Labour Market ADVANCED

Question 1

How can you Mathematically derive labour markets (SUPPLY)?

Answer 1

• OBJECTIVE: MaxU(C,L) =
  [C^(s-1/s) + αL ^(s-1/s)]^{s/s-1}
• Where s is the constant elasticity of substitution
• Constraints: Budget = wN
• Constraints: Time = N+L=1
• To maximise utility, you substitute the constraints into the objectives
• Then differentiate with the chain rule to find:
  δU/δN = s/s-1 [{wN}^(s-1/s) + α{1-N}^(s-1/s)]^-1/s x [(s-1/s) w{wN}^-1/s - (s-1/s)α[1-N]^(s-1/s) via chain rule
• This simplifies to N = 1 + W^s-1 / α^s

Question 2

How does s/s-1 [{wN}^(s-1/s) + α{1-N}^(s-1/s)]^-1/s x [(s-1/s) w{wN}^-1/s + (s-1/s)α[1-N]^(s-1/s) simplify to 1 + W^s-1 / α^s?

Answer 2

• The latter term = 0, and the first term >0, therefore cannot be considered as a non-zero term
• This means that:
  (wN)^-1/s x w = α (1-N) ^-1/s
• Raise to the power of -s gives: wN x w^-s = α^-s (1-N)
• w^(1-s)N = α^-s -α^-sN
• [w^(1-s) + α^-s]N = α^-s
• N = α^-s /[w^(1-s) + α^-s]
• Multiply this by α^-1/s to get 1 + W^s-1 / α^s

Question 3

How can you Mathematically derive labour markets (DEMAND)?

Answer 3

• OBJECTIVE: Maxπ = Y-wN
• CONSTRAINT: Technology = Y = AN^φ, where φ<1 and shows the income share of labour
• π = AN^φ - wN
• δπ / δN = φAN^φ-1 - w = 0
• N = [φA/w] ^1/1-φ
• Cannot be φ-1 as φ<1

Question 4

What is the Labour market equilibrium? How can we find the equilibrium w?

Answer 4

• We know the SS equilibrium of N=1 + w^s-1 / α^s and the DS equilibrium of N = [φA/w] ^1/1-φ
• To find w, we should equate the two variables where there is only w
• This can only be solved by software- not by hand
• w is exogenous to a person, endogenous to a variable

Question 5

How else can the labour market be modelled/solved {econometrics}?

Answer 5

• Via econometrics techniques such as OLS
• The usual estimator can also be a vector
• In application, y = ln(wage) and Xs are job factors
• Due to the unlikeliness of linearity for this, one must approximate at lines to make things more simple

Question 6

What are the four assumptions required for the econometric method to work? What are some issues for econometric techniques?

Answer 6

• A1; Specification between y and x is true
• A2; Exogeneity between x and ε is ensured
• A3; Multicollinearity among x is not perfect
• A4; Sphericality of ε holds [homoskedasticity]
• These assumptions enable the OLS to be BLUE
• BUT/ there are issues of the ommitted variable problem, Sample-Selection and Self-selection bias

Question 7

What are the issues with Econometrics techniques?

Answer 7

• OMMITTED VARIABLE: Occurs when an important variable is left out of the model. This leads to bias as the coefficient includes the effect of the ommitted variable
• SAMPLE SELECTION: The observation included is non-random. This can often be treated as an ommitted variable
• SELF-SELECTION: An independant variable can be endogenous to an individual (a worker can choose his sector). If ignored, the OLS can under/overestimate these effects

Question 8

What is the Blinder-Oaxaca decomposition?

Answer 8

• Used as a mechanism to compare the differences between groups
• By running subsample regressions for both variables, two parts of the regression can be examined- looking at fair/unfair differences in wages