅f)
Where does the explained component of the O-B composition come from?
The intrinsic differences between mens and womens characteristics
What is the UNexplained component of the O-B composition also known as?
The “price effect”
Where might the unobserved component of the O-B composition come from?
(3 points)
Differences in unobserved characteristics
OR
Discrimination
Hence we cannot clearly interpret this
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?
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
What is the potential problem with the assumption that E(ε|X=x)=0 in the extended O-B composition?
There might be correlation between observed and unobserved characteristics, in which case estimates will be biased
In an extended O-B composition, E(ε|X=x)=0. Why might there still be problems?
There may be selection bias
Explain positive selection bias in the context of the observed gender wage gap
(3 verbal points + eqn)
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)
Explain negative selection bias in the context of the observed gender wage gap
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)
What are the implications of selection bias on the gender wage gap over time
Even if the true wage gap remains constant, if participation changes over time then the observed wage gap may change
What do empirical results say about selection bias/the wage gap?
(4 points)
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
Give the formula for the estimate of a CDF function
F ̂(w)=1/N ∑(i=1)^N 1{wi≤w}
